Deep Generative Sampling in the Dual Divergence Space: A Data-efficient
  & Interpretative Approach for Generative AI
Sahil Garg Anderson Schneider Anant Raj Kashif Rasul Yuriy Nevmyvaka Sneihil Gopal Amit Dhurandhar Guillermo Cecchi Irina Rish
Building on the remarkable achievements in generative sampling of natural
images, we propose an innovative challenge, potentially overly ambitious, which
involves generating samples of entire multivariate time series that resemble
images. However, the statistical challenge lies in the small sample size,
sometimes consisting of a few hundred subjects. This issue is especially
problematic for deep generative models that follow the conventional approach of
generating samples from a canonical distribution and then decoding or denoising
them to match the true data distribution. In contrast, our method is grounded
in information theory and aims to implicitly characterize the distribution of
images, particularly the (global and local) dependency structure between
pixels. We achieve this by empirically estimating its KL-divergence in the dual
form with respect to the respective marginal distribution. This enables us to
perform generative sampling directly in the optimized 1-D dual divergence
space. Specifically, in the dual space, training samples representing the data
distribution are embedded in the form of various clusters between two end
points. In theory, any sample embedded between those two end points is
in-distribution w.r.t. the data distribution. Our key idea for generating novel
samples of images is to interpolate between the clusters via a walk as per
gradients of the dual function w.r.t. the data dimensions. In addition to the
data efficiency gained from direct sampling, we propose an algorithm that
offers a significant reduction in sample complexity for estimating the
divergence of the data distribution with respect to the marginal distribution.
We provide strong theoretical guarantees along with an extensive empirical
evaluation using many real-world datasets from diverse domains, establishing
the superiority of our approach w.r.t. state-of-the-art deep learning methods.