20 citations · 113 across the 36 of their papers we have counts for
6 papers · 1 filter
On the Ergodicity, Bias and Asymptotic Normality of Randomized Midpoint Sampling Method
Ye He, Krishnakumar Balasubramanian, Murat A. Erdogdu
The randomized midpoint method, proposed by [SL19], has emerged as an optimal discretization procedure for simulating the continuous time Langevin diffusions. Focusing on the case…
Riemannian Langevin Algorithm for Solving Semidefinite Programs
Mufan Bill Li, Murat A. Erdogdu
We propose a Langevin diffusion-based algorithm for non-convex optimization and sampling on a product manifold of spheres. Under a logarithmic Sobolev inequality, we establish a gu…
An Analysis of Constant Step Size SGD in the Non-convex Regime: Asymptotic Normality and Bias
Lu Yu, Krishnakumar Balasubramanian, Stanislav Volgushev +1
Structured non-convex learning problems, for which critical points have favorable statistical properties, arise frequently in statistical machine learning. Algorithmic convergence…
Convergence of Langevin Monte Carlo in Chi-Squared and Renyi Divergence
Murat A. Erdogdu, Rasa Hosseinzadeh, Matthew S. Zhang
We study sampling from a target distribution using the unadjusted Langevin Monte Carlo (LMC) algorithm when the potential satisfies a strong dissipativity condit…
Hausdorff Dimension, Heavy Tails, and Generalization in Neural Networks
Umut Şimşekli, Ozan Sener, George Deligiannidis +1
Despite its success in a wide range of applications, characterizing the generalization properties of stochastic gradient descent (SGD) in non-convex deep learning problems is still…
On the Convergence of Langevin Monte Carlo: The Interplay between Tail Growth and Smoothness
Murat A. Erdogdu, Rasa Hosseinzadeh
We study sampling from a target distribution using the unadjusted Langevin Monte Carlo (LMC) algorithm. For any potential function whose tails behave like ${\|…