  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 and compares the existing regression
methods with CGAN.
  We notice however, that the existing methods like mixture density networks
(MDN) and XGBoost do quite well compared to CGAN in terms of likelihood and
mean absolute error, respectively. Both these methods are comparatively easier
to train than CGANs. CGANs need more innovation to have a comparable modeling
and ease-of-training with respect to the existing regression solvers. In
summary, for modeling uncertainty MDNs are better while XGBoost is better for
the cases where accurate prediction is more important.
