Terrence Fine - Academia.edu (original) (raw)

Papers by Terrence Fine

Proceedings. IEEE International Symposium on Information Theory, 1993

Proceedings of 1995 IEEE International Symposium on Information Theory, 1995

We address the question of how many training samples are required to ensure that the performance ... more We address the question of how many training samples are required to ensure that the performance of a neural network of given complexity on its training data matches that obtained when fresh data is applied to the network. This desirable property may be termed 'reliable generalization.' Well-known results of Vapnik give conditions on the number of training samples sufficient for reliable generalization, but these are higher by orders of magnitude than practice indicates; other results in the mathematical literature involve unknown constants and are useless for our purposes.

Applied Optics

A number of binary cyclic coding schemes for multiplex spectrometry are discussed and evaluated i... more A number of binary cyclic coding schemes for multiplex spectrometry are discussed and evaluated in terms of a linear, least mean square, unbiased estimate. The optical realization of such codes in dispersion instruments is briefly discussed. We show that there are many advantages both in the construction of the instrument and in its operation which accrue from cyclic codes.

This paper is concerned with an environment consisting of N periodic radars, each emitting a peri... more This paper is concerned with an environment consisting of N periodic radars, each emitting a periodic pulse train. The number of radars and their periodicities are assumed known but the epoch of each pulse train is a random variable with a uniform distribution.

The Annals of Mathematical Statistics, 1966

2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)., 2003

... Chin-Jen Ku, Terrence L. Fine ... It is well known from probability theory that two scalar ra... more ... Chin-Jen Ku, Terrence L. Fine ... It is well known from probability theory that two scalar ran-dom variables X1, XZ are statistically independent if and only if f(X1) and g(X2) remain uncorrelated for all f and g ranging over a separating class of functions [7]. Hence, we may define a ...

... top of page ABSTRACT. An abstract is not available. top of page AUTHORS. Jen-Lun Yuan No cont... more ... top of page ABSTRACT. An abstract is not available. top of page AUTHORS. Jen-Lun Yuan No contact information provided yet. Bibliometrics: publication history Publication years, 1992-1992. Publication count, 1. Citation Count, 1. Available for download, 0.

=1 2 0 =1 w ν w w ν w w . network complexity training set size statistical performance unknown

We adopt the same mathematical model of a set M of probability measures as is central to the theo... more We adopt the same mathematical model of a set M of probability measures as is central to the theory of coherent imprecise probability. However, we endow this model with an objective, frequentist interpretation in place of a behavioral subjective one. We seek to use M to model stable physical sources of time series data that have highly irregular behavior and not to model states of belief or knowledge that are assuredly imprecise. The ap- proach we present in this paper is to understand a set of measures model M not as a traditional compound hypothesis, in which one of the measures in M is a true description, but rather as one in which none of the individual measures in M provides an adequate description of the potential behavior of the physical source as actualized in the form of a long time series. We provide an instrumental interpretation of random process measures consistent with M and the highly irregular physical phenomena we intend to model by M. This construction provides us ...

We propose a new definition for conditioning in the Chaotic Probability framework that in-cludes ... more We propose a new definition for conditioning in the Chaotic Probability framework that in-cludes as a special case the conditional ap-proach of Fierens 2003 [2] and can be given the interpretation of a generalized Markov chain. Chaotic Probabilities were introduced by Fine et al. as an attempt to model chance phenomena with a usual set of measures M endowed with an objective, frequentist inter-pretation instead of a compound hypothesis or behavioral subjective one. We follow the presentation of the univariate case chaotic probability model and provide an instrumen-tal interpretation of random process mea-sures consistent with a conditional chaotic probability source, which can be used as a tool for simulation of our model. Given a fi-nite time series, we also present a universal method for estimation of conditional chaotic probability models that is based on the anal-ysis of the relative frequencies taken along a set of subsequences chosen by a given set of rules.

A Chaotic Probability model is a usual set of proba- bility measures, M, the totality of which is... more A Chaotic Probability model is a usual set of proba- bility measures, M, the totality of which is endowed with an objective, frequentist interpretation as op- posed to being viewed as a statistical compound hy- pothesis or an imprecise behavioral subjective one. In the prior work of Fierens and Fine, given finite time series data, the estimation of the Chaotic Probability model is based on the analysis of a set of relative fre- quencies of events taken along a set of subsequences selected by a set of rules. Fierens and Fine proved the existence of families of causal subsequence selec- tion rules that can make M visible, but they did not provide a methodology for finding such family. This paper provides a universal methodology for finding a family of subsequences that can make M visible such that relative frequencies taken along such subse- quences are provably close enough to a measure in M with high probability.

Proceedings of International Conference on Neural Networks (ICNN'96), 1996

ABSTRACT

IEEE/SP 13th Workshop on Statistical Signal Processing, 2005, 2005

We propose a Bayesian test to assess the statistical dependence when only a small number of sampl... more We propose a Bayesian test to assess the statistical dependence when only a small number of samples are available. Our procedure converts the problem of independence test to a parametric one through quantization and computes the likelihood of the observed cell counts under the independence hypothesis where the marginal cell probabilities are modeled by independent symmetric Dirichlet priors. We tested

2000 IEEE International Symposium on Information Theory (Cat. No.00CH37060), 2000

ABSTRACT A methodology to build interval-valued probability models is presented. It is shown that... more ABSTRACT A methodology to build interval-valued probability models is presented. It is shown that this alternative produces temporally stable models of Internet-generated communications variables