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08/03/2023
Online covariance estimation for stochastic gradient descent under Markovian sampling
We study the online overlapping batch-means covariance estimator for Sto...
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07/11/2023
Stochastic Nested Compositional Bi-level Optimization for Robust Feature Learning
We develop and analyze stochastic approximation algorithms for solving n...
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06/28/2023
Gaussian random field approximation via Stein's method with applications to wide random neural networks
We derive upper bounds on the Wasserstein distance (W_1), with respect t...
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06/21/2023
Optimal Algorithms for Stochastic Bilevel Optimization under Relaxed Smoothness Conditions
Stochastic Bilevel optimization usually involves minimizing an upper-lev...
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05/23/2023
Towards Understanding the Dynamics of Gaussian-Stein Variational Gradient Descent
Stein Variational Gradient Descent (SVGD) is a nonparametric particle-ba...
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04/10/2023
Forward-backward Gaussian variational inference via JKO in the Bures-Wasserstein Space
Variational inference (VI) seeks to approximate a target distribution π ...
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04/03/2023
High-dimensional scaling limits and fluctuations of online least-squares SGD with smooth covariance
We derive high-dimensional scaling limits and fluctuations for the onlin...
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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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02/20/2023
A One-Sample Decentralized Proximal Algorithm for Non-Convex Stochastic Composite Optimization
We focus on decentralized stochastic non-convex optimization, where n ag...
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02/20/2023
High-dimensional Central Limit Theorems for Linear Functionals of Online Least-Squares SGD
Stochastic gradient descent (SGD) has emerged as the quintessential meth...
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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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11/15/2022
Regularized Stein Variational Gradient Flow
The Stein Variational Gradient Descent (SVGD) algorithm is an determinis...
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10/23/2022
Decentralized Stochastic Bilevel Optimization with Improved Per-Iteration Complexity
Bilevel optimization recently has received tremendous attention due to i...
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10/19/2022
A Flexible Approach for Normal Approximation of Geometric and Topological Statistics
We derive normal approximation results for a class of stabilizing functi...
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06/22/2022
Projection-free Constrained Stochastic Nonconvex Optimization with State-dependent Markov Data
We study a projection-free conditional gradient-type algorithm for const...
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06/08/2022
Unified RKHS Methodology and Analysis for Functional Linear and Single-Index Models
Functional linear and single-index models are core regression methods in...
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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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02/09/2022
A Projection-free Algorithm for Constrained Stochastic Multi-level Composition Optimization
We propose a projection-free conditional gradient-type algorithm for smo...
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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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10/26/2021
Topologically penalized regression on manifolds
We study a regression problem on a compact manifold M. In order to take ...
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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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05/18/2021
Nonparametric Modeling of Higher-Order Interactions via Hypergraphons
We study statistical and algorithmic aspects of using hypergraphons, tha...
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02/10/2021
Statistical Inference for Polyak-Ruppert Averaged Zeroth-order Stochastic Gradient Algorithm
As machine learning models are deployed in critical applications, it bec...
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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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09/28/2020
Escaping Saddle-Points Faster under Interpolation-like Conditions
In this paper, we show that under over-parametrization several standard ...
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08/24/2020
Stochastic Multi-level Composition Optimization Algorithms with Level-Independent Convergence Rates
In this paper, we study smooth stochastic multi-level composition optimi...
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08/07/2020
Fractal Gaussian Networks: A sparse random graph model based on Gaussian Multiplicative Chaos
We propose a novel stochastic network model, called Fractal Gaussian Net...
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06/15/2020
Improved Complexities for Stochastic Conditional Gradient Methods under Interpolation-like Conditions
We analyze stochastic conditional gradient type methods for constrained ...
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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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03/25/2020
Zeroth-order Optimization on Riemannian Manifolds
We propose and analyze zeroth-order algorithms for optimization over Rie...
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01/22/2020
Zeroth-Order Algorithms for Nonconvex Minimax Problems with Improved Complexities
In this paper, we study zeroth-order algorithms for minimax optimization...
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12/03/2019
Online and Bandit Algorithms for Nonstationary Stochastic Saddle-Point Optimization
Saddle-point optimization problems are an important class of optimizatio...
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07/31/2019
Multi-Point Bandit Algorithms for Nonstationary Online Nonconvex Optimization
Bandit algorithms have been predominantly analyzed in the convex setting...
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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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02/04/2019
Non-asymptotic Results for Langevin Monte Carlo: Coordinate-wise and Black-box Sampling
Euler-Maruyama and Ozaki discretization of a continuous time diffusion p...
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09/17/2018
Zeroth-order (Non)-Convex Stochastic Optimization via Conditional Gradient and Gradient Updates
In this paper, we propose and analyze zeroth-order stochastic approximat...
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07/17/2018
Tensor Methods for Additive Index Models under Discordance and Heterogeneity
Motivated by the sampling problems and heterogeneity issues common in hi...
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09/26/2017
On Stein's Identity and Near-Optimal Estimation in High-dimensional Index Models
We consider estimating the parametric components of semi-parametric mult...
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09/24/2017
On the Optimality of Kernel-Embedding Based Goodness-of-Fit Tests
The reproducing kernel Hilbert space (RKHS) embedding of distributions o...
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09/26/2013
High-dimensional Joint Sparsity Random Effects Model for Multi-task Learning
Joint sparsity regularization in multi-task learning has attracted much ...
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10/03/2012
Smooth Sparse Coding via Marginal Regression for Learning Sparse Representations
We propose and analyze a novel framework for learning sparse representat...
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06/27/2012
