e case of location and scale parameters, rate constants, and in Bernoulli trials with unknown probability of success. In realistic problems, both the transformation group analysis and the principle of maximum entropy are needed to determine the prior. The distributions thus found are uniquely determined by the prior information, independently of the choice of parameters. In a certain class of problems, therefore, the prior distributions may now be claimed to be fully as "objective" as the sampling distributions. I. Background of the problem Since the time of Laplace, applications of probability theory have been hampered by difficulties in the treatment of prior information. In realistic problems of decision or inference, we often have prior information which is highly relevant to the question being asked; to fail to take it into account is to commit the most obvious inconsistency of reasoning and may lead to absurd or dangerously misleading results. As an extreme examp

We explore how to organize large text databases hierarchically by topic to aid better searching, browsing and filtering. Many corpora, such as internet directories, digital libraries, and patent databases are manually organized into topic hierarchies, also called taxonomies. Similar to indices for relational data, taxonomies make search and access more efficient. However, the exponential growth in the volume of on-line textual information makes it nearly impossible to maintain such taxonomic organization for large, fast-changing corpora by hand. We describe an automatic system that starts with a small sample of the corpus in which topics have been assigned by hand, and then updates the database with new documents as the corpus grows, assigning topics to these new documents with high speed and accuracy. To do this, we use techniques from statistical pattern recognition to efficiently separate the feature words, or...

A counterpart to von Neumann and Morgenstern' expected utility theory is proposed in the framework of possibility theory. The existence of a utility function, representing a preference ordering among possibility distributions (on the consequences of decision-maker's actions) that satisfies a series of axioms pertaining to decision-maker's behavior, is established. The obtained utility is a generalization of Wald's criterion, which is recovered in case of total ignorance; when ignorance is only partial, the utility takes into account the fact that some situations are more plausible than others. Mathematically, the qualitative utility is nothing but the necessity measure of a fuzzy event in the sense of possibility theory (a so-called Sugeno integral). The possibilistic representation of uncertainty, which only requires a linearly ordered scale, is qualitative in nature. Only max, min and order-reversing operations are used on the scale. The axioms express a risk-averse behavior of the d...

We explore how to organize a text database hierarchically to aid better searching and browsing. We propose to exploit the natural hierarchy of topics, or taxonomy, that many corpora,suchas internet directories, digital libraries, and patent databases enjoy. In our system, the user navigates through the query response not as a at unstructured list, but embedded in the familiar taxonomy, and annotated with document signatures computed dynamically with respect to where the user is located at any time. Weshowhowto update such databases with new documents with high speed and accuracy. Weuse techniques from statistical pattern recognition to e ciently separate the feature words or discriminants from the noise words at each node of the taxonomy. Using these, we build a multi-level classi er. At each node, this classi er can ignore the large number of noise words in a document. Thus the classi er has a small model size and is very fast. However, owing to the use of context-sensitive features, the classi er is very accurate. We report on experiences with the Reuters newswire benchmark, the US Patent database, and web document samples from Yahoo!. 1

A decision-theoretic framework is proposed for evaluating the efficiency of simulation estimators. The framework includes the cost of obtaining the estimate as well as the cost of acting based on the estimate. The cost of obtaining the estimate and the estimate itself are represented as realizations of jointly distributed stochastic processes. In this context, the efficiency of a simulation estimator based on a given computational budget is defined as the reciprocal of the risk (the overall expected cost). This framework is appealing philosophically, but it is often difficult to apply in practice (e.g., to compare the efficiency of two different estimators) because only rarely can the efficiency associated with a given computational budget be calculated. However, a useful practical framework emerges in a large sample context when we consider the limiting behavior as the computational budget increases. A limit theorem established for this model supports and extends a fairly well known e...

Abstract: This paper investigates to what extent a purely symbolic approach to decision making under uncertainty is possible, in the scope of Artificial Intelligence. Contrary to classical approaches to decision theory, we try to rank acts without resorting to any numerical representation of utility nor uncertainty, and without using any scale on which both uncertainty and preference could be mapped. Our approach is a variant of Savage's where the setting is finite, and the strict preference on acts is a partial order. It is shown that although many axioms of Savage theory are preserved and despite the intuitive appeal of the ordinal method for constructing a preference over acts, the approach is inconsistent with a probabilistic representation of uncertainty. The latter leads to the kind of paradoxes encountered in the theory of voting. It is shown that the assumption of ordinal invariance enforces a qualitative decision procedure that presupposes a comparative possibility representation of uncertainty, originally due to Lewis, and usual in nonmonotonic reasoning. Our axiomatic investigation thus provides decision-theoretic foundations to preferential inference of Lehmann and colleagues. However, the obtained decision rules are sometimes either not very decisive or may lead to overconfident decisions, although their basic principles look sound. This paper points out some limitations of purely ordinal approaches to Savage-like decision making under uncertainty, in perfect analogy with similar difficulties in voting theory.

This thesis deals with a Bayesian neural network model. The focus is on how to use the model for automatic classification, i.e. on how to train the neural network to classify objects from some domain, given a database of labeled examples from the domain. The original Bayesian neural network is a onelayer network implementing a naive Bayesian classifier. It is based on the assumption that different attributes of the objects appear independently of each other. This work has been aimed at extending the original Bayesian neural network model, mainly focusing on three different aspects. First the model is extended to a multi-layer network, to relax the independence requirement. This is done by introducing a hidden layer of complex columns, groups of units which take input from the same set of input attributes. Two different types of complex column structures in the hidden layer are studied and compared. An information theoretic measure is used to decide which input attributes to consider toget...

. Problems for strict and convex Bayesianism are discussed. A set-based Bayesianism generalizing convex Bayesianism and intervalism is proposed. This approach abandons not only the strict Bayesian requirement of a unique real-valued probability function in any decision-making context but also the requirement of convexity for a set-based representation of uncertainty. Levi's E-admissibility decision criterion is retained and is shown to be applicable in the non-convex case. Keywords: Uncertainty, decision-making, maximum entropy, Bayesian methods. 1. Introduction. The reigning philosophy of uncertainty representation is strict Bayesianism. One of its central principles is that an agent must adopt a single, real-valued probability function over the events recognized as relevant to a given problem. Prescriptions for defining such a function for a given agent in a given situation range from the extreme personalism of deFinetti (1964, 1974) and Savage (1972) to the objective Bayesianism of...

Recent advances in automatic speech recognition are accomplished by designing a plug-in maximum a posteriori decision rule such that the forms of the acoustic and language model distributions are specified and the parameters of the assumed distributions are estimated from a collection of speech and language training corpora. Maximum-likelihood point estimation is by far the most prevailing training method. However, due to the problems of unknown speech distributions, sparse training data, high spectral and temporal variabilities in speech, and possible mismatch between training and testing conditions, a dynamic training strategy is needed. To cope with the changing speakers and speaking conditions in real operational conditions for high-performance speech recognition, such paradigms incorporate a small amount of speaker and environment specific adaptation data into the training process. Bayesian adaptive learning is an optimal way to combine

This paper presents an axiomatic framework for qualitative decision under uncertainty in a finite setting. The corresponding utility is expressed by a sup-min expression, called Sugeno (or fuzzy) integral. Technically speaking, Sugeno integral is a median, which is indeed a qualitative counterpart to the averaging operation underlying expected utility. The axiomatic justification of Sugeno integral-based utility is expressed in terms of preference between acts as in Savage decision theory. Pessimistic and optimistic qualitative utilities, based on necessity and possibility measures, previously introduced by two of the authors, can be retrieved in this setting by adding appropriate axioms. 1