(original) (raw)

%!PS-Adobe-2.0 %%Creator: dvipsk 5.58f Copyright 1986, 1994 Radical Eye Software %%Title: mlbook.dvi %%Pages: 50 %%PageOrder: Ascend %%BoundingBox: 0 0 612 792 %%EndComments %DVIPSCommandLine: dvips -o mlbook.ps mlbook %DVIPSParameters: dpi=300, compressed, comments removed %DVIPSSource: TeX output 1998.04.02:1359 %%BeginProcSet: texc.pro /TeXDict 250 dict def TeXDict begin /N{def}def /B{bind def}N /S{exch}N /X{S N}B /TR{translate}N /isls false N /vsize 11 72 mul N /hsize 8.5 72 mul N /landplus90{false}def /@rigin{isls{[0 landplus90{1 -1}{-1 1} ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR matrix currentmatrix dup dup 4 get round 4 exch put dup dup 5 get round 5 exch put setmatrix}N /@landscape{/isls true N}B /@manualfeed{ statusdict /manualfeed true put}B /@copies{/#copies X}B /FMat[1 0 0 -1 0 0]N /FBB[0 0 0 0]N /nn 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1786 y Fq(\))24 b(=)g Fl(P)12 b Fq(\()p Fl(h)855 1799 y Fj(j)885 1786 y Fq(\))29 b(then)h(can)e(further)h(simplify)-7 b(,)0 1890 y(and)28 b(c)n(ho)r(ose)i(the)f Fk(Maximum)j(likeliho)l(o)l(d)c Fq(\(ML\))0 1993 y(h)n(yp)r(othesis)531 2164 y Fl(h)581 2177 y Fj(M)7 b(L)711 2164 y Fq(=)24 b(arg)16 b(max)944 2212 y Fj(h)978 2224 y Fh(i)997 2212 y Fi(2)p Fj(H)1112 2164 y Fl(P)c Fq(\()p Fl(D)r Fp(j)p Fl(h)1359 2177 y Fj(i)1383 2164 y Fq(\))0 2748 y Fo(128)334 b(lecture)17 b(slides)f(for)f(textb)q(o)q(ok)g Fn(Machine)h(L)n(e)n(arning)p Fo(,)c(T.)j(Mitc)o(hell,)h(McGra)o(w)e(Hill,)j(1997)p eop %%Page: 129 5 129 4 bop 25 160 a Fm(Ba)m(y)m(es)34 b(Theorem)756 160 y 0.8666 0.03137 0.02352 setrgbcolor 756 160 a 0 321 1947 2 v 0 474 a 0 0 0 setrgbcolor 0 474 a 64 x Fq(Do)r(es)29 b(patien)n(t)h(ha)n(v)n(e)f(cancer)g(or)f(not?)104 683 y(A)g(patien)n(t)i(tak)n(es)g(a)e(lab)i(test)g(and)e(the)h(result)104 787 y(comes)f(bac)n(k)h(p)r(ositiv)n(e.)41 b(The)29 b(test)h(returns)e (a)104 891 y(correct)h(p)r(ositiv)n(e)j(result)e(in)f(only)h(98\045)f (of)g(the)104 995 y(cases)g(in)g(whic)n(h)h(the)f(disease)h(is)g (actually)h(presen)n(t,)104 1099 y(and)d(a)h(correct)g(negativ)n(e)i (result)f(in)f(only)h(97\045)f(of)104 1202 y(the)g(cases)g(in)h(whic)n (h)f(the)g(disease)h(is)g(not)f(presen)n(t.)104 1306 y(F)-7 b(urthermore,)27 b Fl(:)p Fq(008)i(of)g(the)g(en)n(tire)h(p)r (opulation)104 1410 y(ha)n(v)n(e)e(this)i(cancer.)134 1709 y Fl(P)12 b Fq(\()p Fl(cancer)r Fq(\))26 b(=)403 b Fl(P)12 b Fq(\()p Fp(:)p Fl(cancer)r Fq(\))26 b(=)89 1825 y Fl(P)12 b Fq(\(+)p Fp(j)p Fl(cancer)r Fq(\))26 b(=)357 b Fl(P)12 b Fq(\()p Fp(\000j)p Fl(cancer)r Fq(\))26 b(=)60 1941 y Fl(P)12 b Fq(\(+)p Fp(j:)p Fl(cancer)r Fq(\))26 b(=)329 b Fl(P)12 b Fq(\()p Fp(\000j:)p Fl(cancer)r Fq(\))26 b(=)0 2748 y Fo(129)334 b(lecture)17 b(slides)f(for)f(textb)q (o)q(ok)g Fn(Machine)h(L)n(e)n(arning)p Fo(,)c(T.)j(Mitc)o(hell,)h (McGra)o(w)e(Hill,)j(1997)p eop %%Page: 130 6 130 5 bop 25 170 a Fm(Basic)34 b(F)-9 b(orm)m(ulas)36 b(for)f(Probabilities)1509 170 y 0.8666 0.03137 0.02352 setrgbcolor 1509 170 a 0 321 1947 2 v 0 474 a 0 0 0 setrgbcolor 0 474 a 40 597 a Fp(\017)21 b Fk(Pr)l(o)l(duct)30 b(R)n(ule)p Fq(:)37 b(probabilit)n(y)32 b Fl(P)12 b Fq(\()p Fl(A)19 b Fp(^)h Fl(B)t Fq(\))30 b(of)f(a)104 701 y(conjunction)h(of)f (t)n(w)n(o)g(ev)n(en)n(ts)g(A)f(and)h(B:)235 854 y Fl(P)12 b Fq(\()p Fl(A)19 b Fp(^)h Fl(B)t Fq(\))25 b(=)f Fl(P)12 b Fq(\()p Fl(A)p Fp(j)p Fl(B)t Fq(\))p Fl(P)g Fq(\()p Fl(B)t Fq(\))27 b(=)d Fl(P)12 b Fq(\()p Fl(B)t Fp(j)p Fl(A)p Fq(\))p Fl(P)g Fq(\()p Fl(A)p Fq(\))40 1029 y Fp(\017)21 b Fk(Sum)32 b(R)n(ule)p Fq(:)37 b(probabilit)n(y)31 b(of)f(a)e(disjunction)j(of)e(t)n(w)n(o)104 1132 y(ev)n(en)n(ts)g(A)f (and)h(B:)297 1286 y Fl(P)12 b Fq(\()p Fl(A)20 b Fp(_)f Fl(B)t Fq(\))25 b(=)f Fl(P)12 b Fq(\()p Fl(A)p Fq(\))20 b(+)f Fl(P)12 b Fq(\()p Fl(B)t Fq(\))21 b Fp(\000)e Fl(P)12 b Fq(\()p Fl(A)20 b Fp(^)f Fl(B)t Fq(\))40 1460 y Fp(\017)i Fk(The)l(or)l(em)29 b(of)j(total)e(pr)l(ob)l(ability)p Fq(:)37 b(if)30 b(ev)n(en)n(ts)f Fl(A)1612 1473 y Fg(1)1643 1460 y Fl(;)15 b(:)f(:)g(:)g(;)h(A)1900 1473 y Fj(n)104 1564 y Fq(are)29 b(m)n(utually)g(exclusiv)n(e)j(with)1169 1522 y Ff(P)1213 1533 y Fj(n)1213 1585 y(i)p Fg(=1)1326 1564 y Fl(P)12 b Fq(\()p Fl(A)1491 1577 y Fj(i)1514 1564 y Fq(\))24 b(=)g(1,)29 b(then)542 1733 y Fl(P)12 b Fq(\()p Fl(B)t Fq(\))26 b(=)891 1670 y Fj(n)879 1682 y Ff(X)861 1791 y Fj(i)p Fg(=1)972 1733 y Fl(P)12 b Fq(\()p Fl(B)t Fp(j)p Fl(A)1230 1745 y Fj(i)1254 1733 y Fq(\))p Fl(P)g Fq(\()p Fl(A)1452 1745 y Fj(i)1475 1733 y Fq(\))0 2748 y Fo(130)334 b(lecture)17 b(slides)f(for)f(textb)q(o)q(ok)g Fn(Machine)h(L)n(e)n(arning)p Fo(,)c(T.)j(Mitc)o(hell,)h(McGra)o(w)e (Hill,)j(1997)p eop %%Page: 131 7 131 6 bop 25 160 a Fm(Brute)35 b(F)-9 b(orce)36 b(MAP)e(Hyp)s(othesis)h (Learner)1783 160 y 0.8666 0.03137 0.02352 setrgbcolor 1783 160 a 0 321 1947 2 v 0 474 a 0 0 0 setrgbcolor 0 474 a 16 592 a Fq(1.)21 b(F)-7 b(or)28 b(eac)n(h)h(h)n(yp)r(othesis)h Fl(h)f Fq(in)g Fl(H)7 b Fq(,)28 b(calculate)k(the)104 696 y(p)r(osterior)e(probabilit)n(y)590 889 y Fl(P)12 b Fq(\()p Fl(h)p Fp(j)p Fl(D)r Fq(\))25 b(=)991 831 y Fl(P)12 b Fq(\()p Fl(D)r Fp(j)p Fl(h)p Fq(\))p Fl(P)g Fq(\()p Fl(h)p Fq(\))p 991 869 466 2 v 1119 949 a Fl(P)g Fq(\()p Fl(D)r Fq(\))16 1105 y(2.)21 b(Output)29 b(the)g(h)n(yp)r (othesis)h Fl(h)1032 1117 y Fj(M)7 b(AP)1219 1105 y Fq(with)30 b(the)f(highest)104 1208 y(p)r(osterior)h(probabilit)n(y)576 1362 y Fl(h)626 1375 y Fj(M)7 b(AP)808 1362 y Fq(=)24 b(argmax)974 1427 y Fj(h)p Fi(2)p Fj(H)1193 1362 y Fl(P)12 b Fq(\()p Fl(h)p Fp(j)p Fl(D)r Fq(\))0 2748 y Fo(131)334 b(lecture)17 b(slides)f(for)f(textb)q(o)q(ok)g Fn(Machine)h(L)n(e)n (arning)p Fo(,)c(T.)j(Mitc)o(hell,)h(McGra)o(w)e(Hill,)j(1997)p eop %%Page: 132 8 132 7 bop 25 160 a Fm(Relation)35 b(to)g(Concept)f(Learning)1405 160 y 0.8666 0.03137 0.02352 setrgbcolor 1405 160 a 0 321 1947 2 v 0 474 a 0 0 0 setrgbcolor 0 474 a 64 x Fq(Consider)29 b(our)g(usual)g(concept)h(learning)g(task)40 696 y Fp(\017)21 b Fq(instance)30 b(space)f Fl(X)7 b Fq(,)29 b(h)n(yp)r(othesis)h(space)f Fl(H)7 b Fq(,)28 b(training)104 800 y(examples)h Fl(D)40 945 y Fp(\017)21 b Fq(consider)29 b(the)h Fe(FindS)e Fq(learning)i(algorithm)g (\(outputs)104 1049 y(most)e(sp)r(eci\014c)i(h)n(yp)r(othesis)g(from)e (the)h(v)n(ersion)h(space)104 1153 y Fl(V)19 b(S)226 1165 y Fj(H)r(;D)347 1153 y Fq(\))0 1360 y(What)30 b(w)n(ould)f(Ba)n(y) n(es)f(rule)i(pro)r(duce)f(as)f(the)i(MAP)0 1464 y(h)n(yp)r(othesis?)0 1617 y(Do)r(es)f Fl(F)12 b(indS)33 b Fq(output)c(a)g(MAP)f(h)n(yp)r (othesis??)0 2748 y Fo(132)334 b(lecture)17 b(slides)f(for)f(textb)q(o) q(ok)g Fn(Machine)h(L)n(e)n(arning)p Fo(,)c(T.)j(Mitc)o(hell,)h(McGra)o (w)e(Hill,)j(1997)p eop %%Page: 133 9 133 8 bop 25 160 a Fm(Relation)35 b(to)g(Concept)f(Learning)1405 160 y 0.8666 0.03137 0.02352 setrgbcolor 1405 160 a 0 321 1947 2 v 0 474 a 0 0 0 setrgbcolor 0 474 a 69 x Fq(Assume)27 b(\014xed)i(set)g(of)h(instances)g Fp(h)p Fl(x)1211 556 y Fg(1)1243 543 y Fl(;)15 b(:)f(:)g(:)g(;)h(x)1484 556 y Fj(m)1539 543 y Fp(i)0 647 y Fq(Assume)27 b Fl(D)k Fq(is)f(the)f(set)h(of)f(classi\014cations)0 751 y Fl(D)e Fq(=)c Fp(h)p Fl(c)p Fq(\()p Fl(x)340 763 y Fg(1)374 751 y Fq(\))p Fl(;)15 b(:)f(:)g(:)g(;)h(c)p Fq(\()p Fl(x)718 763 y Fj(m)773 751 y Fq(\))p Fp(i)0 904 y Fq(Cho)r(ose)29 b Fl(P)12 b Fq(\()p Fl(D)r Fp(j)p Fl(h)p Fq(\):)0 2748 y Fo(133)334 b(lecture)17 b(slides)f(for)f(textb)q(o)q(ok)g Fn(Machine)h(L)n(e)n(arning)p Fo(,)c(T.)j(Mitc)o(hell,)h(McGra)o(w)e (Hill,)j(1997)p eop %%Page: 134 10 134 9 bop 25 160 a Fm(Relation)35 b(to)g(Concept)f(Learning)1405 160 y 0.8666 0.03137 0.02352 setrgbcolor 1405 160 a 0 321 1947 2 v 0 474 a 0 0 0 setrgbcolor 0 474 a 69 x Fq(Assume)27 b(\014xed)i(set)g(of)h(instances)g Fp(h)p Fl(x)1211 556 y Fg(1)1243 543 y Fl(;)15 b(:)f(:)g(:)g(;)h(x)1484 556 y Fj(m)1539 543 y Fp(i)0 647 y Fq(Assume)27 b Fl(D)k Fq(is)f(the)f(set)h(of)f(classi\014cations)0 751 y Fl(D)e Fq(=)c Fp(h)p Fl(c)p Fq(\()p Fl(x)340 763 y Fg(1)374 751 y Fq(\))p Fl(;)15 b(:)f(:)g(:)g(;)h(c)p Fq(\()p Fl(x)718 763 y Fj(m)773 751 y Fq(\))p Fp(i)0 854 y Fq(Cho)r(ose)29 b Fl(P)12 b Fq(\()p Fl(D)r Fp(j)p Fl(h)p Fq(\))40 1000 y Fp(\017)21 b Fl(P)12 b Fq(\()p Fl(D)r Fp(j)p Fl(h)p Fq(\))25 b(=)f(1)29 b(if)h Fl(h)e Fq(consisten)n(t)i(with)g Fl(D)40 1145 y Fp(\017)21 b Fl(P)12 b Fq(\()p Fl(D)r Fp(j)p Fl(h)p Fq(\))25 b(=)f(0)29 b(otherwise)0 1290 y(Cho)r(ose)g Fl(P)12 b Fq(\()p Fl(h)p Fq(\))30 b(to)f(b)r(e)g Fk(uniform)i Fq(distribution)40 1435 y Fp(\017)21 b Fl(P)12 b Fq(\()p Fl(h)p Fq(\))24 b(=)436 1402 y Fg(1)p 407 1415 88 2 v 407 1465 a Fi(j)p Fj(H)5 b Fi(j)529 1435 y Fq(for)29 b(all)h Fl(h)e Fq(in)i Fl(H)0 1586 y Fq(Then,)142 1844 y Fl(P)12 b Fq(\()p Fl(h)p Fp(j)p Fl(D)r Fq(\))26 b(=)539 1661 y Ff(8)539 1698 y(>)539 1711 y(>)539 1723 y(>)539 1736 y(>)539 1748 y(>)539 1760 y(>)539 1773 y(>)539 1785 y(<)539 1860 y(>)539 1873 y(>)539 1885 y(>)539 1897 y(>)539 1910 y(>)539 1922 y(>)539 1935 y(>)539 1947 y(:)695 1695 y Fg(1)p 601 1708 218 2 v 601 1759 a Fi(j)p Fj(V)13 b(S)703 1772 y Fh(H)q(;D)802 1759 y Fi(j)865 1729 y Fq(if)30 b Fl(h)e Fq(is)i(consisten)n(t)g(with)g Fl(D)688 1958 y Fq(0)134 b(otherwise)0 2748 y Fo(134)334 b(lecture)17 b(slides)f(for)f(textb)q(o)q(ok)g Fn(Machine)h(L)n(e)n(arning)p Fo(,)c(T.)j(Mitc)o(hell,)h(McGra)o(w)e(Hill,)j(1997)p eop %%Page: 135 11 135 10 bop 25 170 a Fm(Ev)m(olution)36 b(of)d(P)m(osterior)j (Probabiliti)q(es)1661 170 y 0.8666 0.03137 0.02352 setrgbcolor 1661 170 a 0 321 1947 2 v 0 474 a 0 0 0 setrgbcolor 0 474 a 0 478 a 26049576 7814871 10064609 25852231 35653713 33680261 startTexFig 0 478 a %%BeginDocument: ./bookps/bayes-vs.ps 50 dict begin /arrowHeight 8 def /arrowWidth 4 def /none null def /numGraphicParameters 17 def /stringLimit 65535 def /Begin { save numGraphicParameters dict begin } def /End { end restore } def /SetB { dup type /nulltype eq { pop false /brushRightArrow idef false /brushLeftArrow idef true /brushNone idef } { /brushDashOffset idef /brushDashArray idef 0 ne /brushRightArrow idef 0 ne /brushLeftArrow idef /brushWidth idef false /brushNone idef } ifelse } def /SetCFg { /fgblue idef /fggreen idef /fgred idef } def /SetCBg { /bgblue idef /bggreen idef /bgred idef } def /SetF { /printSize idef /printFont idef } def /SetP { dup type /nulltype eq { pop true /patternNone idef } { /patternGrayLevel idef patternGrayLevel -1 eq { /patternString idef } if false /patternNone idef } ifelse } def /BSpl { 0 begin storexyn newpath n 1 gt { 0 0 0 0 0 0 1 1 true subspline n 2 gt { 0 0 0 0 1 1 2 2 false subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 2 copy false subspline } if n 2 sub dup n 1 sub dup 2 copy 2 copy false subspline patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Circ { newpath 0 360 arc patternNone not { ifill } if brushNone not { istroke } if } def /CBSpl { 0 begin dup 2 gt { storexyn newpath n 1 sub dup 0 0 1 1 2 2 true subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 0 0 false subspline n 2 sub dup n 1 sub dup 0 0 1 1 false subspline patternNone not { ifill } if brushNone not { istroke } if } { Poly } ifelse end } dup 0 4 dict put def /Elli { 0 begin newpath 4 2 roll translate scale 0 0 1 0 360 arc patternNone not { ifill } if brushNone not { istroke } if end } dup 0 1 dict put def /Line { 0 begin 2 storexyn newpath x 0 get y 0 get moveto x 1 get y 1 get lineto brushNone not { istroke } if 0 0 1 1 leftarrow 0 0 1 1 rightarrow end } dup 0 4 dict put def /MLine { 0 begin storexyn newpath n 1 gt { x 0 get y 0 get moveto 1 1 n 1 sub { /i exch def x i get y i get lineto } for patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Poly { 3 1 roll newpath moveto -1 add { lineto } repeat closepath patternNone not { ifill } if brushNone not { istroke } if } def /Rect { 0 begin /t exch def /r exch def /b exch def /l exch def newpath l b moveto l t lineto r t lineto r b lineto closepath patternNone not { ifill } if brushNone not { istroke } if end } dup 0 4 dict put def /Text { ishow } def /idef { dup where { pop pop pop } { exch def } ifelse } def /ifill { 0 begin gsave patternGrayLevel -1 ne { fgred bgred fgred sub patternGrayLevel mul add fggreen bggreen fggreen sub patternGrayLevel mul add fgblue bgblue fgblue sub patternGrayLevel mul add setrgbcolor eofill } { eoclip originalCTM setmatrix pathbbox /t exch def /r exch def /b exch def /l exch def /w r l sub ceiling cvi def /h t b sub ceiling cvi def /imageByteWidth w 8 div ceiling cvi def /imageHeight h def bgred bggreen bgblue setrgbcolor eofill fgred fggreen fgblue setrgbcolor w 0 gt h 0 gt and { l b translate w h scale w h true [w 0 0 h neg 0 h] { patternproc } imagemask } if } ifelse grestore end } dup 0 8 dict put def /istroke { gsave brushDashOffset -1 eq { [] 0 setdash 1 setgray } { brushDashArray brushDashOffset setdash fgred fggreen fgblue setrgbcolor } ifelse brushWidth setlinewidth originalCTM setmatrix stroke grestore } def /ishow { 0 begin gsave fgred fggreen fgblue setrgbcolor /fontDict printFont findfont printSize scalefont dup setfont def /descender fontDict begin 0 [FontBBox] 1 get FontMatrix end transform exch pop def /vertoffset 0 descender sub printSize sub printFont /Courier ne printFont /Courier-Bold ne and { 1 add } if def { 0 vertoffset moveto show /vertoffset vertoffset printSize sub def } forall grestore end } dup 0 3 dict put def /patternproc { 0 begin /patternByteLength patternString length def /patternHeight patternByteLength 8 mul sqrt cvi def /patternWidth patternHeight def /patternByteWidth patternWidth 8 idiv def /imageByteMaxLength imageByteWidth imageHeight mul stringLimit patternByteWidth sub min def /imageMaxHeight imageByteMaxLength imageByteWidth idiv patternHeight idiv patternHeight mul patternHeight max def /imageHeight imageHeight imageMaxHeight sub store /imageString imageByteWidth imageMaxHeight mul patternByteWidth add string def 0 1 imageMaxHeight 1 sub { /y exch def /patternRow y patternByteWidth mul patternByteLength mod def /patternRowString patternString patternRow patternByteWidth getinterval def /imageRow y imageByteWidth mul def 0 patternByteWidth imageByteWidth 1 sub { /x exch def imageString imageRow x add patternRowString putinterval } for } for imageString end } dup 0 12 dict put def /min { dup 3 2 roll dup 4 3 roll lt { exch } if pop } def /max { dup 3 2 roll dup 4 3 roll gt { exch } if pop } def /arrowhead { 0 begin transform originalCTM itransform /taily exch def /tailx exch def transform originalCTM itransform /tipy exch def /tipx exch def /dy tipy taily sub def /dx tipx tailx sub def /angle dx 0 ne dy 0 ne or { dy dx atan } { 90 } ifelse def gsave originalCTM setmatrix tipx tipy translate angle rotate newpath 0 0 moveto arrowHeight neg arrowWidth 2 div lineto arrowHeight neg arrowWidth 2 div neg lineto closepath patternNone not { originalCTM setmatrix /padtip arrowHeight 2 exp 0.25 arrowWidth 2 exp mul add sqrt brushWidth mul arrowWidth div def /padtail brushWidth 2 div def tipx tipy translate angle rotate padtip 0 translate arrowHeight padtip add padtail add arrowHeight div dup scale arrowheadpath ifill } if brushNone not { originalCTM setmatrix tipx tipy translate angle rotate arrowheadpath istroke } if grestore end } dup 0 9 dict put def /arrowheadpath { newpath 0 0 moveto arrowHeight neg arrowWidth 2 div lineto arrowHeight neg arrowWidth 2 div neg lineto closepath } def /leftarrow { 0 begin y exch get /taily exch def x exch get /tailx exch def y exch get /tipy exch def x exch get /tipx exch def brushLeftArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /rightarrow { 0 begin y exch get /tipy exch def x exch get /tipx exch def y exch get /taily exch def x exch get /tailx exch def brushRightArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /midpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 x1 add 2 div y0 y1 add 2 div end } dup 0 4 dict put def /thirdpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 2 mul x1 add 3 div y0 2 mul y1 add 3 div end } dup 0 4 dict put def /subspline { 0 begin /movetoNeeded exch def y exch get /y3 exch def x exch get /x3 exch def y exch get /y2 exch def x exch get /x2 exch def y exch get /y1 exch def x exch get /x1 exch def y exch get /y0 exch def x exch get /x0 exch def x1 y1 x2 y2 thirdpoint /p1y exch def /p1x exch def x2 y2 x1 y1 thirdpoint /p2y exch def /p2x exch def x1 y1 x0 y0 thirdpoint p1x p1y midpoint /p0y exch def /p0x exch def x2 y2 x3 y3 thirdpoint p2x p2y midpoint /p3y exch def /p3x exch def movetoNeeded { p0x p0y moveto } if p1x p1y p2x p2y p3x p3y curveto end } dup 0 17 dict put def /storexyn { /n exch def /y n array def /x n array def n 1 sub -1 0 { /i exch def y i 3 2 roll put x i 3 2 roll put } for } def %I Idraw 7 Grid 8 Begin %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 0.799705 0 0 0.799705 0 0 ] concat /originalCTM matrix currentmatrix def Begin %I Line %I b 65535 0 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 204.067 274.176 ] concat %I 29 259 29 363 Line End Begin %I Line %I b 65535 0 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 203.067 275.176 ] concat %I 30 258 129 258 Line End Begin %I Rect none SetB %I b n %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0.5 SetP %I t [ 1 0 0 1 218.067 513.176 ] concat %I 16 20 114 34 Rect End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-140-* /Times-Roman 14 SetF %I t [ 1 0 0 1 250.067 526.676 ] concat %I [ (hypotheses) ] Text End Begin %I Line %I b 65535 0 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 369.067 273.676 ] concat %I 29 259 29 363 Line End Begin %I Line %I b 65535 0 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 368.067 275.176 ] concat %I 30 258 129 258 Line End Begin %I Rect none SetB %I b n %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0.5 SetP %I t [ 1 0 0 1 257.067 514.176 ] concat %I 165 19 224 48 Rect End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-140-* /Times-Roman 14 SetF %I t [ 1 0 0 1 415.067 526.676 ] concat %I [ (hypotheses) ] Text End Begin %I Line %I b 65535 0 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 546.067 274.176 ] concat %I 29 259 29 363 Line End Begin %I Line %I b 65535 0 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 545.067 275.176 ] concat %I 30 258 129 258 Line End Begin %I Rect none SetB %I b n %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0.5 SetP %I t [ 1 0 0 1 321.067 512.176 ] concat %I 297 21 313 106 Rect End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-140-* /Times-Roman 14 SetF %I t [ 1 0 0 1 592.067 526.676 ] concat %I [ (hypotheses) ] Text End Begin %I Pict %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 1 0 0 1 441.163 -255.143 ] concat Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-i-*-140-* /Times-Italic 14 SetF %I t [ 1.00037 0 0 1.00037 59.0218 869.32 ] concat %I [ (P\(h|D) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-140-* /Times-Roman 14 SetF %I t [ 1.00037 0 0 1.00037 94.0347 869.32 ] concat %I [ (1,) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-i-*-140-* /Times-Italic 14 SetF %I t [ 1.00037 0 0 1.00037 106.039 869.32 ] concat %I [ (D) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-140-* /Times-Roman 14 SetF %I t [ 1.00037 0 0 1.00037 117.043 869.32 ] concat %I [ (2\)) ] Text End End %I eop Begin %I Pict %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 1 0 0 1 289.107 -185.117 ] concat Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-i-*-140-* /Times-Italic 14 SetF %I t [ 1.00037 0 0 1.00037 57.0211 799.294 ] concat %I [ (P\(h|D) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-140-* /Times-Roman 14 SetF %I t [ 1.00037 0 0 1.00037 92.034 799.294 ] concat %I [ (1) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-140-* /Times-Roman 14 SetF %I t [ 1.00037 0 0 1.00037 99.0364 799.294 ] concat %I [ (\)) ] Text End End %I eop Begin %I Pict %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 1 0 0 1 90.0332 -175.113 ] concat Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-i-*-140-* /Times-Italic 14 SetF %I t [ 1.00037 0 0 1.00037 106.039 789.291 ] concat %I [ (P) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-i-*-140-* /Times-Italic 14 SetF %I t [ 1.00037 0 0 1.00037 122.045 789.291 ] concat %I [ (h) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-140-* /Times-Roman 14 SetF %I t [ 1.00037 0 0 1.00037 131.048 789.291 ] concat %I [ (\)) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-140-* /Times-Roman 14 SetF %I t [ 1.00037 0 0 1.00037 116.043 789.291 ] concat %I [ (\() ] Text End End %I eop Begin %I Pict %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 1 0 0 1 163.023 -425.157 ] concat Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-i-*-140-* /Times-Italic 14 SetF %I t [ 1.00037 0 0 1.00037 116.043 933.344 ] concat %I [ (a) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-140-* /Times-Roman 14 SetF %I t [ 1.00037 0 0 1.00037 111.041 933.344 ] concat %I [ (\() ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-140-* /Times-Roman 14 SetF %I t [ 1.00037 0 0 1.00037 123.045 933.344 ] concat %I [ (\)) ] Text End End %I eop Begin %I Pict %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 1 0 0 1 330.524 -357.132 ] concat Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-i-*-140-* /Times-Italic 14 SetF %I t [ 1.00037 0 0 1.00037 114.042 865.319 ] concat %I [ (b) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-140-* /Times-Roman 14 SetF %I t [ 1.00037 0 0 1.00037 108.04 865.319 ] concat %I [ (\() ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-140-* /Times-Roman 14 SetF %I t [ 1.00037 0 0 1.00037 121.044 865.319 ] concat %I [ (\)) ] Text End End %I eop Begin %I Pict %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 1 0 0 1 506.524 -289.107 ] concat Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-i-*-140-* /Times-Italic 14 SetF %I t [ 1.00037 0 0 1.00037 115.042 797.294 ] concat %I [ (c) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-140-* /Times-Roman 14 SetF %I t [ 1.00037 0 0 1.00037 109.041 797.294 ] concat %I [ (\() ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-140-* /Times-Roman 14 SetF %I t [ 1.00037 0 0 1.00037 122.045 797.294 ] concat %I [ (\)) ] Text End End %I eop End %I eop showpage end %%EndDocument endTexFig 0 2748 a Fo(135)334 b(lecture)17 b(slides)f(for)f(textb)q(o)q(ok)g Fn(Machine)h(L)n(e)n(arning)p Fo(,)c(T.)j(Mitc)o(hell,)h(McGra)o(w)e (Hill,)j(1997)p eop %%Page: 136 12 136 11 bop 25 155 a Fm(Characterizing)77 b(Learning)f(Algorithms)i(b)m (y)25 279 y(Equiv)-6 b(alen)m(t)36 b(MAP)f(Learners)1238 279 y 0.8666 0.03137 0.02352 setrgbcolor 1238 279 a 0 434 1947 2 v 0 587 a 0 0 0 setrgbcolor 0 587 a 0 591 a 26049576 25789068 8156938 20458127 27825684 40061091 startTexFig 0 591 a %%BeginDocument: ./bookps2/vs-map-equivalent.ps /arrowHeight 10 def /arrowWidth 5 def /IdrawDict 52 dict def IdrawDict begin /reencodeISO { dup dup findfont dup length dict begin { 1 index /FID ne { def }{ pop pop } ifelse } forall /Encoding ISOLatin1Encoding def currentdict end definefont } def /ISOLatin1Encoding [ /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /space/exclam/quotedbl/numbersign/dollar/percent/ampersand/quoteright /parenleft/parenright/asterisk/plus/comma/minus/period/slash /zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon /less/equal/greater/question/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N /O/P/Q/R/S/T/U/V/W/X/Y/Z/bracketleft/backslash/bracketright /asciicircum/underscore/quoteleft/a/b/c/d/e/f/g/h/i/j/k/l/m /n/o/p/q/r/s/t/u/v/w/x/y/z/braceleft/bar/braceright/asciitilde /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/dotlessi/grave/acute/circumflex/tilde/macron/breve /dotaccent/dieresis/.notdef/ring/cedilla/.notdef/hungarumlaut /ogonek/caron/space/exclamdown/cent/sterling/currency/yen/brokenbar /section/dieresis/copyright/ordfeminine/guillemotleft/logicalnot /hyphen/registered/macron/degree/plusminus/twosuperior/threesuperior /acute/mu/paragraph/periodcentered/cedilla/onesuperior/ordmasculine /guillemotright/onequarter/onehalf/threequarters/questiondown /Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla /Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex /Idieresis/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis /multiply/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute /Thorn/germandbls/agrave/aacute/acircumflex/atilde/adieresis /aring/ae/ccedilla/egrave/eacute/ecircumflex/edieresis/igrave /iacute/icircumflex/idieresis/eth/ntilde/ograve/oacute/ocircumflex /otilde/odieresis/divide/oslash/ugrave/uacute/ucircumflex/udieresis /yacute/thorn/ydieresis ] def /Times-Roman reencodeISO def /Times-Italic reencodeISO def /none null def /numGraphicParameters 17 def /stringLimit 65535 def /Begin { save numGraphicParameters dict begin } def /End { end restore } def /SetB { dup type /nulltype eq { pop false /brushRightArrow idef false /brushLeftArrow idef true /brushNone idef } { /brushDashOffset idef /brushDashArray idef 0 ne /brushRightArrow idef 0 ne /brushLeftArrow idef /brushWidth idef false /brushNone idef } ifelse } def /SetCFg { /fgblue idef /fggreen idef /fgred idef } def /SetCBg { /bgblue idef /bggreen idef /bgred idef } def /SetF { /printSize idef /printFont idef } def /SetP { dup type /nulltype eq { pop true /patternNone idef } { dup -1 eq { /patternGrayLevel idef /patternString idef } { /patternGrayLevel idef } ifelse false /patternNone idef } ifelse } def /BSpl { 0 begin storexyn newpath n 1 gt { 0 0 0 0 0 0 1 1 true subspline n 2 gt { 0 0 0 0 1 1 2 2 false subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 2 copy false subspline } if n 2 sub dup n 1 sub dup 2 copy 2 copy false subspline patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Circ { newpath 0 360 arc patternNone not { ifill } if brushNone not { istroke } if } def /CBSpl { 0 begin dup 2 gt { storexyn newpath n 1 sub dup 0 0 1 1 2 2 true subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 0 0 false subspline n 2 sub dup n 1 sub dup 0 0 1 1 false subspline patternNone not { ifill } if brushNone not { istroke } if } { Poly } ifelse end } dup 0 4 dict put def /Elli { 0 begin newpath 4 2 roll translate scale 0 0 1 0 360 arc patternNone not { ifill } if brushNone not { istroke } if end } dup 0 1 dict put def /Line { 0 begin 2 storexyn newpath x 0 get y 0 get moveto x 1 get y 1 get lineto brushNone not { istroke } if 0 0 1 1 leftarrow 0 0 1 1 rightarrow end } dup 0 4 dict put def /MLine { 0 begin storexyn newpath n 1 gt { x 0 get y 0 get moveto 1 1 n 1 sub { /i exch def x i get y i get lineto } for patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Poly { 3 1 roll newpath moveto -1 add { lineto } repeat closepath patternNone not { ifill } if brushNone not { istroke } if } def /Rect { 0 begin /t exch def /r exch def /b exch def /l exch def newpath l b moveto l t lineto r t lineto r b lineto closepath patternNone not { ifill } if brushNone not { istroke } if end } dup 0 4 dict put def /Text { ishow } def /idef { dup where { pop pop pop } { exch def } ifelse } def /ifill { 0 begin gsave patternGrayLevel -1 ne { fgred bgred fgred sub patternGrayLevel mul add fggreen bggreen fggreen sub patternGrayLevel mul add fgblue bgblue fgblue sub patternGrayLevel mul add setrgbcolor eofill } { eoclip originalCTM setmatrix pathbbox /t exch def /r exch def /b exch def /l exch def /w r l sub ceiling cvi def /h t b sub ceiling cvi def /imageByteWidth w 8 div ceiling cvi def /imageHeight h def bgred bggreen bgblue setrgbcolor eofill fgred fggreen fgblue setrgbcolor w 0 gt h 0 gt and { l b translate w h scale w h true [w 0 0 h neg 0 h] { patternproc } imagemask } if } ifelse grestore end } dup 0 8 dict put def /istroke { gsave brushDashOffset -1 eq { [] 0 setdash 1 setgray } { brushDashArray brushDashOffset setdash fgred fggreen fgblue setrgbcolor } ifelse brushWidth setlinewidth originalCTM setmatrix stroke grestore } def /ishow { 0 begin gsave fgred fggreen fgblue setrgbcolor /fontDict printFont printSize scalefont dup setfont def /descender fontDict begin 0 [FontBBox] 1 get FontMatrix end transform exch pop def /vertoffset 1 printSize sub descender sub def { 0 vertoffset moveto show /vertoffset vertoffset printSize sub def } forall grestore end } dup 0 3 dict put def /patternproc { 0 begin /patternByteLength patternString length def /patternHeight patternByteLength 8 mul sqrt cvi def /patternWidth patternHeight def /patternByteWidth patternWidth 8 idiv def /imageByteMaxLength imageByteWidth imageHeight mul stringLimit patternByteWidth sub min def /imageMaxHeight imageByteMaxLength imageByteWidth idiv patternHeight idiv patternHeight mul patternHeight max def /imageHeight imageHeight imageMaxHeight sub store /imageString imageByteWidth imageMaxHeight mul patternByteWidth add string def 0 1 imageMaxHeight 1 sub { /y exch def /patternRow y patternByteWidth mul patternByteLength mod def /patternRowString patternString patternRow patternByteWidth getinterval def /imageRow y imageByteWidth mul def 0 patternByteWidth imageByteWidth 1 sub { /x exch def imageString imageRow x add patternRowString putinterval } for } for imageString end } dup 0 12 dict put def /min { dup 3 2 roll dup 4 3 roll lt { exch } if pop } def /max { dup 3 2 roll dup 4 3 roll gt { exch } if pop } def /midpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 x1 add 2 div y0 y1 add 2 div end } dup 0 4 dict put def /thirdpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 2 mul x1 add 3 div y0 2 mul y1 add 3 div end } dup 0 4 dict put def /subspline { 0 begin /movetoNeeded exch def y exch get /y3 exch def x exch get /x3 exch def y exch get /y2 exch def x exch get /x2 exch def y exch get /y1 exch def x exch get /x1 exch def y exch get /y0 exch def x exch get /x0 exch def x1 y1 x2 y2 thirdpoint /p1y exch def /p1x exch def x2 y2 x1 y1 thirdpoint /p2y exch def /p2x exch def x1 y1 x0 y0 thirdpoint p1x p1y midpoint /p0y exch def /p0x exch def x2 y2 x3 y3 thirdpoint p2x p2y midpoint /p3y exch def /p3x exch def movetoNeeded { p0x p0y moveto } if p1x p1y p2x p2y p3x p3y curveto end } dup 0 17 dict put def /storexyn { /n exch def /y n array def /x n array def n 1 sub -1 0 { /i exch def y i 3 2 roll put x i 3 2 roll put } for } def /SSten { fgred fggreen fgblue setrgbcolor dup true exch 1 0 0 -1 0 6 -1 roll matrix astore } def /FSten { dup 3 -1 roll dup 4 1 roll exch newpath 0 0 moveto dup 0 exch lineto exch dup 3 1 roll exch lineto 0 lineto closepath bgred bggreen bgblue setrgbcolor eofill SSten } def /Rast { exch dup 3 1 roll 1 0 0 -1 0 6 -1 roll matrix astore } def /arrowhead { 0 begin transform originalCTM itransform /taily exch def /tailx exch def transform originalCTM itransform /tipy exch def /tipx exch def /dy tipy taily sub def /dx tipx tailx sub def /angle dx 0 ne dy 0 ne or { dy dx atan } { 90 } ifelse def gsave originalCTM setmatrix tipx tipy translate angle rotate newpath arrowHeight neg arrowWidth 2 div moveto 0 0 lineto arrowHeight neg arrowWidth 2 div neg lineto patternNone not { originalCTM setmatrix /padtip arrowHeight 2 exp 0.25 arrowWidth 2 exp mul add sqrt brushWidth mul arrowWidth div def /padtail brushWidth 2 div def tipx tipy translate angle rotate padtip 0 translate arrowHeight padtip add padtail add arrowHeight div dup scale arrowheadpath ifill } if brushNone not { originalCTM setmatrix tipx tipy translate angle rotate arrowheadpath istroke } if grestore end } dup 0 9 dict put def /arrowheadpath { newpath arrowHeight neg arrowWidth 2 div moveto 0 0 lineto arrowHeight neg arrowWidth 2 div neg lineto } def /leftarrow { 0 begin y exch get /taily exch def x exch get /tailx exch def y exch get /tipy exch def x exch get /tipx exch def brushLeftArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /rightarrow { 0 begin y exch get /tipy exch def x exch get /tipx exch def y exch get /taily exch def x exch get /tailx exch def brushRightArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def %I Idraw 10 Grid 8 8 Begin %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 0.8 0 0 0.8 0 0 ] concat /originalCTM matrix currentmatrix def Begin %I Rect %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1.02222 157 258.555 ] concat %I 131 381 260 470 Rect End Begin %I Line %I b 65535 1 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 158 207 ] concat %I 260 490 370 490 Line %I 1 End Begin %I Line %I b 65535 1 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1.56471 0 0 1 82.6171 207 ] concat %I 51 500 131 500 Line %I 1 End Begin %I Line %I b 65535 1 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1.56471 0 0 1 82.6171 207 ] concat %I 51 461 131 461 Line %I 1 End Begin %I Rect %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1.33333 158 -49.667 ] concat %I 131 381 260 470 Rect End Begin %I Line %I b 65535 1 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 158 47 ] concat %I 260 490 370 490 Line %I 1 End Begin %I Line %I b 65535 1 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1.56471 0 0 1 82.6171 62.9941 ] concat %I 51 500 131 500 Line %I 1 End Begin %I Line %I b 65535 1 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1.56471 0 0 1 82.6171 62.994 ] concat %I 51 461 131 461 Line %I 1 End Begin %I Line %I b 65535 1 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1.56471 0 0 1 82.6171 7 ] concat %I 51 461 131 461 Line %I 1 End Begin %I Line %I b 65535 1 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 1 SetP %I t [ 0.657143 0 0 1 128.946 177 ] concat %I 119 251 149 281 Line %I 1 End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-120-* Times-Roman 12 SetF %I t [ 1 0 0 1 309 757.016 ] concat %I [ (Inductive system) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-120-* Times-Roman 12 SetF %I t [ 1 0 0 1 429.001 715.041 ] concat %I [ (Output hypotheses) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-120-* Times-Roman 12 SetF %I t [ 1 0 0 1 428.005 556.102 ] concat %I [ (Output hypotheses) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-120-* Times-Roman 12 SetF %I t [ 1 0 0 1 320.997 530.01 ] concat %I [ (Brute force) (MAP learner) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-120-* Times-Roman 12 SetF %I t [ 1 0 0 1 325.494 709.507 ] concat %I [ (Candidate) (Elimination) (Algorithm ) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-i-*-140-* Times-Italic 14 SetF %I t [ 1 0 0 1 179 418 ] concat %I [ (Prior assumptions) ( made explicit) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-120-* Times-Roman 12 SetF %I t [ 1 0 0 1 157.001 504.128 ] concat %I [ (P\(h\) uniform) (P\(D|h\) = 0 if inconsistent,) ( = 1 if consistent) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-120-* Times-Roman 12 SetF %I t [ 1 0 0 1 255.017 599.013 ] concat %I [ (Equivalent Bayesian inference system) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-120-* Times-Roman 12 SetF %I t [ 1 0 0 1 157.001 721 ] concat %I [ (Training examples D) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-120-* Times-Roman 12 SetF %I t [ 1 0 0 1 157.001 686 ] concat %I [ (Hypothesis space H ) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-120-* Times-Roman 12 SetF %I t [ 1 0 0 1 157.001 540.057 ] concat %I [ (Hypothesis space H ) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-times-medium-r-*-120-* Times-Roman 12 SetF %I t [ 1 0 0 1 157.001 576.995 ] concat %I [ (Training examples D) ] Text End End %I eop showpage end %%EndDocument endTexFig 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currentscreen 3 1 roll pop pop def /currentcolorscreen where { begin currentcolorscreen end 3 1 roll pop pop 4 2 roll pop pop 5 -2 roll pop pop 6 -2 roll pop pop /kProc exch def /bProc exch def /gProc exch def /rProc exch def } if /Max {2 copy gt {pop}{exch pop} ifelse} bind def /Min {2 copy lt {pop}{exch pop} ifelse} bind def /cellPenW 72.0 /currentcolorscreen where {begin currentcolorscreen end pop pop 10 1 roll pop pop 8 1 roll pop pop 6 1 roll pop pop Max Max Max } {currentscreen pop pop} ifelse div 2.0 div def /rect { /saveobj save def R PC PF LC SS saveobj restore } bind def /R { newpath pbox astore pop 0 792 translate 1 -1 scale CTMR currentmatrix pop exch translate /objectCord mstore def pbox right get 2 div dup pbox left get exch sub pbox left 3 -1 roll put dup pbox right 3 -1 roll put pbox bottom get 2 div dup pbox top get exch sub pbox top 3 -1 roll put dup pbox bottom 3 -1 roll put translate CTM currentmatrix pop 57.3 mul rotate RT } bind def /SaveScreenBW { currentscreen /scrnProc exch def /scrnAngle exch def /scrnFreq exch def } bind def /RestoreScreenBW { scrnFreq scrnAngle MAV /scrnProc get setscreen } bind def /SetFreqAngleBW { currentscreen 3 1 roll pop pop setscreen } bind def /SaveScreenColor { currentcolorscreen /grayProc exch def /grayAngle exch def /grayFreq exch def /bProc exch def /bAngle exch def /bFreq exch def /gProc exch def /gAngle exch def /gFreq exch def /rProc exch def /rAngle exch def /rFreq exch def } bind def /RestoreColorScreen { rFreq rAngle MAV /rProc get gFreq gAngle MAV /gProc get bFreq bAngle MAV /bProc get grayFreq grayAngle MAV /grayProc get setcolorscreen } bind def /SetFreqAngleColor { currentcolorscreen 3 1 roll pop pop 4 2 roll pop pop 5 -2 roll pop pop 6 -2 roll pop pop 4 1 roll 6 1 roll 8 1 roll 10 1 roll setcolorscreen } bind def /initmsaverestore { userdict begin /mdict 10 dict def mdict begin /mindex -1 def /mstacksize 25 def /mstack mstacksize array def /incmindex { /mindex mindex 1 add def } bind def /decmindex { /mindex mindex 1 sub def } bind def /checkmindex { mindex 0 lt { (%ERROR: msave/mrestore stack underflow: Offending command 'mrestore' ) print flush stop } { mindex mstacksize ge { (%ERROR: msave/mrestore stack overflow: Offending command 'msave' ) print flush stop } if } ifelse } bind def /mpush { incmindex checkmindex mstack mindex 3 -1 roll put } bind def /mpop { checkmindex mstack mindex get decmindex } bind def end end } bind def /msave { mdict begin matrix currentmatrix mpush end } bind def /mrestore { mdict begin mpop setmatrix end } bind def /msavelevel { mdict begin mindex 1 add end } bind def /mstore { matrix currentmatrix } bind def /AutoSizeY { 0 0 pl dup 3 1 roll 4 -1 roll add pl exch pop exch sub } bind def /pl { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add exch itransform } bind def /pll { transform round exch round exch itransform } bind def /pr { dtransform round exch round exch idtransform } bind def /m { pl moveto } bind def /l { pl lineto } bind def /c { pl curveto } bind def /rm { pr rmoveto } bind def /rl { pr rlineto } bind def /ar { 5 -2 roll pl 5 2 roll arc } bind def /an { 5 -2 roll pl 5 2 roll arcn } bind def /MakePatternFont { /FontDict 20 dict def FontDict begin /FontName exch def /Encoding exch def /FontMatrix [1 0 0 1 0 0 ] def /FontType 3 def /FontBBox [ 0 0 1 1 ] def /PatternDict exch def /RenderPattern { patternDict exch get exec } bind def /BuildChar { exch begin 1 0 0 0 1 1 setcachedevice Encoding exch get RenderPattern end } bind def FontName FontDict definefont pop end } bind def /SnapToPattenGrid { exch dup 0 lt { 1 index sub } if 1 index div truncate mul } bind def /FillPatternString { dup length 1 sub 0 1 3 -1 roll { 2 index 2 index 3 -2 roll put } for pop pop } bind def /AutoSizeY { 0.0 exch dtransform round idtransform exch pop } bind def /AutoSizeX { 0.0 dtransform exch round exch idtransform pop } bind def /AutoCellSize { AutoSizeY exch AutoSizeX exch } bind def /CheckPath { false { pop pop pop true exit} { pop pop pop true exit} { pop pop pop pop pop pop pop true exit} { pop true exit} pathforall } bind def /PatternFill { % patternCharacter /patternString 1 string def /cm mstore def patternMatrix setmatrix 1 1 AutoCellSize dup 0 eq { pop 1} if exch dup 0 eq { pop 1} if exch /patternSize exch 24.0 mul def /PatternSizeX exch 24.0 mul patternString length mul def /flaterror 0 def patternString FillPatternString gsave flaterror 1 add setflat flattenpath pathbbox grestore psy add flaterror add psy SnapToPattenGrid exch psx add flaterror add psx SnapToPattenGrid 3 -1 roll flaterror sub psy SnapToPattenGrid 4 -1 roll flaterror sub psx SnapToPattenGrid 4 2 roll pll 4 2 roll pll /llxsnap exch def /llysnap exch def /urxsnap exch def /urysnap exch def gsave useClip true eq {clip}{eoclip} ifelse newpath /PatternFont findfont [psx 0.0 0.0 psy 0.0 0.0] makefont setfont llysnap patternSize urysnap { llxsnap exch moveto llxsnap PatternSizeX urxsnap { pop patternString show %currentpoint am } for } bind for grestore cm setmatrix } bind def % End 'PatternFill' /DefaultPatternFont { /cm mstore def patternMatrix setmatrix 1 1 AutoCellSize dup 0 eq { pop 1} if exch dup 0 eq { pop 1} if exch /psy exch iSizeY mul def /psx exch iSizeX mul def /patternDict 64 dict def patternDict begin /NotDef {} def /LiteDiagLines { iSizeX iSizeY false [iSizeX 0.0 0.0 iSizeY -1.0 mul 0.0 iSizeY] {pat} imagemask } bind def end /CustEncoding 256 array def 0 255 1 { CustEncoding exch /NotDef put } bind for CustEncoding 65 /LiteDiagLines put patternDict CustEncoding /PatternFont MakePatternFont /pathSegProc { strokepath CheckPath { 65 PatternFill newpath } if } bind def cm setmatrix } bind def /XRound { dup 3 -1 roll exch mul round exch div } bind def /RoundMatrix { /i 0 def dup { 100000.0 XRound 1 index exch i exch put /i i 1 add def } forall } bind def /GetBoxesRatio { 3 -1 roll sub 7 1 roll exch sub 6 1 roll 3 -1 roll sub 5 1 roll exch sub 4 1 roll 3 -1 roll div 3 1 roll exch div exch } bind def /T {792 exch sub} bind def /sx 0 def /sy 0 def /ex 0 def /ey 0 def /lw 0 def /siz 0 def /U {gsave 0 setlinecap /lw siz 0.078125 mul def /ey exch neg def /ex exch def /sy exch neg def /sx exch def fontkind plain eq { lw siz 0.0119444 mul sub setlinewidth sx sy moveto ex ey lineto stroke } { currentdict /outlineFontSize known outlineFontSize 0 gt and { fontkind outline eq { /sy sy 0.0119444 siz mul sub def /ey ey 0.0119444 siz mul sub def gsave 1 1 1 setrgbcolor lw siz 0.0119444 mul sub setlinewidth sx sy moveto ex ey lineto stroke grestore lw siz 0.0119444 mul sub setlinewidth sx sy moveto ex ey lineto strokepath 0.0119444 siz mul setlinewidth stroke } if fontkind shadow eq fontkind outlineshadow eq or { /sy sy 0.0358332 siz mul sub def /ey ey 0.0358332 siz mul sub def lw setlinewidth lw 2 div sx add sy lw 2 div sub moveto lw 2 div ex add ey lw 2 div sub lineto stroke gsave 1 1 1 setrgbcolor lw siz 0.0119444 mul sub setlinewidth sx sy moveto ex ey lineto stroke grestore lw siz 0.0119444 mul sub setlinewidth sx sy moveto ex ey lineto strokepath 0.0119444 siz mul setlinewidth stroke } if } if } ifelse grestore} bind def /plain 1 def /outline 2 def /shadow 3 def /outlineshadow 4 def /fess { currentdict /outlineFontSize known { /outlineFontSize 2 index def } if findfont exch dup /siz exch def scalefont setfont } bind def /SHDW {gsave siz oldfontname fess siz 0.055 mul x add y siz 0.05 mul sub moveto c show grestore} def /NRML {gsave 1 1 1 setrgbcolor siz oldfontname fess x y moveto c show grestore siz /Outline fess x y moveto c show} def /S { fontkind plain eq {neg moveto show} if fontkind outline eq {neg /y exch def /x exch def /c exch def NRML} if fontkind shadow eq {neg /y exch def /x exch def /c exch def SHDW NRML} if fontkind outlineshadow eq {neg /y exch def /x exch def /c exch def SHDW NRML} if } bind def /F { /fontkind exch def fontkind plain eq {fess} if fontkind outline eq {dup /oldfontname exch def exch dup /siz exch def exch OLF} if fontkind shadow eq {dup /oldfontname exch def exch dup /siz exch def exch OLF} if fontkind outlineshadow eq {dup /oldfontname exch def exch dup /siz exch def exch OLF} if } bind def /makeoutlinedict 15 dict def /makeoutlinefont { makeoutlinedict begin /uniqueid exch def /strokewidth exch def /newfontname exch def /basefontname exch def FontDirectory basefontname known not { /basefontname /Times-Roman def } if /basefontdict basefontname findfont def /numentries basefontdict maxlength 1 add def basefontdict /UniqueID known not {/numentries numentries 1 add def} if /outfontdict numentries dict def basefontdict { exch dup /FID ne {exch outfontdict 3 1 roll put} {pop pop} ifelse }forall outfontdict /FontName newfontname put outfontdict /PaintType 2 put outfontdict /StrokeWidth strokewidth put outfontdict /UniqueID uniqueid put newfontname outfontdict definefont pop end }def /UID { findfont dup /UniqueID known {/UniqueID get 1 add} {pop 1} ifelse } def /OLF { dup /Outline 1000 62 div 4 -1 roll UID /outlineFontSize 5 index def makeoutlinefont /Outline findfont exch scalefont setfont } def /CopyEncoding { findfont /Encoding get dup length array /tarrayz exch def tarrayz 0 3 -1 roll putinterval tarrayz } bind def /Re-encode { dup length array copy /eap 0 def exch { dup type /integertype eq { /eap exch def } { 1 index exch eap exch put /eap eap 1 add def } ifelse } forall } bind def /EncodeFont { findfont dup length dict begin { 1 index /FID ne { def } { pop pop } ifelse } forall /FontName exch def /Encoding exch def FontName currentdict end definefont pop } bind def /clip2pathbbox { /magicNum linewidth 2 div 1 2 sqrt div mul def pathbbox /urymn exch magicNum add def /urxmn exch magicNum add def /llymn exch magicNum sub def /llxmn exch magicNum sub def newpath llxmn llymn moveto llxmn urymn lineto urxmn urymn lineto urxmn llymn lineto closepath clip newpath } bind def /Line { MAV /LC get length 0 ne { gsave newpath MAV /ArrowType get length 0 eq MAV /SD get length 0 eq and {2 setlinecap /UseClip {clip2pathbbox} def } {0 setlinecap /UseClip {} def } ifelse 0 792 translate 1 -1 scale CTM currentmatrix pop /yStart exch def /xStart exch def /yEnd exch def /xEnd exch def /linewidth exch def MAV /ArrowType get length 0 eq xStart xEnd ne yStart yEnd ne and and {xStart yStart moveto xEnd yEnd lineto UseClip xStart yStart moveto xEnd yEnd lineto} {xStart yStart moveto xEnd yEnd lineto} ifelse linewidth setlinewidth SD strokepath CheckPath {LC PF ArrowType} if grestore } {pop pop pop pop pop} ifelse } bind def /ZeroLine { gsave newpath MAV /ArrowType get length 0 ne { /UseClip {} def 0 792 translate 1 -1 scale pop pop pop pop pop CTM currentmatrix pop ArrowType } if grestore } bind def /CompensateForStroke { sin currentlinewidth mul exch cos currentlinewidth mul dup 0 translate 4 -1 roll exch 2.0 mul sub 3 1 roll 2.0 mul sub } bind def /arrowdict 10 dict def arrowdict begin /SwallowTail { newpath 0.0 0.0 moveto 1.0 -.5 lineto .666 0.0 lineto 1.0 .5 lineto closepath } bind def /Triangular { newpath 0.0 0.0 moveto 1.0 -.5 lineto 1.0 .5 lineto closepath } bind def /OpenTri { newpath 1.0 0.5 moveto 0.0 0.0 lineto 1.0 -0.5 lineto } bind def /ClosedTri { newpath 1.0 0.5 moveto 0.0 0.0 lineto 1.0 -0.5 lineto closepath } bind def /SlashBar { newpath 0.5 -.5 moveto -.5 0.5 lineto } bind def /Dot { newpath 0.5 0.0 moveto 0 0 1 0 360 arc closepath } bind def /ExtSlashBar { newpath 1.0 -.5 moveto 0.0 0.5 lineto } bind def end /ScaleArrowHead { 0 0 4 -2 roll 0 0 1 1 8 -4 roll GetBoxesRatio scale } bind def /DrawArrowHead { gsave [] 0 setdash currentpoint translate rotate { 4 copy gsave initmatrix 100 200 translate msave ScaleArrowHead pop arrowdict exch get exec mrestore strokepath 0 0 3 index 3 index pathbbox 8 4 roll GetBoxesRatio 4 2 roll grestore 3 index 1.0 exch sub 6 -1 roll { 2 index mul 0 translate }{ pop } ifelse msave ScaleArrowHead scale arrowdict exch get exec mrestore strokepath } { msave ScaleArrowHead arrowdict exch get exec mrestore } ifelse CheckPath { LC PF } if grestore } bind def /SR { pbox left get pbox top get moveto pbox right get pbox top get lineto pbox right get pbox bottom get lineto pbox left get pbox bottom get lineto closepath } bind def /E { 1.415 setmiterlimit CM currentmatrix pop pbox right get pbox left get sub abs dup pbox bottom get pbox top get sub abs dup 3 -1 roll lt {exch dup 3 -1 roll exch div 1 exch} {dup 3 -1 roll exch div 1} ifelse scale 0 0 3 -1 roll 2 div 0 360 arc closepath CM setmatrix } bind def /StripFromFront { dup length 2 index sub 3 1 roll exch 3 -1 roll getinterval } bind def /MakePathArray { /k 0 def {/k k 1 add def pop pop}{/k k 1 add def pop pop}{/k k 1 add def pop pop pop pop pop pop}{/k k 1 add def }pathforall k array /k 0 def {{moveto} 3 array astore 1 index k 3 -1 roll put /k k 1 add def} {{lineto} 3 array astore 1 index k 3 -1 roll put /k k 1 add def} {{curveto} 7 array astore 1 index k 3 -1 roll put /k k 1 add def} {{closepath} 1 array astore 1 index k 3 -1 roll put /k k 1 add def} pathforall }bind def /MakeFlatPathArray { /k 0 def {/k k 1 add def pop pop}{/k k 1 add def pop pop}{pop pop pop pop pop pop}{}pathforall k array /k 0 def {{moveto} 3 array astore 1 index k 3 -1 roll put /k k 1 add def} {{lineto} 3 array astore 1 index k 3 -1 roll put /k k 1 add def} { pop pop pop pop pop pop} {} pathforall }bind def /FractionalLine { 2 index sub .00001 mul exch 3 index sub .00001 mul 4 -1 roll add 3 1 roll add } bind def /calcLineLength { exch 4 -1 roll sub dup mul 3 1 roll exch sub dup mul add sqrt } bind def /InitTotalLineLength { /oldY exch def /oldX exch def theDash aload pop currentLineLength add setdash } bind def /AccumeLineLength { 3 copy pop 2 copy oldX oldY 4 2 roll calcLineLength /segmentLength exch def /currentLineLength currentLineLength segmentLength add def /oldY exch def /oldX exch def } bind def /DecumeLastLineLength { /currentLineLength currentLineLength segmentLength sub def } bind def /DrawFlattendSegment { /pointCount 2 def dup 0 lt { pop 0 } if fpc 3 1 roll 2 index 1 index gt { 2 copy get dup length dup 3 eq { pop dup 0 get exch 1 get 2 copy InitTotalLineLength m } { } ifelse } { pop 1 index } ifelse dup 1 add 3 index exch sub dup 10 gt { pop 10} if { 1 add 2 copy get aload pop AccumeLineLength exec } repeat 3 1 roll pop pop DecumeLastLineLength } bind def /IncFPC { fpc add /fpc exch def } bind def /DrawFlatPathArray { fpc 0 { dup 2 index 1 sub lt { flatPathArray exch newpath 1 sub DrawFlattendSegment gsave pathSegProc grestore newpath } { pop pop exit } ifelse } loop } bind def /RecordFirstSubSegment { closepathArray 0 pathArray 0 get put closepathArray 1 pathArray 0 get aload pop pop pathArray 1 get dup length 3 eq { aload pop pop } { newpath 0 0 moveto aload pop exec /segmentArray flattenpath MakeFlatPathArray def segmentArray 1 get aload pop pop } ifelse FractionalLine {lineto} 3 array astore put } bind def /AppendClosePath { closepathArray 0 get 2 {lineto} put flatPathArray fpc closepathArray 0 get put 1 IncFPC flatPathArray fpc closepathArray 1 get put 1 IncFPC } bind def /RecordCurrentDash { /theDash currentdash 2 array astore def /currentLineLength 0 def } bind def /PatternStroke { 0 setlinecap RecordCurrentDash /saveFlat currentflat def .5 setflat /pathArray MakePathArray def /closepathArray 2 array def /pathLength pathArray length def /flatPathArray 513 array def /currentLineLength 0 def /fpc 0 def pathArray pathLength 1 sub get length 1 eq { /usingClosepath true def RecordFirstSubSegment /pathLength pathLength 1 sub def } { /usingClosepath false def } ifelse 0 1 pathLength 1 sub { pathArray exch get dup length 3 eq { fpc 1 add 512 ge { DrawFlatPathArray fpc 2 ge { flatPathArray flatPathArray fpc 2 sub get 0 put flatPathArray flatPathArray fpc 1 sub get 1 put /fpc 2 def }{ /fpc 0 def } ifelse } if flatPathArray exch fpc exch put 1 IncFPC } { dup length 7 eq { newpath /nToStrip 0 def fpc 1 gt { flatPathArray fpc 2 sub get aload pop pop m flatPathArray fpc 1 sub get aload pop exec /nToStrip 2 def } { fpc 1 eq { flatPathArray fpc 1 sub get aload pop exec /nToStrip 2 def } if } ifelse aload pop exec /segmentArray flattenpath MakeFlatPathArray def /segmentArray nToStrip segmentArray StripFromFront def segmentArray length fpc add 512 lt { flatPathArray fpc segmentArray putinterval segmentArray length IncFPC } { DrawFlatPathArray fpc 1 gt { flatPathArray flatPathArray fpc 2 sub get 0 exch put flatPathArray flatPathArray fpc 1 sub get 1 exch put /fpc 2 def }{ /fpc 0 def } ifelse segmentArray length 512 lt { flatPathArray fpc segmentArray putinterval segmentArray length IncFPC } { segmentArray length /exitLoop false def 0 { 2 copy sub dup 500 gt { pop 500 } { /exitLoop true def } ifelse segmentArray 2 index 2 index getinterval flatPathArray fpc 3 -1 roll putinterval dup IncFPC add exitLoop { exit } { DrawFlatPathArray fpc 1 gt { flatPathArray flatPathArray fpc 2 sub get 0 exch put flatPathArray flatPathArray fpc 1 sub get 1 exch put /fpc 2 def }{ /fpc 0 def } ifelse } ifelse } loop } ifelse } ifelse } if } ifelse } for fpc 0 gt { usingClosepath { AppendClosePath } if DrawFlatPathArray } if saveFlat setflat } bind def initmsaverestore /tctm matrix currentmatrix def tctm RoundMatrix setmatrix /patternMatrix mstore def 10 setmiterlimit 2 setlinecap newpath % %tLayer % %@BeginRuler %@ 9.0000000000000000000e+0 viewScale %@ 1.1111111111111110490e-1 realScale %@ 8 realDivs %@ 0000 rulerFormat %@EndRuler %@BeginLine /ArrowType{ 1.000 setlinewidth 72.000 396.000 moveto /Triangular 14.099 7.049 false 90.006 DrawArrowHead } bind def /SD {} def /SS {setlinewidth SD stroke} def /LC { /setcmykcolor where {begin 0.000 0.000 0.000 1.000 setcmykcolor end} {0.000 0.000 0.000 setrgbcolor} ifelse } def /PF {gsave fill grestore} def /SS {setlinewidth SD stroke} def 1.000 72.000 648.000 72.000 398.000 Line %@EndLine %@BeginRuler %@ 9.0000000000000000000e+0 viewScale %@ 1.1111111111111110490e-1 realScale %@ 8 realDivs %@ 0000 rulerFormat %@EndRuler %@BeginLine /ArrowType{ 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{setlinewidth SD stroke} def /LC { /setcmykcolor where {begin 0.000 0.000 0.000 1.000 setcmykcolor end} {0.000 0.000 0.000 setrgbcolor} ifelse } def /PC { /setcmykcolor where {begin 0.000 0.000 0.000 1.000 setcmykcolor end} {0.000 0.000 0.000 setrgbcolor} ifelse } def /PF {gsave fill grestore} def 0.750 0 527.536 134.305 0.000 0.000 6.750 6.750 rect %@EndOval %@BeginRuler %@ 9.0000000000000000000e+0 viewScale %@ 1.1111111111111110490e-1 realScale %@ 8 realDivs %@ 0000 rulerFormat %@EndRuler %@BeginLine /ArrowType{ } def /SD {[9.000 9.000 ] 0 setdash} def /SS {setlinewidth SD stroke} def /LC { /setcmykcolor where {begin 0.000 0.000 0.000 1.000 setcmykcolor end} {0.000 0.000 0.000 setrgbcolor} ifelse } def /PF {gsave fill grestore} def /SS {setlinewidth SD stroke} def 1.000 360.000 477.000 63.000 576.000 Line %@EndLine %@BeginText save [ 39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis /Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute 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Fq(\))25 b(=)f Fp(\000)40 1966 y(\017)d Fq(What's)29 b(most)f(probable)h(classi\014cati)q(on)i(of)f Fl(x)p Fq(?)0 2748 y Fo(142)334 b(lecture)17 b(slides)f(for)f(textb)q (o)q(ok)g Fn(Machine)h(L)n(e)n(arning)p Fo(,)c(T.)j(Mitc)o(hell,)h (McGra)o(w)e(Hill,)j(1997)p eop %%Page: 143 19 143 18 bop 25 160 a Fm(Ba)m(y)m(es)34 b(Optimal)i(Classi\014er)1170 160 y 0.8666 0.03137 0.02352 setrgbcolor 1170 160 a 0 321 1947 2 v 0 474 a 0 0 0 setrgbcolor 0 474 a 64 x Fb(Ba)m(y)m(es)f(optimal)f(classi\014cation:)434 709 y Fq(arg)16 b(max)579 756 y Fj(v)608 768 y Fh(j)633 756 y Fi(2)p Fj(V)788 658 y Ff(X)744 769 y Fj(h)778 781 y Fh(i)797 769 y Fi(2)p Fj(H)906 709 y Fl(P)c Fq(\()p Fl(v)1048 721 y Fj(j)1079 709 y Fp(j)p Fl(h)1153 721 y Fj(i)1175 709 y Fq(\))p Fl(P)g Fq(\()p Fl(h)1358 721 y Fj(i)1381 709 y Fp(j)p Fl(D)r Fq(\))0 899 y(Example:)196 1156 y Fl(P)g Fq(\()p Fl(h)346 1169 y Fg(1)378 1156 y Fp(j)p Fl(D)r Fq(\))25 b(=)f Fl(:)p Fq(4)p Fl(;)42 b(P)12 b Fq(\()p Fp(\000j)p Fl(h)998 1169 y Fg(1)1030 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rightarrow } if end } dup 0 4 dict put def /Poly { 3 1 roll newpath moveto -1 add { lineto } repeat closepath patternNone not { ifill } if brushNone not { istroke } if } def /Rect { 0 begin /t exch def /r exch def /b exch def /l exch def newpath l b moveto l t lineto r t lineto r b lineto closepath patternNone not { ifill } if brushNone not { istroke } if end } dup 0 4 dict put def /Text { ishow } def /idef { dup where { pop pop pop } { exch def } ifelse } def /ifill { 0 begin gsave patternGrayLevel -1 ne { fgred bgred fgred sub patternGrayLevel mul add fggreen bggreen fggreen sub patternGrayLevel mul add fgblue bgblue fgblue sub patternGrayLevel mul add setrgbcolor eofill } { eoclip originalCTM setmatrix pathbbox /t exch def /r exch def /b exch def /l exch def /w r l sub ceiling cvi def /h t b sub ceiling cvi def /imageByteWidth w 8 div ceiling cvi def /imageHeight h def bgred bggreen bgblue setrgbcolor eofill fgred fggreen fgblue setrgbcolor w 0 gt h 0 gt and { l b translate w h scale w h true [w 0 0 h neg 0 h] { patternproc } imagemask } if } ifelse grestore end } dup 0 8 dict put def /istroke { gsave brushDashOffset -1 eq { [] 0 setdash 1 setgray } { brushDashArray brushDashOffset setdash fgred fggreen fgblue setrgbcolor } ifelse brushWidth setlinewidth originalCTM setmatrix stroke grestore } def /ishow { 0 begin gsave fgred fggreen fgblue setrgbcolor /fontDict printFont printSize scalefont dup setfont def /descender fontDict begin 0 [FontBBox] 1 get FontMatrix end transform exch pop def /vertoffset 1 printSize sub descender sub def { 0 vertoffset moveto show /vertoffset vertoffset printSize sub def } forall grestore end } dup 0 3 dict put def /patternproc { 0 begin /patternByteLength patternString length def /patternHeight patternByteLength 8 mul sqrt cvi def /patternWidth patternHeight def /patternByteWidth patternWidth 8 idiv def /imageByteMaxLength imageByteWidth imageHeight mul stringLimit patternByteWidth sub min def /imageMaxHeight imageByteMaxLength imageByteWidth idiv patternHeight idiv patternHeight mul patternHeight max def /imageHeight imageHeight imageMaxHeight sub store /imageString imageByteWidth imageMaxHeight mul patternByteWidth add string def 0 1 imageMaxHeight 1 sub { /y exch def /patternRow y patternByteWidth mul patternByteLength mod def /patternRowString patternString patternRow patternByteWidth getinterval def /imageRow y imageByteWidth mul def 0 patternByteWidth imageByteWidth 1 sub { /x exch def imageString imageRow x add patternRowString putinterval } for } for imageString end } dup 0 12 dict put def /min { dup 3 2 roll dup 4 3 roll lt { exch } if pop } def /max { dup 3 2 roll dup 4 3 roll gt { exch } if pop } def /midpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 x1 add 2 div y0 y1 add 2 div end } dup 0 4 dict put def /thirdpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 2 mul x1 add 3 div y0 2 mul y1 add 3 div end } dup 0 4 dict put def /subspline { 0 begin /movetoNeeded exch def y exch get /y3 exch def x exch get /x3 exch def y exch get /y2 exch def x exch get /x2 exch def y exch get /y1 exch def x exch get /x1 exch def y exch get /y0 exch def x exch get /x0 exch def x1 y1 x2 y2 thirdpoint /p1y exch def /p1x exch def x2 y2 x1 y1 thirdpoint /p2y exch def /p2x exch def x1 y1 x0 y0 thirdpoint p1x p1y midpoint /p0y exch def /p0x exch def x2 y2 x3 y3 thirdpoint p2x p2y midpoint /p3y exch def /p3x exch def movetoNeeded { p0x p0y moveto } if p1x p1y p2x p2y p3x p3y curveto end } dup 0 17 dict put def /storexyn { /n exch def /y n array def /x n array def n 1 sub -1 0 { /i exch def y i 3 2 roll put x i 3 2 roll put } for } def /SSten { fgred fggreen fgblue setrgbcolor dup true exch 1 0 0 -1 0 6 -1 roll matrix astore } def /FSten { dup 3 -1 roll dup 4 1 roll exch newpath 0 0 moveto dup 0 exch lineto exch dup 3 1 roll exch lineto 0 lineto closepath bgred bggreen bgblue setrgbcolor eofill SSten } def /Rast { exch dup 3 1 roll 1 0 0 -1 0 6 -1 roll matrix astore } def /arrowhead { 0 begin transform originalCTM itransform /taily exch def /tailx exch def transform originalCTM itransform /tipy exch def /tipx exch def /dy tipy taily sub def /dx tipx tailx sub def /angle dx 0 ne dy 0 ne or { dy dx atan } { 90 } ifelse def gsave originalCTM setmatrix tipx tipy translate angle rotate newpath arrowHeight neg arrowWidth 2 div moveto 0 0 lineto arrowHeight neg arrowWidth 2 div neg lineto patternNone not { originalCTM setmatrix /padtip arrowHeight 2 exp 0.25 arrowWidth 2 exp mul add sqrt brushWidth mul arrowWidth div def /padtail brushWidth 2 div def tipx tipy translate angle rotate padtip 0 translate arrowHeight padtip add padtail add arrowHeight div dup scale arrowheadpath ifill } if brushNone not { originalCTM setmatrix tipx tipy translate angle rotate arrowheadpath istroke } if grestore end } dup 0 9 dict put def /arrowheadpath { newpath arrowHeight neg arrowWidth 2 div moveto 0 0 lineto arrowHeight neg arrowWidth 2 div neg lineto } def /leftarrow { 0 begin y exch get /taily exch def x exch get /tailx exch def y exch get /tipy exch def x exch get /tipx exch def brushLeftArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /rightarrow { 0 begin y exch get /tipy exch def x exch get /tipx exch def y exch get /taily exch def x exch get /tailx exch def brushRightArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def %I Idraw 10 Grid 8 8 Begin %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 0.799705 0 0 0.799705 0 0 ] concat /originalCTM matrix currentmatrix def Begin %I Elli %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 -22 -29.5 ] concat %I 147 237 48 24 Elli End Begin %I Elli %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 123.5 -29.5 ] concat %I 147 237 48 24 Elli End Begin %I Elli %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 87.5 -117.5 ] concat %I 147 237 48 24 Elli End Begin %I Elli %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 -67.5 -205.5 ] concat %I 147 237 48 24 Elli End Begin %I Elli %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 78 -205.5 ] concat %I 147 237 48 24 Elli End Begin %I Elli %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 -81 -117.5 ] concat %I 147 237 48 24 Elli End Begin %I Line %I b 65535 1 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 -27 -21 ] concat %I 131 205 91 165 Line %I 1 End Begin %I Line %I b 65535 1 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 -27 -21 ] concat %I 171 205 259 165 Line %I 1 End Begin %I Line %I b 65535 1 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 -27 -21 ] concat %I 291 205 259 165 Line %I 1 End Begin %I Line %I b 65535 1 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 -27 -21 ] concat %I 91 117 99 77 Line %I 1 End Begin %I Line %I b 65535 1 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 -27 -21 ] concat %I 259 117 251 77 Line %I 1 End Begin %I Elli %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 339.5 -174 ] concat %I 147 237 48 24 Elli End Begin %I Rect %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 -48.5 -12.9999 ] concat %I 427 101 643 181 Rect End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-times-medium-i-normal-*-14-*-*-*-*-*-*-* Times-Italic 14 SetF %I t [ 1 0 0 1 108.5 213 ] concat %I [ (Storm) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-times-medium-i-normal-*-14-*-*-*-*-*-*-* Times-Italic 14 SetF %I t [ 1 0 0 1 208 125 ] concat %I [ (Campfire) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-times-medium-i-normal-*-14-*-*-*-*-*-*-* Times-Italic 14 SetF %I t [ 1 0 0 1 39.5 125 ] concat %I [ (Lightning) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-times-medium-i-normal-*-14-*-*-*-*-*-*-* Times-Italic 14 SetF %I t [ 1 0 0 1 56 37 ] concat %I [ (Thunder) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-times-medium-i-normal-*-14-*-*-*-*-*-*-* Times-Italic 14 SetF %I t [ 1 0 0 1 193.5 37 ] concat %I [ (ForestFire) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-times-medium-i-normal-*-14-*-*-*-*-*-*-* Times-Italic 14 SetF %I t [ 1 0 0 1 460 68.5 ] concat %I [ (Campfire) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-times-medium-i-normal-*-14-*-*-*-*-*-*-* Times-Italic 14 SetF %I t [ 1 0 0 1 394.5 134 ] concat %I [ (C) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-times-medium-i-normal-*-14-*-*-*-*-*-*-* Times-Italic 14 SetF %I t [ 1 0 0 1 386.5 110 ] concat %I [ (\254C) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-times-medium-i-normal-*-14-*-*-*-*-*-*-* Times-Italic 14 SetF %I t [ 1 0 0 1 506.5 158 ] concat %I [ (\254S,B) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-times-medium-i-normal-*-14-*-*-*-*-*-*-* Times-Italic 14 SetF %I t [ 1 0 0 1 546.5 158 ] concat %I [ (\254S,\254B) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-times-medium-r-normal-*-14-*-*-*-*-*-*-* Times-Roman 14 SetF %I t [ 1 0 0 1 434.5 134 ] concat %I [ (0.4) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-times-medium-r-normal-*-14-*-*-*-*-*-*-* Times-Roman 14 SetF %I t [ 1 0 0 1 434.5 110 ] concat %I [ (0.6) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-times-medium-r-normal-*-14-*-*-*-*-*-*-* Times-Roman 14 SetF %I t [ 1 0 0 1 474.5 134 ] concat %I [ (0.1) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-times-medium-r-normal-*-14-*-*-*-*-*-*-* Times-Roman 14 SetF %I t [ 1 0 0 1 474.5 110 ] concat %I [ (0.9) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-times-medium-r-normal-*-14-*-*-*-*-*-*-* Times-Roman 14 SetF %I t [ 1 0 0 1 514.5 134 ] concat %I [ (0.8) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-times-medium-r-normal-*-14-*-*-*-*-*-*-* Times-Roman 14 SetF %I t [ 1 0 0 1 514.5 110 ] concat %I [ (0.2) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-times-medium-r-normal-*-14-*-*-*-*-*-*-* Times-Roman 14 SetF %I t [ 1 0 0 1 562.5 134 ] concat %I [ (0.2) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-times-medium-r-normal-*-14-*-*-*-*-*-*-* Times-Roman 14 SetF %I t [ 1 0 0 1 562.5 110 ] concat %I [ (0.8) ] Text End Begin %I Line %I b 65535 1 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 -0 -0 1 -42 -6 ] concat %I 106 102 257 61 Line %I 1 End Begin %I Line %I b 65535 1 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 -0 -0 1 -42 -6 ] concat %I 168 189 261 61 Line %I 1 End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-times-medium-i-normal-*-14-*-*-*-*-*-*-* Times-Italic 14 SetF %I t [ 1 0 0 1 466.5 158 ] concat %I [ (S,\254B) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-times-medium-i-normal-*-14-*-*-*-*-*-*-* Times-Italic 14 SetF %I t [ 1 0 0 1 229 213 ] concat %I [ (BusTourGroup) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-times-medium-i-normal-*-14-*-*-*-*-*-*-* Times-Italic 14 SetF %I t [ 1 0 0 1 432.5 158 ] concat %I [ (S,B) ] Text End End %I eop showpage end %%EndDocument endTexFig 0 1401 a Fq(Net)n(w)n(ork)29 b(represen)n(ts)f(a)h(set)g(of)g (conditional)0 1505 y(indep)r(endence)h(assertions:)40 1663 y Fp(\017)21 b Fq(Eac)n(h)28 b(no)r(de)h(is)g(asserted)h(to)f(b)r (e)g(conditionall)q(y)104 1766 y(indep)r(enden)n(t)h(of)f(its)h (nondescendan)n(ts,)e(giv)n(en)i(its)104 1870 y(immediate)f (predecessors.)40 2016 y Fp(\017)21 b Fq(Directed)30 b(acyclic)i(graph)0 2748 y Fo(160)334 b(lecture)17 b(slides)f(for)f (textb)q(o)q(ok)g Fn(Machine)h(L)n(e)n(arning)p Fo(,)c(T.)j(Mitc)o (hell,)h(McGra)o(w)e(Hill,)j(1997)p eop %%Page: 161 37 161 36 bop 25 160 a Fr(Ba)m(y)m(esian)40 b(Belief)j(Net)m(w)m(ork)1339 160 y 0.8666 0.03137 0.02352 setrgbcolor 1339 160 a 0 321 1947 2 v 0 441 a 0 0 0 setrgbcolor 0 441 a -77 446 a 33154007 12930060 855162 263127 31312117 12235407 startTexFig -77 446 a %%BeginDocument: ./bookps/bayesnet.ps /arrowHeight 10 def /arrowWidth 5 def /IdrawDict 52 dict def IdrawDict begin /reencodeISO { dup dup findfont dup length dict begin { 1 index /FID ne { def }{ pop pop } ifelse } forall /Encoding ISOLatin1Encoding def currentdict end definefont } def /ISOLatin1Encoding [ /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /space/exclam/quotedbl/numbersign/dollar/percent/ampersand/quoteright /parenleft/parenright/asterisk/plus/comma/minus/period/slash /zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon /less/equal/greater/question/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N /O/P/Q/R/S/T/U/V/W/X/Y/Z/bracketleft/backslash/bracketright /asciicircum/underscore/quoteleft/a/b/c/d/e/f/g/h/i/j/k/l/m /n/o/p/q/r/s/t/u/v/w/x/y/z/braceleft/bar/braceright/asciitilde /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/dotlessi/grave/acute/circumflex/tilde/macron/breve /dotaccent/dieresis/.notdef/ring/cedilla/.notdef/hungarumlaut /ogonek/caron/space/exclamdown/cent/sterling/currency/yen/brokenbar /section/dieresis/copyright/ordfeminine/guillemotleft/logicalnot /hyphen/registered/macron/degree/plusminus/twosuperior/threesuperior /acute/mu/paragraph/periodcentered/cedilla/onesuperior/ordmasculine /guillemotright/onequarter/onehalf/threequarters/questiondown /Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla /Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex /Idieresis/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis /multiply/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute /Thorn/germandbls/agrave/aacute/acircumflex/atilde/adieresis /aring/ae/ccedilla/egrave/eacute/ecircumflex/edieresis/igrave /iacute/icircumflex/idieresis/eth/ntilde/ograve/oacute/ocircumflex /otilde/odieresis/divide/oslash/ugrave/uacute/ucircumflex/udieresis /yacute/thorn/ydieresis ] def /Times-Italic reencodeISO def /Times-Roman reencodeISO def /none null def /numGraphicParameters 17 def /stringLimit 65535 def /Begin { save numGraphicParameters dict begin } def /End { end restore } def /SetB { dup type /nulltype eq { pop false /brushRightArrow idef false /brushLeftArrow idef true /brushNone idef } { /brushDashOffset idef /brushDashArray idef 0 ne /brushRightArrow idef 0 ne /brushLeftArrow idef /brushWidth idef false /brushNone idef } ifelse } def /SetCFg { /fgblue idef /fggreen idef /fgred idef } def /SetCBg { /bgblue idef /bggreen idef /bgred idef } def /SetF { /printSize idef /printFont idef } def /SetP { dup type /nulltype eq { pop true /patternNone idef } { dup -1 eq { /patternGrayLevel idef /patternString idef } { /patternGrayLevel idef } ifelse false /patternNone idef } ifelse } def /BSpl { 0 begin storexyn newpath n 1 gt { 0 0 0 0 0 0 1 1 true subspline n 2 gt { 0 0 0 0 1 1 2 2 false subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 2 copy false subspline } if n 2 sub dup n 1 sub dup 2 copy 2 copy false subspline patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Circ { newpath 0 360 arc patternNone not { ifill } if brushNone not { istroke } if } def /CBSpl { 0 begin dup 2 gt { storexyn newpath n 1 sub dup 0 0 1 1 2 2 true subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 0 0 false subspline n 2 sub dup n 1 sub dup 0 0 1 1 false subspline patternNone not { ifill } if brushNone not { istroke } if } { Poly } ifelse end } dup 0 4 dict put def /Elli { 0 begin newpath 4 2 roll translate scale 0 0 1 0 360 arc patternNone not { ifill } if brushNone not { istroke } if end } dup 0 1 dict put def /Line { 0 begin 2 storexyn newpath x 0 get y 0 get moveto x 1 get y 1 get lineto brushNone not { istroke } if 0 0 1 1 leftarrow 0 0 1 1 rightarrow end } dup 0 4 dict put def /MLine { 0 begin storexyn newpath n 1 gt { x 0 get y 0 get moveto 1 1 n 1 sub { /i exch def x i get y i get lineto } for patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Poly { 3 1 roll newpath moveto -1 add { lineto } repeat closepath patternNone not { ifill } if brushNone not { istroke } if } def /Rect { 0 begin /t exch def /r exch def /b exch def /l exch def newpath l b moveto l t lineto r t lineto r b lineto closepath patternNone not { ifill } if brushNone not { istroke } if end } dup 0 4 dict put def /Text { ishow } def /idef { dup where { pop pop pop } { exch def } ifelse } def /ifill { 0 begin gsave patternGrayLevel -1 ne { fgred bgred fgred sub patternGrayLevel mul add fggreen bggreen fggreen sub patternGrayLevel mul add fgblue bgblue fgblue sub patternGrayLevel mul add setrgbcolor eofill } { eoclip originalCTM setmatrix pathbbox /t exch def /r exch def /b exch def /l exch def /w r l sub ceiling cvi def /h t b sub ceiling cvi def /imageByteWidth w 8 div ceiling cvi def /imageHeight h def bgred bggreen bgblue setrgbcolor eofill fgred fggreen fgblue setrgbcolor w 0 gt h 0 gt and { l b translate w h scale w h true [w 0 0 h neg 0 h] { patternproc } imagemask } if } ifelse grestore end } dup 0 8 dict put def /istroke { gsave brushDashOffset -1 eq { [] 0 setdash 1 setgray } { brushDashArray brushDashOffset setdash fgred fggreen fgblue setrgbcolor } ifelse brushWidth setlinewidth originalCTM setmatrix stroke grestore } def /ishow { 0 begin gsave fgred fggreen fgblue setrgbcolor /fontDict printFont printSize scalefont dup setfont def /descender fontDict begin 0 [FontBBox] 1 get FontMatrix end transform exch pop def /vertoffset 1 printSize sub descender sub def { 0 vertoffset moveto show /vertoffset vertoffset printSize sub def } forall grestore end } dup 0 3 dict put def /patternproc { 0 begin /patternByteLength patternString length def /patternHeight patternByteLength 8 mul sqrt cvi def /patternWidth patternHeight def /patternByteWidth patternWidth 8 idiv def /imageByteMaxLength imageByteWidth imageHeight mul stringLimit patternByteWidth sub min def /imageMaxHeight imageByteMaxLength imageByteWidth idiv patternHeight idiv patternHeight mul patternHeight max def /imageHeight imageHeight imageMaxHeight sub store /imageString imageByteWidth imageMaxHeight mul patternByteWidth add string def 0 1 imageMaxHeight 1 sub { /y exch def /patternRow y patternByteWidth mul patternByteLength mod def /patternRowString patternString patternRow patternByteWidth getinterval def /imageRow y imageByteWidth mul def 0 patternByteWidth imageByteWidth 1 sub { /x exch def imageString imageRow x add patternRowString putinterval } for } for imageString end } dup 0 12 dict put def /min { dup 3 2 roll dup 4 3 roll lt { exch } if pop } def /max { dup 3 2 roll dup 4 3 roll gt { exch } if pop } def /midpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 x1 add 2 div y0 y1 add 2 div end } dup 0 4 dict put def /thirdpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 2 mul x1 add 3 div y0 2 mul y1 add 3 div end } dup 0 4 dict put def /subspline { 0 begin /movetoNeeded exch def y exch get /y3 exch def x exch get /x3 exch def y exch get /y2 exch def x exch get /x2 exch def y exch get /y1 exch def x exch get /x1 exch def y exch get /y0 exch def x exch get /x0 exch def x1 y1 x2 y2 thirdpoint /p1y exch def /p1x exch def x2 y2 x1 y1 thirdpoint /p2y exch def /p2x exch def x1 y1 x0 y0 thirdpoint p1x p1y midpoint /p0y exch def /p0x exch def x2 y2 x3 y3 thirdpoint p2x p2y midpoint /p3y exch def /p3x exch def movetoNeeded { p0x p0y moveto } if p1x p1y p2x p2y p3x p3y curveto end } dup 0 17 dict put def /storexyn { /n exch def /y n array def /x n array def n 1 sub -1 0 { /i exch def y i 3 2 roll put x i 3 2 roll put } for } def /SSten { fgred fggreen fgblue setrgbcolor dup true exch 1 0 0 -1 0 6 -1 roll matrix astore } def /FSten { dup 3 -1 roll dup 4 1 roll exch newpath 0 0 moveto dup 0 exch lineto exch dup 3 1 roll exch lineto 0 lineto closepath bgred bggreen bgblue setrgbcolor eofill SSten } def /Rast { exch dup 3 1 roll 1 0 0 -1 0 6 -1 roll matrix astore } def /arrowhead { 0 begin transform originalCTM itransform /taily exch def /tailx exch def transform originalCTM itransform /tipy exch def /tipx exch def /dy tipy taily sub def /dx tipx tailx sub def /angle dx 0 ne dy 0 ne or { dy dx atan } { 90 } ifelse def gsave originalCTM setmatrix tipx tipy translate angle rotate newpath arrowHeight neg arrowWidth 2 div moveto 0 0 lineto arrowHeight neg arrowWidth 2 div neg lineto patternNone not { originalCTM setmatrix /padtip arrowHeight 2 exp 0.25 arrowWidth 2 exp mul add sqrt brushWidth mul arrowWidth div def /padtail brushWidth 2 div def tipx tipy translate angle rotate padtip 0 translate arrowHeight padtip add padtail add arrowHeight div dup scale arrowheadpath ifill } if brushNone not { originalCTM setmatrix tipx tipy translate angle rotate arrowheadpath istroke } if grestore end } dup 0 9 dict put def /arrowheadpath { newpath arrowHeight neg arrowWidth 2 div moveto 0 0 lineto arrowHeight neg arrowWidth 2 div neg lineto } def /leftarrow { 0 begin y exch get /taily exch def x exch get /tailx exch def y exch get /tipy exch def x exch get /tipx exch def brushLeftArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /rightarrow { 0 begin y exch get /tipy exch def x exch get /tipx exch def y exch get /taily exch def x exch get /tailx exch def brushRightArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def %I Idraw 10 Grid 8 8 Begin %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 0.799705 0 0 0.799705 0 0 ] concat /originalCTM matrix currentmatrix def Begin %I Elli %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 -22 -29.5 ] concat %I 147 237 48 24 Elli End Begin %I Elli %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 123.5 -29.5 ] concat %I 147 237 48 24 Elli End Begin %I Elli %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 87.5 -117.5 ] concat %I 147 237 48 24 Elli End Begin %I Elli %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 -67.5 -205.5 ] concat %I 147 237 48 24 Elli End Begin %I Elli %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 78 -205.5 ] concat %I 147 237 48 24 Elli End Begin %I Elli %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 -81 -117.5 ] concat %I 147 237 48 24 Elli End Begin %I Line %I b 65535 1 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 -27 -21 ] concat %I 131 205 91 165 Line %I 1 End Begin %I Line %I b 65535 1 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 -27 -21 ] concat %I 171 205 259 165 Line %I 1 End Begin %I Line %I b 65535 1 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 -27 -21 ] concat %I 291 205 259 165 Line %I 1 End Begin %I Line %I b 65535 1 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 -27 -21 ] concat %I 91 117 99 77 Line %I 1 End Begin %I Line %I b 65535 1 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 -27 -21 ] concat %I 259 117 251 77 Line %I 1 End Begin %I Elli %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 339.5 -174 ] concat %I 147 237 48 24 Elli End Begin %I Rect %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 -48.5 -12.9999 ] concat %I 427 101 643 181 Rect End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-times-medium-i-normal-*-14-*-*-*-*-*-*-* Times-Italic 14 SetF %I t [ 1 0 0 1 108.5 213 ] concat %I [ (Storm) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-times-medium-i-normal-*-14-*-*-*-*-*-*-* Times-Italic 14 SetF %I t [ 1 0 0 1 208 125 ] concat %I [ (Campfire) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-times-medium-i-normal-*-14-*-*-*-*-*-*-* Times-Italic 14 SetF %I t [ 1 0 0 1 39.5 125 ] concat %I [ (Lightning) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-times-medium-i-normal-*-14-*-*-*-*-*-*-* Times-Italic 14 SetF %I t [ 1 0 0 1 56 37 ] concat %I [ (Thunder) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-times-medium-i-normal-*-14-*-*-*-*-*-*-* Times-Italic 14 SetF %I t [ 1 0 0 1 193.5 37 ] concat %I [ (ForestFire) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-times-medium-i-normal-*-14-*-*-*-*-*-*-* Times-Italic 14 SetF %I t [ 1 0 0 1 460 68.5 ] concat %I [ (Campfire) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-times-medium-i-normal-*-14-*-*-*-*-*-*-* Times-Italic 14 SetF %I t [ 1 0 0 1 394.5 134 ] concat %I [ (C) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-times-medium-i-normal-*-14-*-*-*-*-*-*-* Times-Italic 14 SetF %I t [ 1 0 0 1 386.5 110 ] concat %I [ (\254C) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-times-medium-i-normal-*-14-*-*-*-*-*-*-* Times-Italic 14 SetF %I t [ 1 0 0 1 506.5 158 ] concat %I [ (\254S,B) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-times-medium-i-normal-*-14-*-*-*-*-*-*-* Times-Italic 14 SetF %I t [ 1 0 0 1 546.5 158 ] concat %I [ (\254S,\254B) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-times-medium-r-normal-*-14-*-*-*-*-*-*-* Times-Roman 14 SetF %I t [ 1 0 0 1 434.5 134 ] concat %I [ (0.4) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-times-medium-r-normal-*-14-*-*-*-*-*-*-* Times-Roman 14 SetF %I t [ 1 0 0 1 434.5 110 ] concat %I [ (0.6) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-times-medium-r-normal-*-14-*-*-*-*-*-*-* Times-Roman 14 SetF %I t [ 1 0 0 1 474.5 134 ] concat %I [ (0.1) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-times-medium-r-normal-*-14-*-*-*-*-*-*-* Times-Roman 14 SetF %I t [ 1 0 0 1 474.5 110 ] concat %I [ (0.9) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-times-medium-r-normal-*-14-*-*-*-*-*-*-* Times-Roman 14 SetF %I t [ 1 0 0 1 514.5 134 ] concat %I [ (0.8) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-times-medium-r-normal-*-14-*-*-*-*-*-*-* Times-Roman 14 SetF %I t [ 1 0 0 1 514.5 110 ] concat %I [ (0.2) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-times-medium-r-normal-*-14-*-*-*-*-*-*-* Times-Roman 14 SetF %I t [ 1 0 0 1 562.5 134 ] concat %I [ (0.2) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-times-medium-r-normal-*-14-*-*-*-*-*-*-* Times-Roman 14 SetF %I t [ 1 0 0 1 562.5 110 ] concat %I [ (0.8) ] Text End Begin %I Line %I b 65535 1 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 -0 -0 1 -42 -6 ] concat %I 106 102 257 61 Line %I 1 End Begin %I Line %I b 65535 1 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 -0 -0 1 -42 -6 ] concat %I 168 189 261 61 Line %I 1 End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-times-medium-i-normal-*-14-*-*-*-*-*-*-* Times-Italic 14 SetF %I t [ 1 0 0 1 466.5 158 ] concat %I [ (S,\254B) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-times-medium-i-normal-*-14-*-*-*-*-*-*-* Times-Italic 14 SetF %I t [ 1 0 0 1 229 213 ] concat %I [ (BusTourGroup) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f -*-times-medium-i-normal-*-14-*-*-*-*-*-*-* Times-Italic 14 SetF %I t [ 1 0 0 1 432.5 158 ] concat %I [ (S,B) ] Text End End %I eop showpage end %%EndDocument endTexFig 0 1368 a Fq(Represen)n(ts)29 b(join)n(t)h(probabilit)n(y)h (distribution)h(o)n(v)n(er)c(all)0 1472 y(v)-5 b(ariables)40 1593 y Fp(\017)21 b Fq(e.g.,)29 b Fl(P)12 b Fq(\()p Fl(S)5 b(tor)r(m;)14 b(B)t(usT)e(our)r(Gr)r(oup;)k(:)e(:)h(:)f(;)g(F)e(or)r (estF)g(ir)r(e)p Fq(\))40 1730 y Fp(\017)21 b Fq(in)29 b(general,)332 1865 y Fl(P)12 b Fq(\()p Fl(y)474 1878 y Fg(1)507 1865 y Fl(;)j(:)f(:)g(:)g(;)h(y)741 1878 y Fj(n)779 1865 y Fq(\))24 b(=)958 1802 y Fj(n)949 1814 y Ff(Y)927 1923 y Fj(i)p Fg(=1)1038 1865 y Fl(P)12 b Fq(\()p Fl(y)1180 1878 y Fj(i)1204 1865 y Fp(j)p Fl(P)g(ar)r(ents)p Fq(\()p Fl(Y)1627 1878 y Fj(i)1651 1865 y Fq(\)\))104 2017 y(where)29 b Fl(P)12 b(ar)r(ents)p Fq(\()p Fl(Y)752 2029 y Fj(i)776 2017 y Fq(\))29 b(denotes)h(immediate)104 2120 y(predecessors)f(of)g Fl(Y)742 2133 y Fj(i)793 2120 y Fq(in)g(graph)40 2257 y Fp(\017)21 b Fq(so,)28 b(join)n(t)i (distribution)i(is)d(fully)i(de\014ned)e(b)n(y)g(graph,)104 2361 y(plus)g(the)g Fl(P)12 b Fq(\()p Fl(y)576 2374 y Fj(i)600 2361 y Fp(j)p Fl(P)g(ar)r(ents)p Fq(\()p Fl(Y)1023 2374 y Fj(i)1047 2361 y Fq(\)\))0 2748 y Fo(161)334 b(lecture)17 b(slides)f(for)f(textb)q(o)q(ok)g Fn(Machine)h(L)n(e)n(arning)p Fo(,)c(T.)j(Mitc)o(hell,)h(McGra)o(w)e(Hill,)j(1997)p eop %%Page: 162 38 162 37 bop 25 160 a Fr(Inference)41 b(in)f(Ba)m(y)m(esian)g(Net)m(w)m (orks)1707 160 y 0.8666 0.03137 0.02352 setrgbcolor 1707 160 a 0 321 1947 2 v 0 474 a 0 0 0 setrgbcolor 0 474 a 69 x Fq(Ho)n(w)28 b(can)h(one)g(infer)h(the)f(\(probabiliti)q(es) j(of)7 b(\))29 b(v)-5 b(alues)30 b(of)0 647 y(one)f(or)f(more)g(net)n (w)n(ork)h(v)-5 b(ariables,)31 b(giv)n(en)e(observ)n(ed)0 751 y(v)-5 b(alues)30 b(of)f(others?)40 908 y Fp(\017)21 b Fq(Ba)n(y)n(es)28 b(net)i(con)n(tains)f(all)i(information)e(needed)g (for)104 1012 y(this)h(inference)40 1157 y Fp(\017)21 b Fq(If)29 b(only)h(one)f(v)-5 b(ariable)31 b(with)f(unkno)n(wn)e(v)-5 b(alue,)30 b(easy)g(to)104 1261 y(infer)g(it)40 1406 y Fp(\017)21 b Fq(In)28 b(general)i(case,)f(problem)f(is)i(NP)e(hard)0 1564 y(In)h(practice,)h(can)f(succeed)g(in)h(man)n(y)d(cases)40 1709 y Fp(\017)21 b Fq(Exact)29 b(inference)i(metho)r(ds)d(w)n(ork)h(w) n(ell)h(for)f(some)104 1813 y(net)n(w)n(ork)g(structures)40 1959 y Fp(\017)21 b Fq(Mon)n(te)29 b(Carlo)g(metho)r(ds)f(\\sim)n (ulate")i(the)f(net)n(w)n(ork)104 2062 y(randomly)f(to)h(calculate)j (appro)n(ximate)d(solutions)0 2748 y Fo(162)334 b(lecture)17 b(slides)f(for)f(textb)q(o)q(ok)g Fn(Machine)h(L)n(e)n(arning)p Fo(,)c(T.)j(Mitc)o(hell,)h(McGra)o(w)e(Hill,)j(1997)p eop %%Page: 163 39 163 38 bop 25 160 a Fr(Learning)41 b(of)g(Ba)m(y)m(esian)f(Net)m(w)m (orks)1683 160 y 0.8666 0.03137 0.02352 setrgbcolor 1683 160 a 0 321 1947 2 v 0 474 a 0 0 0 setrgbcolor 0 474 a 64 x Fq(Sev)n(eral)30 b(v)-5 b(arian)n(ts)30 b(of)f(this)h (learning)g(task)40 696 y Fp(\017)21 b Fq(Net)n(w)n(ork)28 b(structure)i(migh)n(t)e(b)r(e)h Fk(known)g Fq(or)g Fk(unknown)40 841 y Fp(\017)21 b Fq(T)-7 b(raining)30 b(examples)f(migh)n(t)f(pro)n (vide)i(v)-5 b(alues)30 b(of)f Fk(al)t(l)104 945 y Fq(net)n(w)n(ork)g (v)-5 b(ariables,)31 b(or)d(just)h Fk(some)0 1103 y Fq(If)g(structure)g (kno)n(wn)g(and)f(observ)n(e)h(all)i(v)-5 b(ariables)40 1248 y Fp(\017)21 b Fq(Then)26 b(it's)h(easy)g(as)f(training)h(a)f (Naiv)n(e)h(Ba)n(y)n(es)f(classi\014er)0 2748 y Fo(163)334 b(lecture)17 b(slides)f(for)f(textb)q(o)q(ok)g Fn(Machine)h(L)n(e)n (arning)p Fo(,)c(T.)j(Mitc)o(hell,)h(McGra)o(w)e(Hill,)j(1997)p eop %%Page: 164 40 164 39 bop 25 160 a Fr(Learning)41 b(Ba)m(y)m(es)f(Nets)1141 160 y 0.8666 0.03137 0.02352 setrgbcolor 1141 160 a 0 321 1947 2 v 0 474 a 0 0 0 setrgbcolor 0 474 a 64 x Fq(Supp)r(ose)29 b(structure)g(kno)n(wn,)f(v)-5 b(ariables)32 b(partially)0 642 y(observ)-5 b(able)0 796 y(e.g.,)29 b(observ)n(e)g Fk(F)-7 b(or)l(estFir)l(e,)31 b(Storm,)h(BusT)-7 b(ourGr)l(oup,)0 899 y(Thunder)p Fq(,)29 b(but)g(not)g Fk(Lightning,)i(Camp\014r)l(e)p Fq(...)40 1057 y Fp(\017)21 b Fq(Similar)30 b(to)f(training)h(neural)g(net)n(w)n(ork)e(with)j (hidden)104 1161 y(units)40 1306 y Fp(\017)21 b Fq(In)28 b(fact,)i(can)f(learn)g(net)n(w)n(ork)g(conditional)104 1410 y(probabilit)n(y)i(tables)f(using)g(gradien)n(t)f(ascen)n(t!)40 1555 y Fp(\017)21 b Fq(Con)n(v)n(erge)28 b(to)i(net)n(w)n(ork)f Fl(h)f Fq(that)h(\(lo)r(call)q(y)q(\))j(maximizes)104 1659 y Fl(P)12 b Fq(\()p Fl(D)r Fp(j)p Fl(h)p Fq(\))0 2748 y Fo(164)334 b(lecture)17 b(slides)f(for)f(textb)q(o)q(ok)g Fn(Machine)h(L)n(e)n(arning)p Fo(,)c(T.)j(Mitc)o(hell,)h(McGra)o(w)e (Hill,)j(1997)p eop %%Page: 165 41 165 40 bop 25 160 a Fr(Gradien)m(t)41 b(Ascen)m(t)e(for)h(Ba)m(y)m(es)g (Nets)1723 160 y 0.8666 0.03137 0.02352 setrgbcolor 1723 160 a 0 321 1947 2 v 0 474 a 0 0 0 setrgbcolor 0 474 a 64 x Fq(Let)29 b Fl(w)216 551 y Fj(ij)s(k)328 538 y Fq(denote)h(one)f(en)n(try)g(in)g(the)g(conditional)0 642 y(probabilit)n(y)i(table)g(for)d(v)-5 b(ariable)31 b Fl(Y)1160 655 y Fj(i)1212 642 y Fq(in)e(the)g(net)n(w)n(ork)0 796 y Fl(w)62 808 y Fj(ij)s(k)169 796 y Fq(=)24 b Fl(P)12 b Fq(\()p Fl(Y)410 808 y Fj(i)457 796 y Fq(=)24 b Fl(y)590 808 y Fj(ij)641 796 y Fp(j)p Fl(P)12 b(ar)r(ents)p Fq(\()p Fl(Y)1064 808 y Fj(i)1088 796 y Fq(\))25 b(=)f(the)29 b(list)i Fl(u)1578 808 y Fj(ik)1663 796 y Fq(of)e(v)-5 b(alues\))0 949 y(e.g.,)29 b(if)h Fl(Y)311 962 y Fj(i)357 949 y Fq(=)24 b Fl(C)6 b(ampf)j(ir)r(e)p Fq(,)29 b(then)g Fl(u)1140 962 y Fj(ik)1225 949 y Fq(migh)n(t)f(b)r(e)0 1053 y Fp(h)p Fl(S)5 b(tor)r(m)24 b Fq(=)g Fl(T)7 b(;)14 b(B)t(usT)e(our)r(Gr)r(oup)26 b Fq(=)e Fl(F)12 b Fp(i)0 1207 y Fq(P)n(erform)27 b(gradien)n(t)i(ascen)n(t)g(b)n(y)g(rep)r (eatedly)16 1352 y(1.)21 b(up)r(date)29 b(all)i Fl(w)575 1365 y Fj(ij)s(k)687 1352 y Fq(using)e(training)i(data)e Fl(D)425 1553 y(w)487 1566 y Fj(ij)s(k)595 1553 y Fp( )24 b Fl(w)767 1566 y Fj(ij)s(k)869 1553 y Fq(+)19 b Fl(\021)1046 1503 y Ff(X)1015 1613 y Fj(d)p Fi(2)p Fj(D)1157 1495 y Fl(P)1212 1508 y Fj(h)1249 1495 y Fq(\()p Fl(y)1324 1508 y Fj(ij)1375 1495 y Fl(;)14 b(u)1462 1508 y Fj(ik)1518 1495 y Fp(j)p Fl(d)p Fq(\))p 1157 1532 464 2 v 1316 1612 a Fl(w)1378 1625 y Fj(ij)s(k)16 1771 y Fq(2.)21 b(then,)29 b(renormalize)g(the)g Fl(w)998 1784 y Fj(ij)s(k)1111 1771 y Fq(to)g(assure)131 1917 y Fp(\017)195 1874 y Ff(P)239 1929 y Fj(j)283 1917 y Fl(w)345 1929 y Fj(ij)s(k)453 1917 y Fq(=)24 b(1)131 2041 y Fp(\017)d Fq(0)j Fp(\024)g Fl(w)415 2054 y Fj(ij)s(k)522 2041 y Fp(\024)g Fq(1)0 2748 y Fo(165)334 b(lecture)17 b(slides)f(for)f(textb)q(o)q(ok)g Fn(Machine)h(L)n(e)n(arning)p Fo(,)c(T.)j(Mitc)o(hell,)h(McGra)o(w)e (Hill,)j(1997)p eop %%Page: 166 42 166 41 bop 25 160 a Fr(More)40 b(on)g(Learning)h(Ba)m(y)m(es)f(Nets) 1621 160 y 0.8666 0.03137 0.02352 setrgbcolor 1621 160 a 0 321 1947 2 v 0 474 a 0 0 0 setrgbcolor 0 474 a 64 x Fq(EM)28 b(algorithm)i(can)e(also)i(b)r(e)f(used.)38 b(Rep)r(eatedly)q(:)16 683 y(1.)21 b(Calculate)31 b(probabiliti)q(es)h (of)d(unobserv)n(ed)f(v)-5 b(ariables,)104 787 y(assuming)28 b Fl(h)16 933 y Fq(2.)21 b(Calculate)31 b(new)e Fl(w)725 945 y Fj(ij)s(k)837 933 y Fq(to)h(maximize)f Fl(E)5 b Fq([ln)14 b Fl(P)e Fq(\()p Fl(D)r Fp(j)p Fl(h)p Fq(\)])104 1036 y(where)29 b Fl(D)i 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Fq(using)c(observ)n(ed)e Fl(X)36 b Fq(and)28 b(curren)n(t)0 751 y(parameters)g Fl(h)g Fq(to)h(estimate)h Fl(Z)424 921 y(Q)p Fq(\()p Fl(h)575 885 y Fi(0)594 921 y Fp(j)p Fl(h)p Fq(\))24 b Fp( )g Fl(E)5 b Fq([ln)14 b Fl(P)e Fq(\()p Fl(Y)20 b Fp(j)p Fl(h)1257 885 y Fi(0)1275 921 y Fq(\))p Fp(j)p Fl(h;)15 b(X)7 b Fq(])0 1124 y(EM)28 b(Algorithm:)104 1282 y Fk(Estimation)k(\(E\))f(step:)38 b Fq(Calculate)31 b Fl(Q)p Fq(\()p Fl(h)1449 1251 y Fi(0)1467 1282 y Fp(j)p Fl(h)p Fq(\))e(using)f(the)104 1386 y(curren)n(t)f(h)n(yp)r(othesis)i Fl(h)f Fq(and)f(the)h(observ)n(ed)g(data)g Fl(X)34 b Fq(to)104 1490 y(estimate)c(the)f(probabilit)n(y)i(distribution)h(o)n (v)n(er)c Fl(Y)19 b Fq(.)476 1643 y Fl(Q)p Fq(\()p Fl(h)627 1608 y Fi(0)646 1643 y Fp(j)p Fl(h)p Fq(\))24 b Fp( )g Fl(E)5 b Fq([ln)14 b Fl(P)e Fq(\()p Fl(Y)20 b Fp(j)p Fl(h)1309 1608 y Fi(0)1327 1643 y Fq(\))p Fp(j)p Fl(h;)14 b(X)7 b Fq(])104 1818 y Fk(Maximization)32 b(\(M\))e(step:)38 b Fq(Replace)30 b(h)n(yp)r(othesis)f Fl(h)f Fq(b)n(y)104 1921 y(the)h(h)n(yp)r(othesis)h Fl(h)726 1890 y Fi(0)773 1921 y Fq(that)g(maximizes)f(this)h Fl(Q)104 2025 y Fq(function.)648 2129 y Fl(h)24 b Fp( )g Fq(argmax)946 2197 y Fj(h)980 2180 y Fc(0)1126 2129 y Fl(Q)p Fq(\()p Fl(h)1277 2093 y Fi(0)1296 2129 y Fp(j)p Fl(h)p Fq(\))0 2748 y Fo(174)334 b(lecture)17 b(slides)f(for)f(textb)q(o)q(ok)g Fn(Machine)h(L)n(e)n (arning)p Fo(,)c(T.)j(Mitc)o(hell,)h(McGra)o(w)e(Hill,)j(1997)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF