Related papers: A note on the relations between mixture models, ma…
This chapter describes techniques for the numerical resolution of optimal transport problems. We will consider several discretizations of these problems, and we will put a strong focus on the mathematical analysis of the algorithms to solve…
Mixture modeling is a general technique for making any simple model more expressive through weighted combination. This generality and simplicity in part explains the success of the Expectation Maximization (EM) algorithm, in which updates…
Any clustering algorithm must synchronously learn to model the clusters and allocate data to those clusters in the absence of labels. Mixture model-based methods model clusters with pre-defined statistical distributions and allocate data to…
The purpose of this note is to show how the method of maximum entropy in the mean (MEM) may be used to improve parametric estimation when the measurements are corrupted by large level of noise. The method is developed in the context on a…
This paper addresses the estimation of parameters of a Bayesian network from incomplete data. The task is usually tackled by running the Expectation-Maximization (EM) algorithm several times in order to obtain a high log-likelihood…
Entropic optimal transport (OT) and the Sinkhorn algorithm have made it practical for machine learning practitioners to perform the fundamental task of calculating transport distance between statistical distributions. In this work, we focus…
In this paper, we present a new ensemble-based filter method by reconstructing the analysis step of the particle filter through a transport map, which directly transports prior particles to posterior particles. The transport map is…
In this study, we address the problem of clustering string data in an unsupervised manner by developing a theory of a mixture model and an EM algorithm for string data based on probability theory on a topological monoid of strings developed…
In this work, we propose a novel machine learning approach to compute the optimal transport map between two continuous distributions from their unpaired samples, based on the DeepParticle methods. The proposed method leads to a min-min…
Gaussian mixture models (GMM) are powerful parametric tools with many applications in machine learning and computer vision. Expectation maximization (EM) is the most popular algorithm for estimating the GMM parameters. However, EM…
We propose a new algorithm to approximate the Earth Mover's distance (EMD). Our main idea is motivated by the theory of optimal transport, in which EMD can be reformulated as a familiar $L_1$ type minimization. We use a regularization which…
In this paper, Bayesian parameter estimation through the consideration of the Maximum A Posteriori (MAP) criterion is revisited under the prism of the Expectation-Maximization (EM) algorithm. By incorporating a sparsity-promoting penalty…
We present a bipartite network model that captures intermediate stages of optimization by blending the Maximum Entropy approach with Optimal Transport. In this framework, the network's constraints define the total mass each node can supply…
Mismatch capacity characterizes the highest information rate for a channel under a prescribed decoding metric, and is thus a highly relevant fundamental performance metric when dealing with many practically important communication…
Mechanistic network models specify the mechanisms by which networks grow and change, allowing researchers to investigate complex systems using both simulation and analytical techniques. Unfortunately, it is difficult to write likelihoods…
The Expectation Maximization (EM) algorithm is widely used as an iterative modification to maximum likelihood estimation when the data is incomplete. We focus on a semi-supervised case to learn the model from labeled and unlabeled samples.…
To avoid specification of the error distribution in a regression model, we propose a general nonparametric scale mixture model for the error distribution. For fitting such mixtures, the predictive recursion method is a simple and…
Estimators derived from an EM algorithm are not robust since they are based on the maximization of the likelihood function. We propose a proximal-point algorithm based on the EM algorithm which aim to minimize a divergence criterion.…
Optimal transport has become part of the standard quantitative economics toolbox. It is the framework of choice to describe models of matching with transfers, but beyond that, it allows to: extend quantile regression; identify discrete…
Optimal Transport is a theory that allows to define geometrical notions of distance between probability distributions and to find correspondences, relationships, between sets of points. Many machine learning applications are derived from…