Related papers: Mean field variational framework for integer optim…
Variational inference is a popular method for estimating model parameters and conditional distributions in hierarchical and mixed models, which arise frequently in many settings in the health, social, and biological sciences. Variational…
We propose a method for variable selection in discriminant analysis with mixed categorical and continuous variables. This method is based on a criterion that permits to reduce the variable selection problem to a problem of estimating…
In this paper, we study a mean-variance optimization problem in an infinite horizon discrete time discounted Markov decision process (MDP). The objective is to minimize the variance of system rewards with the constraint of mean performance.…
In many applications of machine learning, a large number of variables are considered. Motivated by machine learning of interacting particle systems, we consider the situation when the number of input variables goes to infinity. First, we…
In this paper, we propose an efficient and flexible algorithm to solve dynamic mean-field planning problems based on an accelerated proximal gradient method. Besides an easy-to-implement gradient descent step in this algorithm, a crucial…
Variational inference uses optimization, rather than integration, to approximate the marginal likelihood, and thereby the posterior, in a Bayesian model. Thanks to advances in computational scalability made in the last decade, variational…
The policy iteration method is a classical algorithm for solving optimal control problems. In this paper, we introduce a policy iteration method for Mean Field Games systems, and we study the convergence of this procedure to a solution of…
Unsupervised learning requiring only raw data is not only a fundamental function of the cerebral cortex, but also a foundation for a next generation of artificial neural networks. However, a unified theoretical framework to treat sensory…
We present a generalization of the variational principle that is compatible with any Hamiltonian eigenstate that can be specified uniquely by a list of properties. This variational principle appears to be compatible with a wide range of…
We investigate systems of interacting stochastic differential equations with two kinds of heterogeneity: one originating from different weights of the linkages, and one concerning their asymptotic relevance when the system becomes large. To…
We consider a stochastic variant of the packing-type integer linear programming problem, which contains random variables in the objective vector. We are allowed to reveal each entry of the objective vector by conducting a query, and the…
Estimating and optimizing Mutual Information (MI) is core to many problems in machine learning; however, bounding MI in high dimensions is challenging. To establish tractable and scalable objectives, recent work has turned to variational…
The article develops a hybrid Variational Bayes algorithm that combines the mean-field and fixed-form Variational Bayes methods. The new estimation algorithm can be used to approximate any posterior without relying on conjugate priors. We…
This work focuses on the mean field stochastic partial differential equations with nonlinear kernels. We first prove the existence and uniqueness of strong and weak solutions for mean field stochastic partial differential equations in the…
In this paper we provide an analytical framework for investigating the efficiency of a consensus-based model for tackling global optimization problems. This work justifies the optimization algorithm in the mean-field sense showing the…
The mean field variational inference (MFVI) formulation restricts the general Bayesian inference problem to the subspace of product measures. We present a framework to analyze MFVI algorithms, which is inspired by a similar development for…
Feature selection is one of the most fundamental problems in machine learning. An extensive body of work on information-theoretic feature selection exists which is based on maximizing mutual information between subsets of features and class…
With dramatic improvements in optimization software, the solution of large-scale problems that seemed intractable decades ago are now a routine task. This puts even more real-world applications into the reach of optimizers. At the same…
We introduce a novel framework to model and solve mean-field game systems with nonlocal interactions. Our approach relies on kernel-based representations of mean-field interactions and feature-space expansions in the spirit of kernel…
We describe a variational approximation method for efficient inference in large-scale probabilistic models. Variational methods are deterministic procedures that provide approximations to marginal and conditional probabilities of interest.…