Regression via Implicit Models and Optimal Transport Cost Minimization Article Swipe

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Saurav Manchanda , Khoa D. Doan , Pranjul Yadav , S. Sathiya Keerthi · YOU? · · 2020 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2003.01296

This paper addresses the classic problem of regression, which involves the inductive learning of a map, $y=f(x,z)$, $z$ denoting noise, $f:\mathbb{R}^n\times \mathbb{R}^k \rightarrow \mathbb{R}^m$. Recently, Conditional GAN (CGAN) has been applied for regression and has shown to be advantageous over the other standard approaches like Gaussian Process Regression, given its ability to implicitly model complex noise forms. However, the current CGAN implementation for regression uses the classical generator-discriminator architecture with the minimax optimization approach, which is notorious for being difficult to train due to issues like training instability or failure to converge. In this paper, we take another step towards regression models that implicitly model the noise, and propose a solution which directly optimizes the optimal transport cost between the true probability distribution $p(y|x)$ and the estimated distribution $\hat{p}(y|x)$ and does not suffer from the issues associated with the minimax approach. On a variety of synthetic and real-world datasets, our proposed solution achieves state-of-the-art results. The code accompanying this paper is available at "https://github.com/gurdaspuriya/ot_regression".

Type

preprint

Language

en

Landing Page

http://arxiv.org/abs/2003.01296

PDF

https://arxiv.org/pdf/2003.01296

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green

Cited By

2

References

14

Related Works

10

OpenAlex ID

https://openalex.org/W3010516204

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OpenAlex ID

https://openalex.org/W3010516204

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DOI

https://doi.org/10.48550/arxiv.2003.01296

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Title

Regression via Implicit Models and Optimal Transport Cost Minimization

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Type

preprint

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Language

en

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Publication year

2020

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Publication date

2020-03-03

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Authors

Saurav Manchanda, Khoa D. Doan, Pranjul Yadav, S. Sathiya Keerthi

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Landing page

https://arxiv.org/abs/2003.01296

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https://arxiv.org/pdf/2003.01296

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Yes

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OA status

green

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https://arxiv.org/pdf/2003.01296

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Concepts

Minification, Regression, Regression analysis, Computer science, Econometrics, Mathematical optimization, Mathematics, Statistics

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Cited by

2

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Citations by year (recent)

2020: 2

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References (count)

14

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Related works (count)

10

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