Biomedical subjects

J B Tenenbaum

Publications and source records attributed to J B Tenenbaum.

3 recordsLinked to original sources

PubMed2001

Generalization, similarity, and Bayesian inference.

Shepard has argued that a universal law should govern generalization across different domains of perception and cognition, as well as across organisms from different species or even different planets. Starting with some basic assumptions about natural kinds, he derived an exponential decay function as the form of the universal generalization gradient, which accords strikingly well with a wide range of empirical data. However, his original formulation applied only to the ideal case of generalization from a single encountered stimulus to a single novel stimulus, and for stimuli that can be represented as points in a continuous metric psychological space. Here we recast Shepard's theory in a more general Bayesian framework and show how this naturally extends his approach to the more realistic situation of generalizing from multiple consequential stimuli with arbitrary representational structure. Our framework also subsumes a version of Tversky's set-theoretic model of similarity, which is conventionally thought of as the primary alternative to Shepard's continuous metric space model of similarity and generalization. This unification allows us not only to draw deep parallels between the set-theoretic and spatial approaches, but also to significantly advance the explanatory power of set-theoretic models.

Bayes Theorem↗

PubMed2000

A global geometric framework for nonlinear dimensionality reduction.

Scientists working with large volumes of high-dimensional data, such as global climate patterns, stellar spectra, or human gene distributions, regularly confront the problem of dimensionality reduction: finding meaningful low-dimensional structures hidden in their high-dimensional observations. The human brain confronts the same problem in everyday perception, extracting from its high-dimensional sensory inputs-30,000 auditory nerve fibers or 10(6) optic nerve fibers-a manageably small number of perceptually relevant features. Here we describe an approach to solving dimensionality reduction problems that uses easily measured local metric information to learn the underlying global geometry of a data set. Unlike classical techniques such as principal component analysis (PCA) and multidimensional scaling (MDS), our approach is capable of discovering the nonlinear degrees of freedom that underlie complex natural observations, such as human handwriting or images of a face under different viewing conditions. In contrast to previous algorithms for nonlinear dimensionality reduction, ours efficiently computes a globally optimal solution, and, for an important class of data manifolds, is guaranteed to converge asymptotically to the true structure.

Algorithms↗

PubMed2000

Separating style and content with bilinear models.

Perceptual systems routinely separate "content" from "style," classifying familiar words spoken in an unfamiliar accent, identifying a font or handwriting style across letters, or recognizing a familiar face or object seen under unfamiliar viewing conditions. Yet a general and tractable computational model of this ability to untangle the underlying factors of perceptual observations remains elusive (Hofstadter, 1985). Existing factor models (Mardia, Kent, & Bibby, 1979; Hinton & Zemel, 1994; Ghahramani, 1995; Bell & Sejnowski, 1995; Hinton, Dayan, Frey, & Neal, 1995; Dayan, Hinton, Neal, & Zemel, 1995; Hinton & Ghahramani, 1997) are either insufficiently rich to capture the complex interactions of perceptually meaningful factors such as phoneme and speaker accent or letter and font, or do not allow efficient learning algorithms. We present a general framework for learning to solve two-factor tasks using bilinear models, which provide sufficiently expressive representations of factor interactions but can nonetheless be fit to data using efficient algorithms based on the singular value decomposition and expectation-maximization. We report promising results on three different tasks in three different perceptual domains: spoken vowel classification with a benchmark multi-speaker database, extrapolation of fonts to unseen letters, and translation of faces to novel illuminants.

Algorithms↗