Abstract: The presented theory views inductive learning as a heuristic search through a space of symbolic descriptions, generated by an application of various inference rules to the initial observational statements. The inference rules include generalization rules, which perform generalizing transformations on descriptions, and conventional truth-preserving deductive rules. The application of the inference rules to descriptions is constrained by problem background knowledge, and guided by criteria evaluating the “quality” of generated inductive assertions. Based on this theory, a general methodology for learning structural descriptions from examples, called Star, is described and illustrated by a problem from the area of conceptual data analysis.

Abstract: An important task of multidatabase systems is the integration of existing databases. Database Integration is achieved primarily through the use of generalization. Hence, it is important to develop good tactics for processing queries over generalization hierarchies. This paper defines the class of conjunctive generalization queries, and it describes four tactics for processing those queries that have boon developed for the MDLTIDASE system. Since query processing tactics are best describe algebraically, the paper shows how to model generalization as a sequence of algebraic operations. Three of the tactics described here are adapted from convontional distributed query processing techniqaes. However, it is argued that these tactics are of limited applicability to processing queries over generalization hierarchies. A fourth tactic, semioutorjoin, which is more widely applicable. is introduced. This research was jointly supported by the Defense Advanced Research Projects Agency of the Department of Defense and the Naval Electronic Systems Command and was monitored by the Naval Electronic Systems Command under Contract No. NOOO39-82-C-0226. The views and conclusions contained in this document are those of the authors and should not be interpreted as necessarily representing the official policies, oithor expressed or implied, of the DARPA, NAVPLEX, or the U.S. Government.

Abstract: This article reviews and interprets recent mathematics of special functions, with emphasis on integral representations of multiple hypergeometric functions. B.C. Carlson's centrally important parameterized functions R and ℛ, initially defined as Dirichlet averages, are expressed as probability-generating functions of mixed multinomial distributions. Various nested families generalizing the Dirichlet distributions are developed for Bayesian inference in multinomial sampling and contingency tables. In the case of many-way tables, this motivates a new generalization of the function ℛ. These distributions are also useful for the modeling of populations of personal probabilities evolving under the process of inference from statistical data. A remarkable new integral identity is adapted from Carlson to represent the moments of quadratic forms under multivariate normal and, more generally, elliptically contoured distributions. This permits the computation of such moments by simple quadrature.

Abstract: The article reviews the literature on the extratraining effects of bahavioral family intervention relating to parent behaviour. The review classifies generalization and maintenance into several distinct categories suggested by Drabman, Hammer, and Rosenbaum (1979). The authors conclude that only limited aspects of generalization and maintenance questions in parent training have been addressed and highlight several persisting methodological deficiencies that have hampered the development and evaluation of effective generalization programming technologies.

Abstract: Probabilities in a large sparse contingency table are estimated by maximizing the likelihood modified by a roughness penalty. It is shown that if certain smoothness criteria on the underlying probability vector are met, the estimator proposed is consistent in a one-dimensional table under a sparse asymptotic framework. Suggestions are made for techniques to apply the estimator in practice, and generalization to higher dimensional tables is considered.

Abstract: Described in this paper is a computer system, RESEARCHER, being developed at Columbia that reads natural language text in the form of patent abstracts and creates a permanent long-term memory based on concepts generalized from these texts, forming an intelligent information system. This paper is intended to give an overview of RESEARCHER. We will describe briefly the four main areas dealt with in the design of RESEARCHER: 1) knowledge representation, where a canonical scheme for representing physical objects has been developed, 2) memory-based text processing, 3) generalization and generalization-based memory organization that treats concept formation as an integral part of understanding, and 4) generalization-based question answering.

Abstract: In this paper we introduce successively stronger forms of ordinal dependence between categorical variables, corresponding to orderings over the categories of the variables. In our main theorem it is proved that if these forms of dependence are present in contingency tables, then the orderings are reflected in the correspondence analysis solution, whatever a priori ordering may have been given to the categories. This explains two important order phenomena which frequently occur in practice. Furthermore a multivariate generalization of the main theorem is given. The results in this paper support the use of (multi-) correspondence analysis as a scaling technique for categorical variables.

Abstract: The classical results of Routh and Hurwitz on the stability of polynomials are generalized from the open left half plane to certain other subregions G of the complex plane. By our method, arbitrary conic sections can be handled. The results are interpreted as criteria for G -stability of linear systems. A numerical algorithm to compute the criteria is given. An application to a problem in robust controller design is outlined.

Abstract: A class Tk of analytic functions in the unit disc is defined in which the concept of close-to-convexity is generalized. A necessary condition for a function f to belong to Tk, raduis of convexity problem and a coefficient result are solved in this paper.

Abstract: A nonstationary generalization of the classical Yule-Walker equations, relating the (time-varying) autocorrelations of an autoregressive process to the coefficients of the possible models for this process, is given. The corresponding theoretical model-building (or spectral factorization) problem, i.e. that of expressing the above mentioned models in terms of the autocorrelations, is solved. This paper, as well as several others, is part of a work whose purpose is a systematic study of time-varying ARMA models. © 1983.

Abstract: Recent studies pertaining to an extended class of matched pairs tests based on powers of ranks are discussed. Previous questions regarding the asymptotic properties for this class of tests are clarified and a generalization of this class is described. This generalization raises a previously unanticipated concern about whether or not the analytic comparisons resulting from these tests correspond with an intuitive notion of what is being compared.

Abstract: We approach concept learning as a heuristic search through a space of concepts for a concept that satisfies the learning task at hand The heuristics represent bias that the concept learning program employs when forming an inductive generalization. We present a model of bias adjustment and report our experience with an implementation of the model.

Abstract: The present paper deals with the extension of two well-known static discrete choice theories to the dynamic situation in which individuals make choices at several points in (continuous) time. A dynamic version of Luce's Axiom, “independence from irrelevant alternatives”, is proposed and some of its implications are derived. In the static case Yellott ( J. Math. Psych. 1977 , 15 , 109–146) and others have demonstrated that an independent random utility model generated from the extreme value distribution exp(− e − ax − b ) becomes equivalent to Luce's Axiom. Yellott also introduced an axiom called “invariance under uniform expansions of the choice set”, and he proved that within the class of random utility models with independent identically distributed utilities (apart from a location shift) this axiom is equivalent to Luce's Axiom. These results are extended to the dynamic situation and it is shown that if the utility processes are expressed by so-called extremal processes the corresponding choice model is Markovian. A nonstationary generalization is proposed which is a substantial interest in applications where the parameters of the choice process are influenced by previous choice experience or by time-varying exogenous variables. In particular, it is demonstrated that the nonstationary model is Markovian if and only if the joint choice probabilities at two points in time have a particular form. Thus, the paper provides a rationale for applying a specific class of Markov models as the point of departure when modelling mobility processes that involve individual discrete decisions over time.

Abstract: When estimating a single equation with an error generated by an autoregressive process of higher order than one using a sequence of likelihood ratio tests to determine the correct order, the asymptotic size of the tests will be biased because of multiple optima of the likelihood function. A new type is suggested similar to the Durbin test [2] which is not biased in this way. IN HIS ARTICLE on testing for serial correlation in the presence of lagged endogenous variables [2] Durbin proved a general theorem which gives a significance test shown to be generally asymptotically equivalent to a likelihood ratio test. This paper proposes a generalization which gives a test criterion that may be preferred to the existing test criteria insofar as it can be set up using a less arbitrary choice of the parameters to be re-estimated, and also has the advantage of being relatively simple to compute. It seems more appropriate than the general Durbin form of test for application to the dynamic specification problem discussed in the third section of this article.

Abstract: An iterative solution to the generalized Towers of Hanoi problem, and its derivation are presented. In this generalization, one or more towers, consisting of a total ofn discs, are given as an initial legal configuration, and the task is to move them to a specified peg under the usual restrictions. An analysis of the iterative algorithm is also discussed.