Search Results for author: Wuchen Li

Found 18 papers, 9 papers with code

Wasserstein proximal operators describe score-based generative models and resolve memorization

no code implementations9 Feb 2024 Benjamin J. Zhang, Siting Liu, Wuchen Li, Markos A. Katsoulakis, Stanley J. Osher

Via a Cole-Hopf transformation and taking advantage of the fact that the cross-entropy can be related to a linear functional of the density, we show that the HJB equation is an uncontrolled FP equation.

Inductive Bias Memorization

Fisher information dissipation for time inhomogeneous stochastic differential equations

no code implementations1 Feb 2024 Qi Feng, Xinzhe Zuo, Wuchen Li

We also verify the convergence condition for the underdamped Langevin dynamics.

Scaling Limits of the Wasserstein information matrix on Gaussian Mixture Models

no code implementations22 Sep 2023 Wuchen Li, Jiaxi Zhao

We consider the Wasserstein metric on the Gaussian mixture models (GMMs), which is defined as the pullback of the full Wasserstein metric on the space of smooth probability distributions with finite second moment.

Noise-Free Sampling Algorithms via Regularized Wasserstein Proximals

1 code implementation28 Aug 2023 Hong Ye Tan, Stanley Osher, Wuchen Li

The score term is given in closed form by a regularized Wasserstein proximal, using a kernel convolution that is approximated by sampling.

Optimal Neural Network Approximation of Wasserstein Gradient Direction via Convex Optimization

1 code implementation26 May 2022 Yifei Wang, Peng Chen, Mert Pilanci, Wuchen Li

We study the variational problem in the family of two-layer networks with squared-ReLU activations, towards which we derive a semi-definite programming (SDP) relaxation.

Bayesian Inference

Wasserstein Proximal of GANs

no code implementations ICLR 2019 Alex Tong Lin, Wuchen Li, Stanley Osher, Guido Montufar

We introduce a new method for training generative adversarial networks by applying the Wasserstein-2 metric proximal on the generators.

Projected Wasserstein gradient descent for high-dimensional Bayesian inference

1 code implementation12 Feb 2021 Yifei Wang, Peng Chen, Wuchen Li

We propose a projected Wasserstein gradient descent method (pWGD) for high-dimensional Bayesian inference problems.

Bayesian Inference Density Estimation +1

Transport information Hessian distances

no code implementations8 Feb 2021 Wuchen Li

We formulate closed-form Hessian distances of information entropies in one-dimensional probability density space embedded with the L2-Wasserstein metric.

Metric Geometry Information Theory Dynamical Systems Information Theory

Transport information Bregman divergences

no code implementations4 Jan 2021 Wuchen Li

We study Bregman divergences in probability density space embedded with the $L^2$--Wasserstein metric.

Entropy dissipation for some non-reversible stochastic differential equations

no code implementations16 Nov 2020 Qi Feng, Wuchen Li

We formulate explicit bounds to guarantee the exponential dissipation for some non-gradient stochastic differential equations towards their invariant distributions.

Probability Dynamical Systems Optimization and Control

Alternating the Population and Control Neural Networks to Solve High-Dimensional Stochastic Mean-Field Games

1 code implementation24 Feb 2020 Alex Tong Lin, Samy Wu Fung, Wuchen Li, Levon Nurbekyan, Stanley J. Osher

By phrasing the problem in this manner, solving the MFG can be interpreted as a special case of training a generative adversarial network (GAN).

Generative Adversarial Network

Information Newton's flow: second-order optimization method in probability space

no code implementations13 Jan 2020 Yifei Wang, Wuchen Li

We introduce a framework for Newton's flows in probability space with information metrics, named information Newton's flows.

A Machine Learning Framework for Solving High-Dimensional Mean Field Game and Mean Field Control Problems

1 code implementation4 Dec 2019 Lars Ruthotto, Stanley Osher, Wuchen Li, Levon Nurbekyan, Samy Wu Fung

State-of-the-art numerical methods for solving such problems utilize spatial discretization that leads to a curse-of-dimensionality.

BIG-bench Machine Learning

Tropical Optimal Transport and Wasserstein Distances

1 code implementation13 Nov 2019 Wonjun Lee, Wuchen Li, Bo Lin, Anthea Monod

We study the problem of optimal transport in tropical geometry and define the Wasserstein-$p$ distances in the continuous metric measure space setting of the tropical projective torus.

Optimization and Control Metric Geometry Statistics Theory Statistics Theory

Kernelized Wasserstein Natural Gradient

1 code implementation ICLR 2020 Michael Arbel, Arthur Gretton, Wuchen Li, Guido Montufar

Many machine learning problems can be expressed as the optimization of some cost functional over a parametric family of probability distributions.

Wasserstein Diffusion Tikhonov Regularization

no code implementations15 Sep 2019 Alex Tong Lin, Yonatan Dukler, Wuchen Li, Guido Montufar

We propose regularization strategies for learning discriminative models that are robust to in-class variations of the input data.

Data Augmentation

Accelerated Information Gradient flow

1 code implementation4 Sep 2019 Yifei Wang, Wuchen Li

We present a framework for Nesterov's accelerated gradient flows in probability space to design efficient mean-field Markov chain Monte Carlo (MCMC) algorithms for Bayesian inverse problems.

Bayesian Inference

Unnormalized Optimal Transport

1 code implementation9 Feb 2019 Wilfrid Gangbo, Wuchen Li, Stanley Osher, Michael Puthawala

We propose an extension of the computational fluid mechanics approach to the Monge-Kantorovich mass transfer problem, which was developed by Benamou-Brenier.

Optimization and Control

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