483 citations · 760 across the 48 of their papers we have counts for
13 papers · 1 filter
A Geometric Analysis of PCA
Ayoub El Hanchi, Murat Erdogdu, Chris Maddison
What property of the data distribution determines the excess risk of principal component analysis? In this paper, we provide a precise answer to this question. We establish a centr…
Minimax Linear Regression under the Quantile Risk
Ayoub El Hanchi, Chris J. Maddison, Murat A. Erdogdu
We study the problem of designing minimax procedures in linear regression under the quantile risk. We start by considering the realizable setting with independent Gaussian noise, w…
A Separation in Heavy-Tailed Sampling: Gaussian vs. Stable Oracles for Proximal Samplers
Ye He, Alireza Mousavi-Hosseini, Krishnakumar Balasubramanian +1
We study the complexity of heavy-tailed sampling and present a separation result in terms of obtaining high-accuracy versus low-accuracy guarantees i.e., samplers that require only…
Sampling from the Mean-Field Stationary Distribution
Yunbum Kook, Matthew S. Zhang, Sinho Chewi +2
We study the complexity of sampling from the stationary distribution of a mean-field SDE, or equivalently, the complexity of minimizing a functional over the space of probability m…
Optimal Excess Risk Bounds for Empirical Risk Minimization on -Norm Linear Regression
Ayoub El Hanchi, Murat A. Erdogdu
We study the performance of empirical risk minimization on the -norm linear regression problem for . We show that, in the realizable case, under no moment ass…
Towards a Complete Analysis of Langevin Monte Carlo: Beyond Poincaré Inequality
Alireza Mousavi-Hosseini, Tyler Farghly, Ye He +2
Langevin diffusions are rapidly convergent under appropriate functional inequality assumptions. Hence, it is natural to expect that with additional smoothness conditions to handle…
Mean-Square Analysis of Discretized Itô Diffusions for Heavy-tailed Sampling
Ye He, Tyler Farghly, Krishnakumar Balasubramanian +1
We analyze the complexity of sampling from a class of heavy-tailed distributions by discretizing a natural class of Itô diffusions associated with weighted Poincaré inequalities. B…
Improved Discretization Analysis for Underdamped Langevin Monte Carlo
Matthew Zhang, Sinho Chewi, Mufan Bill Li +2
Underdamped Langevin Monte Carlo (ULMC) is an algorithm used to sample from unnormalized densities by leveraging the momentum of a particle moving in a potential well. We provide a…
Towards a Theory of Non-Log-Concave Sampling: First-Order Stationarity Guarantees for Langevin Monte Carlo
Krishnakumar Balasubramanian, Sinho Chewi, Murat A. Erdogdu +2
For the task of sampling from a density on , where is possibly non-convex but -gradient Lipschitz, we prove that averaged Langevin Monte Ca…
Heavy-tailed Sampling via Transformed Unadjusted Langevin Algorithm
Ye He, Krishnakumar Balasubramanian, Murat A. Erdogdu
We analyze the oracle complexity of sampling from polynomially decaying heavy-tailed target densities based on running the Unadjusted Langevin Algorithm on certain transformed vers…
On Empirical Risk Minimization with Dependent and Heavy-Tailed Data
Abhishek Roy, Krishnakumar Balasubramanian, Murat A. Erdogdu
In this work, we establish risk bounds for the Empirical Risk Minimization (ERM) with both dependent and heavy-tailed data-generating processes. We do so by extending the seminal w…
Normal Approximation for Stochastic Gradient Descent via Non-Asymptotic Rates of Martingale CLT
Andreas Anastasiou, Krishnakumar Balasubramanian, Murat A. Erdogdu
We provide non-asymptotic convergence rates of the Polyak-Ruppert averaged stochastic gradient descent (SGD) to a normal random vector for a class of twice-differentiable test func…
Flexible results for quadratic forms with applications to variance components estimation
Lee H. Dicker, Murat A. Erdogdu
We derive convenient uniform concentration bounds and finite sample multivariate normal approximation results for quadratic forms, then describe some applications involving varianc…