ON THE RATIONAL SCOPE OF PROBABILISTIC RULE-BASED INFERENCE SYSTEMS

Belief updating schemes in artificial intelligence may be viewed as three dimensional languages, consisting of a syntax (e.g. probabilities or certainty factors), a calculus (e.g. Bayesian or CF combination rules), and a semantics (i.e. cognitive interpretations of competing formalisms). This paper studies the rational scope of those languages on the syntax and calculus grounds. In particular, the paper presents an endomorphism theorem which highlights the limitations imposed by the conditional independence assumptions implicit in the CF calculus. Implications of the theorem to the relationship between the CF and the Bayesian languages and the Dempster-Shafer theory of evidence are presented. The paper concludes with a discussion of some implications on rule-based knowledge engineering in uncertain domains.Information Systems Working Papers Serie

Ratio-Scale Elicitation of Degrees of Support

During the last decade, the computational paradigms known as inflzcence diagrams and belief networks have become to dominate the diagnostic expert systems field. Using elaborate collections of nodes and arcs, these representations describe how propositions of interest interact with each other through a variety of causal and predictive links. The links are parameterized with inexact degrees of support, typically expressed as subjective conditional probabilities or likelihood ratios. To date, most of the research in this area has focused on developing efficient belief-revision calculi to support decision making under uncertainty. Taking a different perspective, this paper focuses on the inputs of these calculi, i.e. on the human-supplied degrees of support which provide the currency of the belief revision process. Traditional methods for eliciting subjective probability functions are of little use in rule-based settings, where propositions of interest represent causally related and mostly discrete random variables. We describe ratio-scale and graphical methods for (i) eliciting degrees of support from human experts in a credible manner, and (ii) transforming them into the conditional probabilities and likelihood-ratios required by standard belief revision algorithms. As a secondary contribution, the paper offers a new graphical justification to eigenvector techniques for smoothing subjective answers to pair-wise elicitation questions.Information Systems Working Papers Serie

COMPARING THE VALIDITY OF ALTERNATIVE BELIEF LANGUAGES: AN EXPERIMENTAL APPROACH

The problem of modeling uncertainty and inexact reasoning in rule-based expert systems is challenging on nonnative as well on cognitive grounds. First, the modular structure of the rule-based architecture does not lend itself to standard Bayesian inference techniques. Second, there is no consensus on how to model human (expert) judgement under uncertainty. These factors have led to a proliferation of quasi-probabilistic belief calculi which are widely-used in practice. This paper investigates the descriptive and external validity of three well-known "belief languages:" the Bayesian, ad-hoc Bayesian, and the certainty factors languages. These models are implemented in many commercial expert system shells, and their validity is clearly an important issue for users and designers of expert systems. The methodology consists of a controlled, within-subject experiment designed to measure the relative performance of alternative belief languages. The experiment pits the judgement of human experts with the recommendations generated by their simulated expert systems, each using a different belief language. Special emphasis is given to the general issues of validating belief languages and expert systems at large.Information Systems Working Papers Serie

RATIO-SCALE ELICITATION OF DEGREES OF BELIEF

Most research on rule-based inference under uncertainty has focused on the normative validity and efficiency of various belief-update algorithms. In this paper we shift the attention to the inputs of these algorithms, namely, to the degrees of beliefs elicited from domain experts. Classical methods for eliciting continuous probability functions are of little use in a rule-based model, where propositions of interest are taken to be causally related and, typically, discrete, random variables. We take the position that the numerical encoding of degrees of belief in such propositions is somewhat analogous to the measurement of physical stimuli like brightness, weight, and distance. With that in mind, we base our elicitation techniques on statements regarding the relative likelihoods of various clues and hypotheses. We propose a formal procedure designed to (a) elicit such inputs in a credible manner, and, (b) transform them into the conditional probabilities and likelihood-ratios required by Bayesian inference systems.Information Systems Working Papers Serie

AN INTUITIVE INTERPRETATION OF THE THEORY OF EVIDENCE IN THE CONTEXT OF BIBLIOGRAPHICAL INDEXING

Models of bibliographical Indexing concern the construction of effective keyword taxonomies and the representation of relevance between document s and keywords. The theory of evidence concerns the elicitation and manipulation of degrees of belief rendered by multiple sources of evidence to a common set of propositions. The paper presents a formal framework in which adaptive taxonomies and probabilistic indexing are induced dynamically by the relevance opinions of the library's patrons. Different measures of relevance and mechanisms for combining them are presented and shown to be isomorphic to the belief functions and combination rules of the theory of evidence. The paper thus has two objectives: (i) to treat formally slippery concepts like probabilistic indexing and average relevance, and (ii) to provide an intuitive justification to the Dempster Shafer theory of evidence, using bibliographical indexing as a canonical example.Information Systems Working Papers Serie

PROLOG META-INTERPRETERS FOR RULE-BASED INFERENCE UNDER UNCERTAINTY

Uncertain facts and inexact rules can be represented and processed in standard Prolog through meta-interpretation. This requires the specification of appropriate parsers and belief calculi. We present a meta-interpreter that takes a rule-based belief calculus as an external variable. The certainty-factors calculus and a heuristic Bayesian belief-update model are then implemented as stand-alone Prolog predicates. These, in turn, are bound to the meta-interpreter environment through second-order programming. The resulting system is a powerful experimental tool which enables inquiry into the impact of various designs of belief calculi on the external validity of expert systems. The paper also demonstrates the (well-known) role of Prolog meta-interpreters in building expert system shells.Information Systems Working Papers Serie

MULTILAYER FEEDFORWARD NETWORKS WITH NON-POLYNOMIAL ACTIVATION FUNCTIONS CAN APPROXIMATE ANY FUNCTION

Several researchers characterized the activation functions under which multilayer feedforward networks can act as universal approximators. We show that all the characterizations that were reported thus far in the literature ark special cases of the following general result: a standard multilayer feedforward network can approximate any continuous function to any degree of accuracy if and only if the network's activation functions are not polynomial. We also emphasize the important role of the threshold, asserting that without it the last theorem doesn't hold.Information Systems Working Papers Serie

A DEMPSTER-SHAFER MODEL OF RELEVANCE

We present a model for representing relevance and classification decisions of multiple catalogers in the context of a hierarchical bibliographical database. The model is based on the Dempster-Shafer theory of evidence. Concepts like ambiguous relevance, inexact classification, and pooled classification, are discussed using the nomenclature of belief functions and Dempster's rule. The model thus gives a normative framework in which one can describe and address many problematic phenomena which characterize the way people classify and retrieve documents.Information Systems Working Papers Serie