High-dimensional probability distributions play important role in many applications: they encode connections between different variables, and learning such distributions allows to solve different tasks. There are many methods to do so, and in this talk I will overview some of our recent algorithmic and theoretical results:
1. Tensor-train density estimation from sample (Novikov, Panov, Oseledets, UAI 2021): we show, how we can reliably estimate the tensor-train model from the samples and how it can be used.
2. Functional space analysis of local GAN training (Khrulkov, Babenko, Oseledets, ICML 2021): we show, how the convergence of the GAN (generative adversarial network) training method can be analyzed through the Poincare constant.