Variational inference (VI) seeks to approximate a target distribution $\pi $ by an element of a
tractable family of distributions. Of key interest in statistics and machine learning is Gaussian …

Wasserstein gradient flows are continuous time dynamics that define curves of steepest
descent to minimize an objective function over the space of probability measures (ie, the …

We consider the task of sampling with respect to a log concave probability distribution. The
potential of the target distribution is assumed to be composite, ie, written as the sum of a …

We propose a new algorithm---Stochastic Proximal Langevin Algorithm (SPLA)---for
sampling from a log concave distribution. Our method is a generalization of the Langevin …

The need for statistical estimation with large data sets has reinvigorated interest in iterative
procedures and stochastic optimization. Stochastic approximations are at the forefront of this …

We propose a stochastic gradient framework for solving stochastic composite convex
optimization problems with (possibly) infinite number of linear inclusion constraints that need …

In this paper we consider optimization problems with stochastic composite objective function
subject to (possibly) infinite intersection of constraints. The objective function is expressed in …

A regularized optimization problem over a large unstructured graph is studied, where the
regularization term is tied to the graph geometry. Typical regularization examples include …

In optimization the duality gap between the primal and the dual problems is a measure of the
suboptimality of any primal-dual point. In classical mechanics the equations of motion of a …

A new stochastic primal-dual algorithm for solving a composite optimization problem is
proposed. It is assumed that all the functions/operators that enter the optimization problem …