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Quarterly of Applied Mathematics

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A tale of three probabilistic families: Discriminative, descriptive, and generative models


Authors: Ying Nian Wu, Ruiqi Gao, Tian Han and Song-Chun Zhu
Journal: Quart. Appl. Math. 77 (2019), 423-465
MSC (2010): Primary 62M40
DOI: https://doi.org/10.1090/qam/1528
Published electronically: December 31, 2018
MathSciNet review: 3932965
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Abstract | References | Similar Articles | Additional Information

Abstract: The pattern theory of Grenander is a mathematical framework where patterns are represented by probability models on random variables of algebraic structures. In this paper, we review three families of probability models, namely, the discriminative models, the descriptive models, and the generative models. A discriminative model is in the form of a classifier. It specifies the conditional probability of the class label given the input signal. A descriptive model specifies the probability distribution of the signal, based on an energy function defined on the signal. A generative model assumes that the signal is generated by some latent variables via a transformation. We shall review these models within a common framework and explore their connections. We shall also review the recent developments that take advantage of the high approximation capacities of deep neural networks.

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Additional Information

Ying Nian Wu
Affiliation: Department of Statistics, University of California, Los Angeles, California 90095-1554
MR Author ID: 360276
Email: ywu@stat.ucla.edu

Ruiqi Gao
Affiliation: Department of Statistics, University of California, Los Angeles, California 90095-1554
Email: ruiqigao@ucla.edu

Tian Han
Affiliation: Department of Statistics, University of California, Los Angeles, California 90095-1554
Email: hthth0801@gmail.com

Song-Chun Zhu
Affiliation: Department of Statistics, University of California, Los Angeles, California 90095-1554
MR Author ID: 712282
Email: sczhu@stat.ucla.edu

Received by editor(s): February 21, 2018
Received by editor(s) in revised form: October 9, 2018
Published electronically: December 31, 2018
Additional Notes: The work was supported by NSF DMS 1310391, DARPA SIMPLEX N66001-15-C-4035, ONR MURI N00014-16-1-2007, and DARPA ARO W911NF-16-1-0579.
Article copyright: © Copyright 2018 Brown University

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