Related papers: Differentiable Expectation-Maximisation and Applic…

Model error covariances play a central role in the performance of data assimilation methods applied to nonlinear state-space models. However, these covariances are largely unknown in most of the applications. A misspecification of the model…

The learning of Gaussian Mixture Models (also referred to simply as GMMs) plays an important role in machine learning. Known for their expressiveness and interpretability, Gaussian mixture models have a wide range of applications, from…

The Gaussian mixture model is a classic technique for clustering and data modeling that is used in numerous applications. With the rise of big data, there is a need for parameter estimation techniques that can handle streaming data and…

Empirical divergence maximization (EDM) refers to a recently proposed strategy for estimating f-divergences and likelihood ratio functions. This paper extends the idea to empirical vector quantization where one seeks to empirically derive…

We consider a symmetric mixture of linear regressions with random samples from the pairwise comparison design, which can be seen as a noisy version of a type of Euclidean distance geometry problem. We analyze the expectation-maximization…

Maximum likelihood estimation (MLE) is one of the most important methods in machine learning, and the expectation-maximization (EM) algorithm is often used to obtain maximum likelihood estimates. However, EM heavily depends on initial…

Earth System Models (ESMs) are the primary tools for investigating future Earth system states at time scales from decades to centuries, especially in response to anthropogenic greenhouse gas release. State-of-the-art ESMs can reproduce the…

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 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.…

Motivated by a recent result of Daskalakis et al. 2018, we analyze the population version of Expectation-Maximization (EM) algorithm for the case of \textit{truncated} mixtures of two Gaussians. Truncated samples from a $d$-dimensional…

Gromov--Wasserstein (GW) distances compare graphs, shapes, and point clouds through internal distances, without requiring a common coordinate system. This invariance is powerful, but discrete GW is a nonconvex quadratic optimal transport…

The Gaussian mixture model (GMM) provides a simple yet principled framework for clustering, with properties suitable for statistical inference. In this paper, we propose a new model-based clustering algorithm, called EGMM (evidential GMM),…

High-dimensional data clustering has become and remains a challenging task for modern statistics and machine learning, with a wide range of applications. We consider in this work the powerful discriminative latent mixture model, and we…

A novel neural architecture was recently developed that enforces an exact upper bound on the Lipschitz constant of the model by constraining the norm of its weights in a minimal way, resulting in higher expressiveness compared to other…

Expectation maximization (EM) is a technique for estimating maximum-likelihood parameters of a latent variable model given observed data by alternating between taking expectations of sufficient statistics, and maximizing the expected log…

Modeling of high-dimensional data is very important to categorize different classes. We develop a new mixture model called Multinomial cluster-weighted model (MCWM). We derive the identifiability of a general class of MCWM. We estimate the…

We propose a framework, named Aggregated Wasserstein, for computing a dissimilarity measure or distance between two Hidden Markov Models with state conditional distributions being Gaussian. For such HMMs, the marginal distribution at any…

In this article, we discuss two specific classes of models - Gaussian Mixture Copula models and Mixture of Factor Analyzers - and the advantages of doing inference with gradient descent using automatic differentiation. Gaussian mixture…

We consider the problem of estimating the parameters a Gaussian Mixture Model with K components of known weights, all with an identity covariance matrix. We make two contributions. First, at the population level, we present a sharper…

Finite mixture models have been widely used for the modelling and analysis of data from heterogeneous populations. Maximum likelihood estimation of the parameters is typically carried out via the Expectation-Maximization (EM) algorithm. The…