no code implementations • 9 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.

no code implementations • 1 Feb 2024 • Qi Feng, Xinzhe Zuo, Wuchen Li

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

no code implementations • 22 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.

1 code implementation • 28 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.

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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