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09/07/2023
Gradient-Based Feature Learning under Structured Data
Recent works have demonstrated that the sample complexity of gradient-ba...
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07/04/2023
Distributional Model Equivalence for Risk-Sensitive Reinforcement Learning
We consider the problem of learning models for risk-sensitive reinforcem...
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03/07/2023
Towards a Complete Analysis of Langevin Monte Carlo: Beyond Poincaré Inequality
Langevin diffusions are rapidly convergent under appropriate functional ...
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03/01/2023
Mean-Square Analysis of Discretized Itô Diffusions for Heavy-tailed Sampling
We analyze the complexity of sampling from a class of heavy-tailed distr...
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02/16/2023
Improved Discretization Analysis for Underdamped Langevin Monte Carlo
Underdamped Langevin Monte Carlo (ULMC) is an algorithm used to sample f...
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09/29/2022
Neural Networks Efficiently Learn Low-Dimensional Representations with SGD
We study the problem of training a two-layer neural network (NN) of arbi...
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09/19/2022
Generalization Bounds for Stochastic Gradient Descent via Localized ε-Covers
In this paper, we propose a new covering technique localized for the tra...
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07/25/2022
p-DkNN: Out-of-Distribution Detection Through Statistical Testing of Deep Representations
The lack of well-calibrated confidence estimates makes neural networks i...
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02/23/2022
Mirror Descent Strikes Again: Optimal Stochastic Convex Optimization under Infinite Noise Variance
We study stochastic convex optimization under infinite noise variance. S...
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02/10/2022
Towards a Theory of Non-Log-Concave Sampling: First-Order Stationarity Guarantees for Langevin Monte Carlo
For the task of sampling from a density π∝exp(-V) on ℝ^d, where V is pos...
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01/20/2022
Heavy-tailed Sampling via Transformed Unadjusted Langevin Algorithm
We analyze the oracle complexity of sampling from polynomially decaying ...
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12/23/2021
Analysis of Langevin Monte Carlo from Poincaré to Log-Sobolev
Classically, the continuous-time Langevin diffusion converges exponentia...
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09/06/2021
On Empirical Risk Minimization with Dependent and Heavy-Tailed Data
In this work, we establish risk bounds for the Empirical Risk Minimizati...
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06/09/2021
Fractal Structure and Generalization Properties of Stochastic Optimization Algorithms
Understanding generalization in deep learning has been one of the major ...
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06/07/2021
Heavy Tails in SGD and Compressibility of Overparametrized Neural Networks
Neural network compression techniques have become increasingly popular a...
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04/19/2021
Manipulating SGD with Data Ordering Attacks
Machine learning is vulnerable to a wide variety of different attacks. I...
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02/20/2021
Convergence Rates of Stochastic Gradient Descent under Infinite Noise Variance
Recent studies have provided both empirical and theoretical evidence ill...
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11/06/2020
On the Ergodicity, Bias and Asymptotic Normality of Randomized Midpoint Sampling Method
The randomized midpoint method, proposed by [SL19], has emerged as an op...
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10/21/2020
Riemannian Langevin Algorithm for Solving Semidefinite Programs
We propose a Langevin diffusion-based algorithm for non-convex optimizat...
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07/22/2020
A Brief Note on the Convergence of Langevin Monte Carlo in Chi-Square Divergence
We study sampling from a target distribution ν_* ∝ e^-f using the unadju...
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06/16/2020
Hausdorff Dimension, Stochastic Differential Equations, and Generalization in Neural Networks
Despite its success in a wide range of applications, characterizing the ...
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06/14/2020
An Analysis of Constant Step Size SGD in the Non-convex Regime: Asymptotic Normality and Bias
Structured non-convex learning problems, for which critical points have ...
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05/27/2020
On the Convergence of Langevin Monte Carlo: The Interplay between Tail Growth and Smoothness
We study sampling from a target distribution ν_* = e^-f using the unadju...
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06/19/2019
Stochastic Runge-Kutta Accelerates Langevin Monte Carlo and Beyond
Sampling with Markov chain Monte Carlo methods typically amounts to disc...
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04/03/2019
Normal Approximation for Stochastic Gradient Descent via Non-Asymptotic Rates of Martingale CLT
We provide non-asymptotic convergence rates of the Polyak-Ruppert averag...
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10/29/2018
Global Non-convex Optimization with Discretized Diffusions
An Euler discretization of the Langevin diffusion is known to converge t...
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07/12/2018
Convergence Rate of Block-Coordinate Maximization Burer-Monteiro Method for Solving Large SDPs
Semidefinite programming (SDP) with equality constraints arise in many o...
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09/19/2017
Inference in Graphical Models via Semidefinite Programming Hierarchies
Maximum A posteriori Probability (MAP) inference in graphical models amo...
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11/21/2016
Scalable Approximations for Generalized Linear Problems
In stochastic optimization, the population risk is generally approximate...
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11/28/2015
Newton-Stein Method: An optimization method for GLMs via Stein's Lemma
We consider the problem of efficiently computing the maximum likelihood ...
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08/12/2015
