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## Benchmarking Regression Methods: A comparison with CGAN

Karan Aggarwal
• Function : Author
Matthieu Kirchmeyer
• Function : Author
• Function : Author
S. Sathiya Keerthi
• Function : Author
Patrick Gallinari

#### Abstract

In recent years, impressive progress has been made in the design of implicit probabilistic models via Generative Adversarial Networks (GAN) and its extension, the Conditional GAN (CGAN). Excellent solutions have been demonstrated mostly in image processing applications which involve large, continuous output spaces. There is almost no application of these powerful tools to problems having small dimensional output spaces. Regression problems involving the inductive learning of a map, $y=f(x,z)$, $z$ denoting noise, $f:\mathbb{R}^n\times \mathbb{R}^k \rightarrow \mathbb{R}^m$, with $m$ small (e.g., $m=1$ or just a few) is one good case in point. The standard approach to solve regression problems is to probabilistically model the output $y$ as the sum of a mean function $m(x)$ and a noise term $z$; it is also usual to take the noise to be a Gaussian. These are done for convenience sake so that the likelihood of observed data is expressible in closed form. In the real world, on the other hand, stochasticity of the output is usually caused by missing or noisy input variables. Such a real world situation is best represented using an implicit model in which an extra noise vector, $z$ is included with $x$ as input. CGAN is naturally suited to design such implicit models. This paper makes the first step in this direction. Using synthetic datasets we show that CGAN possesses a better ability to model complex noise forms. On real world datasets, CGAN is competitive with the state-of-the-art methods.

### Dates and versions

hal-02457453 , version 1 (28-01-2020)

### Identifiers

• HAL Id : hal-02457453 , version 1
• ARXIV :

### Cite

Karan Aggarwal, Matthieu Kirchmeyer, Pranjul Yadav, S. Sathiya Keerthi, Patrick Gallinari. Benchmarking Regression Methods: A comparison with CGAN. 2020. ⟨hal-02457453⟩

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