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199 /dotaccent 200 /dieresis 201 /onesuperior 202 /ring 203 /cedilla 204 /onequarter 205 /hungarumlaut 206 /ogonek 207 /caron 208 /emdash 209 /ccedilla 210 /copyright 211 /eacute 212 /ecircumflex 213 /edieresis 214 /egrave 215 /iacute 216 /icircumflex 217 /idieresis 218 /igrave 219 /logicalnot 220 /minus 221 /ntilde 222 /oacute 223 /ocircumflex 224 /odieresis 225 /AE 226 /onehalf 227 /ordfeminine 228 /ograve 229 /otilde 230 /registered 231 /scaron 232 /Lslash 233 /Oslash 234 /OE 235 /ordmasculine 236 /trademark 237 /uacute 238 /ucircumflex 239 /udieresis 240 /ugrave 241 /ae 242 /ydieresis 243 /zcaron 244 /Aacute 245 /dotlessi 246 /threequarters 247 /Eth 248 /lslash 249 /oslash 250 /oe 251 /germandbls 252 /multiply 253 /Yacute 254 /Thorn 255 /eth ] def /extended_Symbol [ ] def /extend_font { % stack: fontname newfontname E dup (ZapfDingbats) eq { cvn E cvn extended_Zapf ReencodeSmall } { dup (Symbol) eq { cvn E cvn extended_Symbol ReencodeSmall } { cvn E cvn extended_Standard 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currentmatrix pop [1 0 0 1 59.194 156.361] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m 0 0 m 0 ss (Times-Italic02400240) getfont () s 0.00 SG (ij1) s savemat setmatrix n savemat currentmatrix pop [1 0 0 1 106.556 156.361] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m 0 0 m 0 ss (Times-Italic02400240) getfont () s 0.00 SG (ijk) s savemat setmatrix n savemat currentmatrix pop [1 0 0 1 142 156.361] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m 0 0 m 0 ss (Times-Italic02400240) getfont () s 0.00 SG (ijn) s savemat setmatrix n savemat currentmatrix pop [1 0 0 1 55.611 155.333] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m 0 0 m 0 ss (Symbol03200320) getfont () s 0.00 SG (m) s savemat setmatrix n savemat currentmatrix pop [1 0 0 1 57.056 71.556] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m 0 0 m 0 ss (Symbol03200320) getfont () s 0.00 SG (m) s savemat setmatrix n savemat currentmatrix pop [1 0 0 1 103.417 71.556] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m 0 0 m 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Fm(\021)1643 766 y Fb(T)1643 789 y(i)1666 779 y Fm(x)p 1563 813 167 2 v 1563 830 a Fh(P)1607 873 y Fj(j)1632 861 y Fo(e)1651 842 y Fm(\021)1677 832 y Fb(T)1677 852 y(j)1700 842 y Fm(x)1972 822 y Fl(\()p Fq(4)p Fl(\))1025 933 y Fq(where)17 b Fm(\021)k Fl(=)g Fk(f)p Fm(\021)1289 943 y Fj(i)1303 933 y Fk(g)1324 918 y Fj(n)1324 944 y(i)p Fe(=)p Ff(1)1378 933 y Fq(.)34 b(Note)16 b(that)g(the)h(inner)f (product)f(can)j(be)1025 978 y(written)8 b(as)1327 1029 y Fm(\021)1354 1012 y Fj(T)1354 1040 y(i)1380 1029 y Fm(x)k Fl(=)g Fk(k)p Fm(\021)1510 1040 y Fj(i)1524 1029 y Fk(k)p Fl(\()1586 1001 y Fm(\021)1613 1011 y Fj(i)p 1566 1020 82 2 v 1566 1058 a Fk(k)p Fm(\021)1613 1068 y Fj(i)1627 1058 y Fk(k)1652 1029 y Fl(\))1668 1012 y Fj(T)1695 1029 y Fm(x)1025 1111 y Fq(showing)i(that)h(the)h (probability)d(depends)i(both)g(on)g(the)h(distance)1025 1157 y(of)h(the)g(input)f(vector)i(from)f(the)h(plane)f(orthogonal)f (to)h(the)g(unit)1025 1202 y(vector)11 b Fm(\021)1166 1212 y Fj(i)1180 1202 y Fo(=)p 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b(EFFICIENCY)1025 1828 y Fq(T)m(o)16 b(assess)h(the)f(ef)o(\256ciency)h (of)f(the)f(EM)i(approach)f(to)f(parameter)1025 1874 y(estimation)i(in)g(decision)h(trees,)j(Jordan)d(and)g(Jacobs)h (studied)f(a)1025 1919 y(lar)o(ge)13 b(scale)h(regression)e(problem)g (involving)e(12)j(input)e(variables)1025 1965 y(and)d(15,000)g(data)g (points.)13 b(The)c(tree)g(was)g(a)g(binary)f(tree)g(with)f(linear)1025 2011 y(decision)g(boundaries)g(and)h(linear)f(leaf)h(models.)15 b(The)8 b(tree)g(had)g(four)1025 2056 y(levels)13 b(and)h(a)g(total)e (of)h(1,012)g(parameters.)26 b(Figure)13 b(6)h(shows)f(the)1025 2102 y(conver)o(gence)e(of)f(the)g(relative)g(error)g(on)f(the)i(test)f (set)g(as)h(a)g(function)1025 2148 y(of)j(the)i(iterations)d(through)h (the)h(training)e(set.)31 b(As)15 b(can)h(be)g(seen,)1025 2193 y(the)e(algorithm)f(conver)o(ges)j(rapidly)m(,)f(approximately)e (two)h(orders)1025 2239 y(of)j(magnitude)h(faster)h(than)f (backpropagation)f(in)g(a)i(multilayer)1025 2285 y(perceptron)9 b(with)h(a)g(comparable)h(number)g(of)f(parameters.)1903 2270 y Ff(5)1025 2355 y Fq(Jordan)j(and)h(Xu)g(\(1993\))e(have)i (studied)f(the)h(conver)o(gence)h(of)e(the)1025 2401 y(EM)7 b(algorithm)f(for)g(probabilistic)f(decision)h(trees)i(and)f (have)h(shown)1025 2447 y(that)g(the)h(algorithm)e(conver)o(ges)j (according)f(to)f(a)i(geometric)f(series,)1025 2492 y(with)h(a)j(rate)f (that)g(is)f(a)i(function)d(of)i(the)g(condition)e(number)i(of)f(the) 1025 2538 y(matrix)k Fl(\()p Fo(P)1202 2512 y Fa(1)p 1202 2517 11 2 v 1202 2533 a(2)1220 2538 y Fl(\))1236 2523 y Fj(T)1262 2538 y Fo(H)s Fl(\()p Fm(\036)p Fl(\)\()p Fo(P)1415 2512 y Fa(1)p 1415 2517 V 1415 2533 a(2)1433 2538 y Fl(\))p Fq(,)j(where)e Fo(P)22 b Fq(is)15 b(a)i(covariance)g (matrix)1025 2584 y(and)10 b Fo(H)j Fq(is)d(the)g(Hessian)h(of)f(the)g (log)g(likelihood.)p 1025 2615 250 2 v 1077 2643 a Fd(5)1092 2658 y Fc(The)e(\256nal)g(relative)g(errors)h(were)g(.09)f(for)h(the)g (multilayer)g(perceptron,)1025 2700 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3 3 j 3 2 j 3 3 j 3 3 j 3 2 j 3 3 j 2 2 j 3 3 j 3 2 j 3 3 j 2 3 j 3 2 j 3 3 j 2 2 j 3 3 j 2 2 j 3 3 j 3 2 j 2 3 j 3 2 j 2 3 j 3 2 j 2 3 j 3 2 j 2 2 j 3 3 j 2 2 j 3 3 j 2 2 j 2 3 j 3 2 j 2 2 j 2 3 j 3 2 j 2 2 j 2 3 j 3 2 j 2 2 j 2 3 j 2 2 j 3 2 j 2 2 j 2 3 j 2 2 j 2 2 j 3 2 j 2 3 j 2 2 j 2 2 j 2 2 j 2 2 j 2 3 j 2 2 j 2 2 j 2 2 j 3 2 j 2 2 j 2 2 j 2 2 j 2 2 j 2 3 j 2 2 j 2 2 j 2 2 j 1 2 j 2 2 j 2 2 j 2 2 j 2 2 j 2 2 j 2 1 j 2 2 j 2 2 j 2 2 j 1 2 j 2 2 j 2 2 j 2 2 j 2 2 j 2 1 j 1 2 j 2 2 j 2 2 j 2 2 j 2 2 j 1 1 j 2 2 j 2 2 j 2 2 j 1 1 j 2 2 j 2 2 j 1 1 j 2 2 j 2 2 j 1 1 j 2 2 j 2 2 j 1 1 j 2 2 j 2 2 j 1 1 j 2 2 j 2 2 j 1 1 j 2 2 j 1 1 j 2 2 j 2 1 j 1 2 j 2 1 j 1 2 j 2 2 j 2 1 j 1 2 j 2 1 j 1 2 j 2 1 j 1 1 j 2 2 j 1 1 j 2 2 j 1 1 j 2 2 j 1 1 j 2 2 j 1 1 j 2 1 j 1 2 j 2 1 j 1 2 j 2 1 j 1 1 j 1 2 j 2 1 j 1 2 j 2 1 j 1 1 j 2 2 j 1 1 j 1 1 j 2 2 j 1 1 j 1 1 j 2 2 j 1 1 j 2 1 j 1 2 j 1 1 j 2 1 j 1 1 j 1 2 j 2 1 j 1 1 j 1 2 j 2 1 j 1 1 j 1 1 j 2 2 j 1 1 j 1 1 j 2 1 j 1 2 j 1 1 j 1 1 j 2 1 j 1 2 j 1 1 j 2 1 j 1 1 j 1 2 j 1 1 j 2 1 j 1 1 j 1 2 j 1 1 j 2 1 j 1 1 j 1 1 j 1 2 j 1 1 j 2 1 j 1 1 j 1 1 j 1 2 j 2 1 j 1 1 j 1 1 j 1 2 j 1 1 j 1 1 j 2 1 j 1 1 j 1 1 j 1 2 j 1 1 j 2 1 j 1 1 j 1 1 j 1 2 j 1 1 j 1 1 j 1 1 j 2 1 j 1 2 j 1 1 j 1 1 j 1 1 j 1 1 j 1 1 j 1 2 j 1 1 j 2 1 j 1 1 j 1 1 j 1 2 j 1 1 j 1 1 j 1 1 j 1 1 j 1 1 j 1 2 j 1 1 j 2 1 j 1 1 j 1 1 j 1 1 j 1 2 j 1 1 j 1 1 j 1 1 j 1 1 j 1 1 j 1 2 j 1 1 j 1 1 j 1 1 j 1 1 j 1 1 j 1 2 j 1 1 j 1 1 j 1 1 j 1 1 j 1 2 j 1 1 j 1 1 j 1 1 j 1 1 j 1 1 j 1 2 j 1 1 j 1 1 j 1 1 j 1 1 j 1 1 j 1 2 j 1 1 j 1 1 j 1 1 j 1 1 j 1 1 j 1 2 j 1 1 j 1 1 j 1 1 j 1 1 j 1 1 j 1 2 j 1 1 j 1 1 j 1 1 j 1 1 j 1 1 j 1 2 j 0 1 j 1 1 j 1 1 j 1 1 j 1 1 j 1 2 j 1 1 j 1 1 j 1 1 j 1 1 j 1 1 j 1 2 j 0 1 j 1 1 j 1 1 j 1 1 j 1 1 j 1 2 j 1 1 j 1 1 j 1 1 j 1 1 j 0 1 j 1 2 j 1 1 j 1 1 j 1 1 j 1 1 j 1 1 j 1 2 j 0 1 j 1 1 j 1 1 j 1 1 j 1 1 j 1 2 j 1 1 j 0 1 j 1 1 j 1 1 j 1 1 j 1 2 j 1 1 j 1 1 j 0 1 j 1 1 j 1 1 j 1 1 j 1 2 j 1 1 j 0 1 j 1 1 j 1 1 j 1 1 j 1 2 j 1 1 j 0 1 j 1 1 j 1 1 j 1 1 j 1 1 j 0 2 j 1 1 j 1 1 j 1 1 j 1 1 j 0 1 j 1 1 j 1 2 j 1 1 j 1 1 j 0 1 j 1 1 j 1 1 j 1 1 j 1 2 j 0 1 j 1 1 j 1 1 j 1 1 j 1 1 j 0 1 j 1 1 j 1 2 j 1 1 j 0 1 j 1 1 j 1 1 j 1 1 j 1 1 j 0 1 j 1 2 j 1 1 j 1 1 j 0 1 j stroke % to avoid limitcheck 4053 3222 M 1 1 j 1 1 j 1 1 j 0 1 j 1 2 j 1 1 j 1 1 j 0 1 j 1 1 j 1 1 j 1 1 j 0 1 j 1 1 j 1 2 j 0 1 j 1 1 j 1 1 j 1 1 j 0 1 j 1 1 j 1 1 j 1 1 j 0 1 j 1 1 j 1 2 j 0 1 j 1 1 j 1 1 j 1 1 j 0 1 j 1 1 j 1 1 j 0 1 j 1 1 j 1 1 j 1 1 j 0 2 j 1 1 j 1 1 j 0 1 j 1 1 j 1 1 j 1 1 j 0 1 j 1 1 j 1 1 j 0 1 j 1 1 j 1 1 j 0 1 j 1 1 j 1 1 j 0 2 j 1 1 j 1 1 j 0 1 j 1 1 j 1 1 j 1 1 j 0 1 j 1 1 j 1 1 j 0 1 j 1 1 j 1 1 j 0 1 j 1 1 j 1 1 j 0 1 j 1 1 j 1 1 j 0 1 j 1 1 j 1 1 j 0 1 j 1 1 j 1 1 j 0 1 j 1 1 j 0 1 j 1 1 j 1 1 j 0 1 j 1 1 j 1 1 j 0 1 j 1 1 j 1 1 j 0 1 j 1 1 j 1 1 j 0 1 j 1 1 j 0 1 j 1 1 j 1 1 j 0 1 j 1 1 j 1 1 j 0 1 j 1 1 j 1 1 j 0 1 j 1 1 j 0 1 j 1 1 j 1 1 j 0 1 j 1 1 j 1 1 j 0 1 j 1 1 j 0 1 j 1 1 j 1 1 j 0 1 j 1 1 j 0 1 j 1 1 j 1 1 j 0 1 j 1 0 h 1 1 j 0 1 j 1 1 j 0 1 j 1 1 j 1 1 j 0 1 j 1 1 j 0 1 j 1 1 j 1 1 j 0 1 j 1 1 j 0 1 j 1 0 h 1 1 j 0 1 j 1 1 j 0 1 j 1 1 j 0 1 j 1 1 j 1 1 j 0 1 j 1 1 j 0 1 j 1 0 h 1 1 j 0 1 j 1 1 j 0 1 j 1 1 j 0 1 j 1 1 j 1 1 j 0 1 j 1 0 h 0 1 j 1 1 j 0 1 j 1 1 j 1 1 j 0 1 j 1 1 j 1 1 j 0 1 j 1 1 j 1 1 j 0 1 j 1 1 j 0 1 j 1 0 h 0 1 j 1 1 j 1 1 j 0 1 j 1 1 j 0 1 j 1 0 h 0 1 j 1 1 j 0 1 j 1 1 j 1 1 j 1 1 j 0 1 j 1 1 j 0 1 j 1 1 j 0 1 j 1 0 h 0 1 j 1 1 j 1 1 j 0 1 j 1 0 h 0 1 j 1 1 j 0 1 j 1 1 j 0 1 j 1 0 h 0 1 j 1 1 j 0 1 j 1 1 j 1 0 h 0 1 j 1 1 j 0 1 j 1 1 j 1 1 j 0 1 j 1 1 j 0 1 j 1 0 h 0 1 j 1 1 j 0 1 j 1 1 j 1 1 j 0 1 j 1 1 j 0 1 j 1 0 h 1 1 j 0 1 j 1 1 j 1 1 j 0 1 j 1 1 j 1 1 j 0 1 j 1 1 j 0 1 j 1 0 h 0 1 j 1 1 j 0 1 j 1 0 h 0 1 j 1 1 j 0 1 j 1 0 h 0 1 j 1 1 j 0 1 j 1 0 h 0 1 j 1 1 j 1 1 j 0 1 j 1 1 j 1 1 j 0 1 j 1 1 j 1 1 j 0 1 j 1 0 h 0 1 j 1 1 j 0 1 j 1 0 h 0 1 j 1 1 j 1 1 j 0 1 j 1 1 j 1 1 j 0 1 j 1 1 j 0 1 j 1 0 h 0 1 j 1 1 j 0 1 j 1 0 h 0 1 j 1 1 j 1 1 j 0 1 j 1 0 h 0 1 j 1 1 j 1 1 j 0 1 j 1 0 h 0 1 j 0 1 j 1 0 h 0 1 j 1 1 j 1 1 j 0 1 j 1 0 h 0 1 j 1 1 j 1 1 j 0 1 j 1 0 h 0 1 j 0 1 j 1 0 h 0 1 j 1 0 h 0 1 j 1 1 j 1 1 j 0 1 j 1 0 h 0 1 j 0 1 j 1 0 h 0 1 j 1 0 h 0 1 j 1 1 j 1 1 j 1 1 j 0 1 j 1 1 j 0 1 j 1 0 h 0 1 j 1 0 h 0 1 j 1 1 j 0 1 j 1 0 h 0 1 j 1 1 j 1 1 j 1 1 j 0 1 j 1 1 j 1 1 j 1 1 j 0 1 j 1 0 h 0 1 j 1 1 j 1 1 j 0 1 j 1 0 h 0 1 j 1 1 j 1 1 j 1 1 j 0 1 j 1 1 j 1 1 j 1 1 j 0 1 j 1 0 h 0 1 j 1 0 h 0 1 j 1 1 j 0 1 j 1 0 h 0 1 j 1 0 h 0 1 j 1 1 j 1 1 j 1 1 j 0 1 j 1 0 h 0 1 j 1 0 h 0 1 j 1 1 j 1 1 j 1 1 j 0 1 j 1 0 h 0 1 j 1 0 h 0 1 j 1 1 j 1 1 j 0 1 j 1 0 h 0 1 j 1 0 h 0 1 j 1 0 h 0 1 j 1 0 h 0 1 j 1 0 h 0 1 j 1 1 j 1 1 j 0 1 j 1 0 h 0 1 j 1 0 h 0 1 j 1 0 h 0 1 j 1 1 j 1 0 h 0 1 j 1 1 j 1 1 j 1 1 j 1 1 j 0 1 j 1 0 h 1 1 j 0 1 j 1 0 h 0 1 j 1 0 h 0 1 j 1 0 h 0 1 j 1 0 h 0 1 j 1 0 h 0 1 j 1 0 h 0 1 j 1 0 h 0 1 j 1 0 h 0 1 j 1 0 h 0 1 j 1 0 h 0 1 j 1 0 h 0 1 j 1 0 h 0 1 j 1 0 h 0 1 j 1 0 h 0 1 j 1 0 h 0 1 j 1 0 h 0 1 j 1 0 h 0 1 j 1 0 h 0 1 j 1 0 h 1 1 j 1 1 j 1 1 j 1 0 h 0 1 j 1 0 h 0 1 j 1 0 h 0 1 j 1 0 h 0 1 j 1 0 h 0 1 j 1 0 h 1 1 j 1 1 j 1 1 j 1 0 h 0 1 j 1 0 h 0 1 j 1 0 h 0 1 j 1 0 h 1 1 j 1 1 j 1 0 h 0 1 j 1 0 h 1 1 j 1 1 j 1 0 h 0 1 j 1 0 h 0 1 j 1 0 h 1 1 j 1 0 h 0 1 j 1 0 h 1 1 j 1 0 h 0 1 j 1 0 h 0 1 j 1 0 h 1 0 h 0 1 j 1 0 h stroke % to avoid limitcheck 4359 2811 M 0 1 j 1 0 h 1 0 h 0 1 j 1 0 h 0 1 j 1 0 h 1 0 h 0 1 j 1 0 h 1 1 j 1 0 h 0 1 j 1 0 h 1 0 h 0 1 j 1 0 h 1 1 j 1 0 h 0 1 j 1 0 h 1 0 h 0 1 j 1 0 h 1 1 j 1 0 h 1 1 j 1 0 h 1 1 j 1 0 h 1 1 j 1 0 h 0 1 j 1 0 h 1 0 h 0 1 j 1 0 h 1 0 h 1 1 j 1 0 h 1 1 j 1 0 h 1 0 h 0 1 j 1 0 h 1 0 h 0 1 j 1 0 h 1 0 h 1 0 h 0 1 j 1 0 h 1 0 h 0 1 j 1 0 h 1 0 h 1 1 j 1 0 h 1 0 h 0 1 j 1 0 h 1 0 h 1 0 h 0 1 j 1 0 h 1 0 h 1 0 h 0 1 j 1 0 h 1 0 h 1 0 h 0 1 j 1 0 h 1 0 h 1 0 h 1 1 j 1 0 h 1 0 h 1 0 h 0 1 j 1 0 h 1 0 h 1 0 h 1 1 j 1 0 h 1 0 h 1 0 h 1 0 h 1 0 h 1 0 h 1 0 h 1 0 h 1 0 h 1 0 h 1 0 h 1 0 h 1 0 h 1 0 h 1 0 h 1 0 h 1 0 h 1 0 h 1 0 h 1 0 h 1 0 h 1 0 h 1 0 h 1 0 h 0 1 h 1 0 h 1 0 h 1 0 h 1 0 h 1 0 h 1 0 h 1 0 h 1 0 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6.021 90 141.31 124.18 el 1 Fbw gsave 0 0.352 0 Bbw grestore 6.021 6.021 0 99.972 40.486 el 1 Fbw gsave 0 0.352 0 Bbw grestore 6.021 6.021 0 59.194 82.403 el 1 Fbw gsave 0 0.352 0 Bbw grestore 6.021 6.021 0 141.31 82.403 el 1 Fbw gsave 0 0.352 0 Bbw grestore 6.021 6.021 0 99.972 82.403 el 1 Fbw gsave 0 0.352 0 Bbw grestore n 99.833 16.722 m 99.833 34.444 l 1 Fbw n 99.833 34.444 m 98.648 30.888 l 101.02 30.888 l cl 0 Fbw n 99.833 16.722 m 99.833 30.888 l gsave 0 0.352 0 Bbw grestore n savemat currentmatrix pop [1 0 0 1 98.389 12.222] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m 0 0 m 0 ss (Times-BoldItalic03600360) getfont () s 0.00 SG (x) s savemat setmatrix n 99.75 128.17 m 99.75 160.86 l 1 Fbw n 99.75 160.86 m 98.565 157.3 l 100.94 157.3 l cl 0 Fbw n 99.75 128.17 m 99.75 157.3 l gsave 0 0.352 0 Bbw grestore n 97.917 130 m 60.028 160.86 l 1 Fbw n 60.028 160.86 m 62.037 157.7 l 63.534 159.53 l cl 0 Fbw n 97.917 130 m 62.785 158.62 l gsave 0 0.352 0 Bbw grestore n 101.81 129.92 m 139.69 160.78 l 1 Fbw n 139.69 160.78 m 136.19 159.45 l 137.69 157.61 l cl 0 Fbw n 101.81 129.92 m 136.94 158.53 l gsave 0 0.352 0 Bbw grestore n 99.75 175.83 m 99.75 193.56 l 1 Fbw n 99.75 193.56 m 98.565 190 l 100.94 190 l cl 0 Fbw n 99.75 175.83 m 99.75 190 l gsave 0 0.352 0 Bbw grestore n 86.167 161.03 m 113.06 161.03 l 113.06 176.31 l 86.167 176.31 l cl 1 Fbw gsave 0 0.352 0 Bbw grestore n savemat currentmatrix pop [1 0 0 1 96.556 170.194] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m 0 0 m 0 ss (Symbol03200320) getfont () s 0.00 SG (q) s savemat setmatrix n savemat currentmatrix pop [1 0 0 1 98.389 200.75] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m 0 0 m 0 ss (Times-BoldItalic03600360) getfont () s 0.00 SG (y) s savemat setmatrix 6.021 6.021 90 99.889 124.74 el 1 Fbw gsave 0 0.352 0 Bbw grestore n 141.83 175.75 m 141.83 193.47 l 1 Fbw n 141.83 193.47 m 140.65 189.92 l 143.02 189.92 l cl 0 Fbw n 141.83 175.75 m 141.83 189.92 l gsave 0 0.352 0 Bbw grestore n 128.25 160.94 m 155.14 160.94 l 155.14 176.22 l 128.25 176.22 l cl 1 Fbw gsave 0 0.352 0 Bbw grestore n savemat currentmatrix pop [1 0 0 1 140.472 200.667] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m 0 0 m 0 ss (Times-BoldItalic03600360) getfont () s 0.00 SG (y) s savemat setmatrix n 57.111 175.67 m 57.111 193.39 l 1 Fbw n 57.111 193.39 m 55.926 189.83 l 58.296 189.83 l cl 0 Fbw n 57.111 175.67 m 57.111 189.83 l gsave 0 0.352 0 Bbw grestore n 43.528 160.86 m 70.417 160.86 l 70.417 176.14 l 43.528 176.14 l cl 1 Fbw gsave 0 0.352 0 Bbw grestore n savemat currentmatrix pop [1 0 0 1 55.75 200.583] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m 0 0 m 0 ss (Times-BoldItalic03600360) getfont () s 0.00 SG (y) s savemat setmatrix n savemat currentmatrix pop [1 0 0 1 138.333 170.194] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m 0 0 m 0 ss (Symbol03200320) getfont () s 0.00 SG (q) s savemat setmatrix n savemat currentmatrix pop [1 0 0 1 52.694 170.194] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m 0 0 m 0 ss (Symbol03200320) getfont () s 0.00 SG (q) s savemat setmatrix n savemat currentmatrix pop [1 0 0 1 55.917 170.5] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m 0 0 m 0 ss (Times-Italic02400240) getfont () s 0.00 SG (ij1) s savemat setmatrix n savemat currentmatrix pop [1 0 0 1 99.611 170.5] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m 0 0 m 0 ss (Times-Italic02400240) getfont () s 0.00 SG (ijk) s savemat setmatrix n savemat currentmatrix pop [1 0 0 1 141.472 170.5] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m 0 0 m 0 ss (Times-Italic02400240) getfont () s 0.00 SG (ijn) s savemat setmatrix n savemat currentmatrix pop [1 0 0 1 57.5552 151.888] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m 0 0 m 0 ss (Symbol03200320) getfont () s 0.00 SG (w) s savemat setmatrix n savemat currentmatrix pop [1 0 0 1 56.5276 69.9713] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m 0 0 m 0 ss (Symbol03200320) getfont () s 0.00 SG (w) s savemat setmatrix n savemat currentmatrix pop [1 0 0 1 60.4166 71.4163] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m 0 0 m 0 ss (Times-Italic02400240) getfont () s 0.00 SG (1) s savemat setmatrix n savemat currentmatrix pop [1 0 0 1 90.0557 68.138] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m 0 0 m 0 ss (Symbol03200320) getfont () s 0.00 SG (w) s savemat setmatrix n savemat currentmatrix pop [1 0 0 1 94.0277 69.583] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m 0 0 m 0 ss (Times-Italic02400240) getfont () s 0.00 SG (i) s savemat setmatrix n savemat currentmatrix pop [1 0 0 1 106.472 60.4991] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m 0 0 m 0 ss (Symbol03200320) getfont () s 0.00 SG (w) s savemat setmatrix n savemat currentmatrix pop [1 0 0 1 110.222 61.9441] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m 0 0 m 0 ss (Times-Italic02400240) getfont () s 0.00 SG (n) s savemat setmatrix n savemat currentmatrix pop [1 0 0 1 56.8888 111.195] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m 0 0 m 0 ss (Symbol03200320) getfont () s 0.00 SG (w) s savemat setmatrix n savemat currentmatrix pop [1 0 0 1 61.0278 112.056] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m 0 0 m 0 ss (Times-Italic02400240) getfont () s 0.00 SG (i1) s savemat setmatrix n savemat currentmatrix pop [1 0 0 1 106.222 102.028] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m 0 0 m 0 ss (Symbol03200320) getfont () s 0.00 SG (w) s savemat setmatrix n savemat currentmatrix pop [1 0 0 1 110.528 102.889] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m 0 0 m 0 ss (Times-Italic02400240) getfont () s 0.00 SG (in) s savemat setmatrix n savemat currentmatrix pop [1 0 0 1 89.1946 109.056] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m 0 0 m 0 ss (Symbol03200320) getfont () s 0.00 SG (w) s savemat setmatrix n savemat currentmatrix pop [1 0 0 1 93.4166 109.917] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m 0 0 m 0 ss (Times-Italic02400240) getfont () s 0.00 SG (ij) s savemat setmatrix n savemat currentmatrix pop [1 0 0 1 61.6392 153.305] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m 0 0 m 0 ss (Times-Italic02400240) getfont () s 0.00 SG (ij1) s savemat setmatrix n savemat currentmatrix pop [1 0 0 1 88.0273 150.666] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m 0 0 m 0 ss (Symbol03200320) getfont () s 0.00 SG (w) s savemat setmatrix n savemat currentmatrix pop [1 0 0 1 91.8893 152.083] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m 0 0 m 0 ss (Times-Italic02400240) getfont () s 0.00 SG (ijk) s savemat setmatrix n savemat currentmatrix pop [1 0 0 1 105.361 142.416] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m 0 0 m 0 ss (Symbol03200320) getfont () s 0.00 SG (w) s savemat setmatrix n savemat currentmatrix pop [1 0 0 1 109.611 143.833] concat 25.4 1440 div 1.000000 mul dup scale 0 0 m 0 0 m 0 ss (Times-Italic02400240) getfont () s 0.00 SG (ijn) s savemat setmatrix n 37.889 98.083 m 37.889 98.083 81.889 113.36 99.611 111.83 c gsave 0 0.176 0 Bbw grestore 6.9683 2.4284 126.9 47.889 102.74 el 1 Fbw gsave 0 0.176 0 Bbw grestore 6.9683 2.4284 53.104 38.639 102.96 el 1 Fbw gsave 0 0.176 0 Bbw grestore 6.9683 2.4284 176.99 42.917 95.625 el 1 Fbw gsave 0 0.176 0 Bbw grestore 5.0106 5.0106 0 33.406 96.448 el 1 Fbw gsave 0 0.352 0 Bbw grestore 5.0106 5.0106 0 52.573 96.142 el 1 Fbw gsave 0 0.352 0 Bbw grestore 5.0106 5.0106 0 43.017 109.5 el 1 Fbw gsave 0 0.352 0 Bbw grestore n 43.306 93.417 m 47.278 94.028 l 1 Fbw n 47.278 94.028 m 44.132 94.565 l 44.438 92.57 l cl 0 Fbw n 43.306 93.417 m 44.285 93.567 l gsave 0 0.176 0 Bbw grestore n 42.611 98.222 m 38.639 97.611 l 1 Fbw n 38.639 97.611 m 41.785 97.074 l 41.478 99.069 l cl 0 Fbw n 42.611 98.222 m 41.632 98.072 l gsave 0 0.176 0 Bbw grestore n 37.333 105.17 m 35.194 101.81 l 1 Fbw n 35.194 101.81 m 37.672 103.82 l 35.969 104.9 l cl 0 Fbw n 37.333 105.17 m 36.82 104.36 l gsave 0 0.176 0 Bbw grestore n 40.306 101.11 m 42.444 104.47 l 1 Fbw n 42.444 104.47 m 39.967 102.46 l 41.67 101.38 l cl 0 Fbw n 40.306 101.11 m 40.819 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90 43.239 151.28 el 1 Fbw gsave 0 0.352 0 Bbw grestore n 43.528 135.19 m 47.5 135.81 l 1 Fbw n 47.5 135.81 m 44.354 136.34 l 44.661 134.35 l cl 0 Fbw n 43.528 135.19 m 44.507 135.35 l gsave 0 0.176 0 Bbw grestore n 42.833 140 m 38.861 139.39 l 1 Fbw n 38.861 139.39 m 42.007 138.85 l 41.7 140.85 l cl 0 Fbw n 42.833 140 m 41.854 139.85 l gsave 0 0.176 0 Bbw grestore n 37.556 146.94 m 35.417 143.58 l 1 Fbw n 35.417 143.58 m 37.894 145.6 l 36.191 146.68 l cl 0 Fbw n 37.556 146.94 m 37.042 146.14 l gsave 0 0.176 0 Bbw grestore n 40.528 142.89 m 42.667 146.25 l 1 Fbw n 42.667 146.25 m 40.189 144.24 l 41.893 143.15 l cl 0 Fbw n 40.528 142.89 m 41.041 143.7 l gsave 0 0.176 0 Bbw grestore n 50.917 144.72 m 47.556 148.39 l 1 Fbw n 47.556 148.39 m 48.858 145.47 l 50.346 146.84 l cl 0 Fbw n 50.917 144.72 m 49.602 146.16 l gsave 0 0.176 0 Bbw grestore n 45.333 144.03 m 48.694 140.36 l 1 Fbw n 48.694 140.36 m 47.392 143.28 l 45.904 141.91 l cl 0 Fbw n 45.333 144.03 m 46.648 142.59 l gsave 0 0.176 0 Bbw grestore n 57.361 138.33 m 57.361 138.33 75.694 145.67 121.83 145.67 c gsave 0 0.176 0 Bbw grestore n 47.889 151.47 m 47.889 151.47 57.056 155.44 65.917 155.75 c gsave 0 0.176 0 Bbw grestore n 37.806 57.056 m 37.806 57.056 81.806 72.333 99.528 70.806 c gsave 0 0.176 0 Bbw grestore 6.9683 2.4284 126.9 47.806 61.708 el 1 Fbw gsave 0 0.176 0 Bbw grestore 6.9683 2.4284 53.104 38.556 61.931 el 1 Fbw gsave 0 0.176 0 Bbw grestore 6.9683 2.4284 176.99 42.833 54.597 el 1 Fbw gsave 0 0.176 0 Bbw grestore 5.0106 5.0106 90 33.323 55.42 el 1 Fbw gsave 0 0.352 0 Bbw grestore 5.0106 5.0106 0 52.489 55.115 el 1 Fbw gsave 0 0.352 0 Bbw grestore 5.0106 5.0106 0 42.934 68.476 el 1 Fbw gsave 0 0.352 0 Bbw grestore n 43.222 52.389 m 47.194 53 l 1 Fbw n 47.194 53 m 44.048 53.537 l 44.355 51.542 l cl 0 Fbw n 43.222 52.389 m 44.202 52.54 l gsave 0 0.176 0 Bbw grestore n 42.528 57.194 m 38.556 56.583 l 1 Fbw n 38.556 56.583 m 41.702 56.046 l 41.395 58.041 l cl 0 Fbw n 42.528 57.194 m 41.548 57.044 l gsave 0 0.176 0 Bbw grestore n 37.25 64.139 m 35.111 60.778 l 1 Fbw n 35.111 60.778 m 37.588 62.79 l 35.885 63.874 l cl 0 Fbw n 37.25 64.139 m 36.737 63.332 l gsave 0 0.176 0 Bbw grestore n 40.222 60.083 m 42.361 63.444 l 1 Fbw n 42.361 63.444 m 39.884 61.432 l 41.587 60.348 l cl 0 Fbw n 40.222 60.083 m 40.735 60.89 l gsave 0 0.176 0 Bbw grestore n 50.611 61.917 m 47.25 65.583 l 1 Fbw n 47.25 65.583 m 48.552 62.669 l 50.04 64.033 l cl 0 Fbw n 50.611 61.917 m 49.296 63.351 l gsave 0 0.176 0 Bbw grestore n 45.028 61.222 m 48.389 57.556 l 1 Fbw n 48.389 57.556 m 47.087 60.47 l 45.599 59.106 l cl 0 Fbw n 45.028 61.222 m 46.343 59.788 l gsave 0 0.176 0 Bbw grestore n 57.056 55.528 m 57.056 55.528 75.389 62.861 121.53 62.861 c gsave 0 0.176 0 Bbw grestore n 47.583 68.667 m 47.583 68.667 56.75 72.639 65.611 72.944 c gsave 0 0.176 0 Bbw grestore userdict /#copies 1 put showpage grestore end restore %%EndDocument endTexFig -75 1150 a Fq(Figure)11 b(7:)18 b(A)11 b(hidden)g(Markov)h(decision)f 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