Probability from similarity

The probability calculus provides an attractive canonical form for reasoning but its use requires numerous estimates of chance. Some of the estimates needed in artificial systems can be recorded individually or via Bayesian networks. Others can be tabulated as relative frequencies from stored data. For the shifting contexts of commonsense reasoning, however, the latter sources are likely to prove insufficient. To help fill the gap, we show how sensible conditional probabilities can be derived from absolute probabilities plus information about the similarity of objects and categories. Experimental evidence from studies of human reasoning documents the naturalness of the numbers we derive.

[1]  Peter Norvig,et al.  Artificial Intelligence: A Modern Approach , 1995 .

[2]  Edward E. Smith,et al.  Category-Based Induction , 1990 .

[3]  Daniel N. Osherson,et al.  Eliminating Incoherence from Subjective Estimates of Chance , 2002, KR.

[4]  Daniel N. Osherson,et al.  Some origins of belief , 1986, Cognition.

[5]  Ron Sun,et al.  Robust Reasoning: Integrating Rule-Based and Similarity-Based Reasoning , 1995, Artif. Intell..

[6]  Jonathan Barzilai,et al.  On the foundations of measurement , 2001, 2001 IEEE International Conference on Systems, Man and Cybernetics. e-Systems and e-Man for Cybernetics in Cyberspace (Cat.No.01CH37236).

[7]  David Heckerman,et al.  Probabilistic similarity networks , 1991, Networks.

[8]  R. Narasimhan,et al.  Knowledge processing and commonsense , 1997, Knowl. Based Syst..

[9]  M. Lassaline,et al.  Structural alignment in induction and similarity. , 1996, Journal of experimental psychology. Learning, memory, and cognition.

[10]  Charles L. Ortiz,et al.  A Commonsense Language for Reasoning about Causation and Rational Action , 1999, Artif. Intell..

[11]  Peter C. Fishburn,et al.  Foundations of Measurement:@@@Volume II: Geometrical, Threshold, and Probabilistic Representations@@@Volume III: Representation, Axiomatization, and Invariance. , 1991 .

[12]  Robert L. Goldstone,et al.  Concepts and Categorization , 2003 .

[13]  Peter Gärdenfors,et al.  Conceptual spaces - the geometry of thought , 2000 .

[14]  Jaap Van Brakel,et al.  Foundations of measurement , 1983 .

[15]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems , 1988 .

[16]  D. Gentner,et al.  Respects for similarity , 1993 .

[17]  F. Keil,et al.  Two dogmas of conceptual empiricism: implications for hybrid models of the structure of knowledge , 1998, Cognition.

[18]  Magnus Persson,et al.  PROBabilities from EXemplars (PROBEX): a "lazy" algorithm for probabilistic inference from generic knowledge , 2002 .

[19]  R N Shepard,et al.  Multidimensional Scaling, Tree-Fitting, and Clustering , 1980, Science.

[20]  D. Medin,et al.  Does rank have its privilege? Inductive inferences within folkbiological taxonomies , 1997, Cognition.

[21]  L. Rips.  Inductive judgments about natural categories. , 1975 .

[22]  Pat Langley,et al.  Selection of Relevant Features and Examples in Machine Learning , 1997, Artif. Intell..

[23]  P. Johnson-Laird.  Mental models , 1989 .

[24]  A. Tversky,et al.  Additive similarity trees , 1977 .

[25]  Patrick Suppes,et al.  Foundations of Measurement, Vol. II: Geometrical, Threshold, and Probabilistic Representations , 1989 .

[26]  Hudson Turner,et al.  A Logic of Universal Causation , 1999, Artif. Intell..

[27]  D. Medin,et al.  A relevance theory of induction , 2003, Psychonomic bulletin & review.

[28]  D. Medin,et al.  Asymmetries of comparison , 1999, Psychonomic bulletin & review.

[29]  Douglas L. Medin,et al.  Context theory of classification learning. , 1978 .

[30]  Daniel N. Osherson,et al.  New axioms for the contrast model of similarity , 1987 .

[31]  A. Tversky.  Features of Similarity , 1977 .