Academic journal article Cognitive, Affective and Behavioral Neuroscience

Category-Based Induction from Similarity of Neural Activation

Academic journal article Cognitive, Affective and Behavioral Neuroscience

Category-Based Induction from Similarity of Neural Activation

Article excerpt

Published online: 20 November 2013

© Psychonomic Society, Inc. 2013

Abstract The idea that similarity might be an engine of inductive inference dates back at least as far as David Hume. However, Hume's thesis is difficult to test without begging the question, since judgments of similarity may be infected by inferential processes. We present a one-parameter model of category-based induction that generates predictions about arbitrary statements of conditional probability over a predicate and a set of items. The prediction is based on the unconditional probabilities and similarities that characterize that predicate and those items. To test Hume's thesis, we collected brain activation from various regions of the ventral visual stream during a categorization task that did not invite comparison of categories. We then calculated the similarity of those activation patterns using a simple measure of vectorwise similarity and supplied those similarities to the model. The model's outputs correlated well with subjects' judgments of conditional probability. Our results represent a promising first step toward confirming Hume's thesis; similarity, assessed without reference to induction, may well drive inductive inference.

Keywords Similarity · induction · fMRI · multivariate pattern analysis · categorization · semantics

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The project

David Hume (1748) is well-known for having emphasized the role of similarity in inductive inference. The following remarks are often cited:

In reality, all arguments from experience are founded on the similarity which we discover among natural objects, and by which we are induced to expect effects similar to those which we have found to follow from such objects. . . . From causes which appear similar we expect similar effects.

We understand this assertion about experience and expectation as an empirical claim concerning human psychology. Hume goes on to make the epistemological contention that nondemonstrative inferences lack normative justification, whether they are based on similarity, constant conjunction, or anything else (Morris, 2013). However, we focus here on Hume's empirical claim about similarity; thus, in what follows, "Hume'sthesis" will be interpreted descriptively (concerning psychology), rather than normatively.

Hume's thesis was anticipated by John Locke (1689), for whom analogy was "the great rule of probability." How to interpret the term probability in the writings of Locke and Hume is open to discussion (Cohen, 1980), but the underlying idea seems clear enough: Inductive inference is often based on similarity . The goal of the present article is to sharpen Hume's insight by removing the threat of circularity; as the thesis stands, it is possible that similarity derives from inductive inference. (That is, two events might be judged similar to the extent that one predicts the other; see Tenenbaum & Griffiths, 2001, for an argument to this effect). To avoid circularity, we will evaluate the similarity of categories in neural terms, then embed such similarity in a model of human inductive judgment that will be evaluated empirically.

The present article attempts to relate three types of data: atomic statements of probability about single categories, such as "apples provide at least 10 dietary vitamins"; statements of conditional probability, such as "apples provide at least 10 dietary vitamins given that strawberries do"; and similarities between pairs of categories-such as the similarity between apples and strawberries-defined with recourse to the patterns of neural activation evoked by those categories. Our goal is to estimate human judgments of conditional probability (such as the foregoing inductive inference from strawberries to apples) using just atomic probability and similarity for this purpose. To proceed, we first advance a simple quantitative model that provides such estimates. The model reduces conditional probabilities to a ratio of conjunction probabilities ("apples and strawberries provide at least 10 dietary vitamins") and assigns values to the conjunctions using similarity. …

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