# "Statistics - Machine Learning"

## Unbalanced Sobolev Descent

We introduce Unbalanced Sobolev Descent (USD), a particle descent algorithm for transporting a high dimensional source distribution to a target distribution that does not necessarily have the same mass. We define the Sobolev-Fisher discrepancy …

## Kernel Stein Generative Modeling

We are interested in gradient-based Explicit Generative Modeling where samples can be derived from iterative gradient updates based on an estimate of the score function of the data distribution. Recent advances in Stochastic Gradient Langevin …

## Fast Mixing of Multi-Scale Langevin Dynamics under the Manifold Hypothesis

Recently, the task of image generation has attracted much attention. In particular, the recent empirical successes of the Markov Chain Monte Carlo (MCMC) technique of Langevin Dynamics have prompted a number of theoretical advances; despite this, …

## Generative Modeling with Denoising Auto-Encoders and Langevin Sampling

We study convergence of a generative modeling method that first estimates the score function of the distribution using Denoising Auto-Encoders (DAE) or Denoising Score Matching (DSM) and then employs Langevin diffusion for sampling. We show that both …

## Regularized Finite Dimensional Kernel Sobolev Discrepancy

We show in this note that the Sobolev Discrepancy introduced in Mroueh et al in the context of generative adversarial networks, is actually the weighted negative Sobolev norm $textbartextbar.textbartextbar_dotHtextasciicircum-1(nu_q)$, that is known …