332 citations · 962 across the 43 of their papers we have counts for
15 papers · 1 filter
Distributional Shrinkage II: Higher-Order Scores Encode Brenier Map
Tengyuan Liang
Consider the additive Gaussian model , where is an unknown signal, is independent of , and is known. Let denote the law of .…
Detecting Weak Distribution Shifts via Displacement Interpolation
YoonHaeng Hur, Tengyuan Liang
Detecting weak, systematic distribution shifts and quantitatively modeling individual, heterogeneous responses to policies or incentives have found increasing empirical application…
High-dimensional Asymptotics of Langevin Dynamics in Spiked Matrix Models
Tengyuan Liang, Subhabrata Sen, Pragya Sur
We study Langevin dynamics for recovering the planted signal in the spiked matrix model. We provide a "path-wise" characterization of the overlap between the output of the Langevin…
A Precise High-Dimensional Asymptotic Theory for Boosting and Minimum--Norm Interpolated Classifiers
Tengyuan Liang, Pragya Sur
This paper establishes a precise high-dimensional asymptotic theory for boosting on separable data, taking statistical and computational perspectives. We consider a high-dimensiona…
Estimating Certain Integral Probability Metric (IPM) is as Hard as Estimating under the IPM
Tengyuan Liang
We study the minimax optimal rates for estimating a range of Integral Probability Metrics (IPMs) between two unknown probability measures, based on independent samples from the…
On the Minimax Optimality of Estimating the Wasserstein Metric
Tengyuan Liang
We study the minimax optimal rate for estimating the Wasserstein- metric between two unknown probability measures based on i.i.d. empirical samples from them. We show that e…
On the Multiple Descent of Minimum-Norm Interpolants and Restricted Lower Isometry of Kernels
Tengyuan Liang, Alexander Rakhlin, Xiyu Zhai
We study the risk of minimum-norm interpolants of data in Reproducing Kernel Hilbert Spaces. Our upper bounds on the risk are of a multiple-descent shape for the various scalings o…
How Well Generative Adversarial Networks Learn Distributions
Tengyuan Liang
This paper studies the rates of convergence for learning distributions implicitly with the adversarial framework and Generative Adversarial Networks (GANs), which subsume Wasserste…
Just Interpolate: Kernel "Ridgeless" Regression Can Generalize
Tengyuan Liang, Alexander Rakhlin
In the absence of explicit regularization, Kernel "Ridgeless" Regression with nonlinear kernels has the potential to fit the training data perfectly. It has been observed empirical…
Weighted Message Passing and Minimum Energy Flow for Heterogeneous Stochastic Block Models with Side Information
T. Tony Cai, Tengyuan Liang, Alexander Rakhlin
We study the misclassification error for community detection in general heterogeneous stochastic block models (SBM) with noisy or partial label information. We establish a connecti…
On Detection and Structural Reconstruction of Small-World Random Networks
T. Tony Cai, Tengyuan Liang, Alexander Rakhlin
In this paper, we study detection and fast reconstruction of the celebrated Watts-Strogatz (WS) small-world random graph model \citep{watts1998collective} which aims to describe re…
Inference via Message Passing on Partially Labeled Stochastic Block Models
T. Tony Cai, Tengyuan Liang, Alexander Rakhlin
We study the community detection and recovery problem in partially-labeled stochastic block models (SBM). We develop a fast linearized message-passing algorithm to reconstruct labe…
Computational and Statistical Boundaries for Submatrix Localization in a Large Noisy Matrix
T. Tony Cai, Tengyuan Liang, Alexander Rakhlin
The interplay between computational efficiency and statistical accuracy in high-dimensional inference has drawn increasing attention in the literature. In this paper, we study comp…
Geometric Inference for General High-Dimensional Linear Inverse Problems
T. Tony Cai, Tengyuan Liang, Alexander Rakhlin
This paper presents a unified geometric framework for the statistical analysis of a general ill-posed linear inverse model which includes as special cases noisy compressed sensing,…
Law of Log Determinant of Sample Covariance Matrix and Optimal Estimation of Differential Entropy for High-Dimensional Gaussian Distributions
T. Tony Cai, Tengyuan Liang, Harrison H. Zhou
Differential entropy and log determinant of the covariance matrix of a multivariate Gaussian distribution have many applications in coding, communications, signal processing and st…