332 citations · 962 across the 43 of their papers we have counts for
12 papers · 1 filter
Distributional Shrinkage I: Universal Denoiser Beyond Tweedie's Formula
Tengyuan Liang
We study the problem of denoising when only the noise level is known, not the noise distribution. Independent noise corrupts a signal , yielding the observation …
No-Regret Generative Modeling via Parabolic Monge-Ampère PDE
Nabarun Deb, Tengyuan Liang
We introduce a novel generative modeling framework based on a discretized parabolic Monge-Ampère PDE, which emerges as a continuous limit of the Sinkhorn algorithm commonly used in…
Denoising Diffusions with Optimal Transport: Localization, Curvature, and Multi-Scale Complexity
Tengyuan Liang, Kulunu Dharmakeerthi, Takuya Koriyama
Adding noise is easy; what about denoising? Diffusion is easy; what about reverting a diffusion? Diffusion-based generative models aim to denoise a Langevin diffusion chain, moving…
Blessings and Curses of Covariate Shifts: Adversarial Learning Dynamics, Directional Convergence, and Equilibria
Tengyuan Liang
Covariate distribution shifts and adversarial perturbations present robustness challenges to the conventional statistical learning framework: mild shifts in the test covariate dist…
Universal Prediction Band via Semi-Definite Programming
Tengyuan Liang
We propose a computationally efficient method to construct nonparametric, heteroscedastic prediction bands for uncertainty quantification, with or without any user-specified predic…
Interpolating Classifiers Make Few Mistakes
Tengyuan Liang, Benjamin Recht
This paper provides elementary analyses of the regret and generalization of minimum-norm interpolating classifiers (MNIC). The MNIC is the function of smallest Reproducing Kernel H…
Mehler's Formula, Branching Process, and Compositional Kernels of Deep Neural Networks
Tengyuan Liang, Hai Tran-Bach
We utilize a connection between compositional kernels and branching processes via Mehler's formula to study deep neural networks. This new probabilistic insight provides us a novel…
Training Neural Networks as Learning Data-adaptive Kernels: Provable Representation and Approximation Benefits
Xialiang Dou, Tengyuan Liang
Consider the problem: given the data pair drawn from a population with , specify a neural network model…
Interaction Matters: A Note on Non-asymptotic Local Convergence of Generative Adversarial Networks
Tengyuan Liang, James Stokes
Motivated by the pursuit of a systematic computational and algorithmic understanding of Generative Adversarial Networks (GANs), we present a simple yet unified non-asymptotic local…
How Well Can Generative Adversarial Networks Learn Densities: A Nonparametric View
Tengyuan Liang
We study in this paper the rate of convergence for learning densities under the Generative Adversarial Networks (GAN) framework, borrowing insights from nonparametric statistics. W…
Statistical Inference for the Population Landscape via Moment Adjusted Stochastic Gradients
Tengyuan Liang, Weijie Su
Modern statistical inference tasks often require iterative optimization methods to compute the solution. Convergence analysis from an optimization viewpoint only informs us how wel…
Learning with Square Loss: Localization through Offset Rademacher Complexity
Tengyuan Liang, Alexander Rakhlin, Karthik Sridharan
We consider regression with square loss and general classes of functions without the boundedness assumption. We introduce a notion of offset Rademacher complexity that provides a t…