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1 code implementation • 26 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.

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.

1 code implementation • 12 Feb 2021 • Yifei Wang, Peng Chen, Wuchen Li

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

no code implementations • 8 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

no code implementations • 4 Jan 2021 • Wuchen Li

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

no code implementations • 16 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

1 code implementation • 24 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).

no code implementations • 13 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.

1 code implementation • 4 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.

1 code implementation • 13 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

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.

no code implementations • 15 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.

1 code implementation • 4 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.

1 code implementation • 9 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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