Log Sobolev

Log-Sobolev inequalities are functional inequalities that quantify the concentration of probability measures, playing a crucial role in analyzing the convergence rates of various algorithms and stochastic processes. Current research focuses on leveraging these inequalities to understand and improve the performance of gradient-based methods, including Expectation Maximization, Langevin Monte Carlo, and particle gradient descent, particularly in high-dimensional settings and for non-convex problems. This work extends to applications in Bayesian inference, optimal experimental design, and federated learning, offering improved theoretical guarantees and practical efficiency for these methods. The broader impact lies in providing stronger theoretical foundations and more efficient algorithms for diverse machine learning and statistical inference tasks.