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.
We propose a projected Wasserstein gradient descent method (pWGD) for high-dimensional Bayesian inference problems.
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
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
By phrasing the problem in this manner, solving the MFG can be interpreted as a special case of training a generative adversarial network (GAN).
State-of-the-art numerical methods for solving such problems utilize spatial discretization that leads to a curse-of-dimensionality.
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
We propose regularization strategies for learning discriminative models that are robust to in-class variations of the input data.
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.
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