Related papers: Sharp Analysis of Expectation-Maximization for Wea…

While mixture of linear regressions (MLR) is a well-studied topic, prior works usually do not analyze such models for prediction error. In fact, {\em prediction} and {\em loss} are not well-defined in the context of mixtures. In this paper,…

We propose a novel distributed expectation maximization (EM) method for non-cooperative RF device localization using a wireless sensor network. We consider the scenario where few or no sensors receive line-of-sight signals from the target.…

Deep Learning methods are known to suffer from calibration issues: they typically produce over-confident estimates. These problems are exacerbated in the low data regime. Although the calibration of probabilistic models is well studied,…

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…

Finite mixture models have been widely used to model and analyze data from a heterogeneous populations. Moreover, data of this kind can be missing or subject to some upper and/or lower detection limits because of the restriction of…

Model-based clustering approaches concern the paradigm of exploratory data analysis relying on the finite mixture model to automatically find a latent structure governing observed data. They are one of the most popular and successful…

Error bound conditions (EBC) are properties that characterize the growth of an objective function when a point is moved away from the optimal set. They have recently received increasing attention in the field of optimization for developing…

The Extreme Deconvolution method fits a probability density to a dataset where each observation has Gaussian noise added with a known sample-specific covariance, originally intended for use with astronomical datasets. The existing fitting…

We study the nonparametric maximum likelihood estimator $\widehat{\pi}$ for Gaussian location mixtures in one dimension. It has been known since (Lindsay, 1983) that given an $n$-point dataset, this estimator always returns a mixture with…

This paper deals with parameter estimation when the data are randomly right censored. The maximum likelihood estimates from censored samples are obtained by using the expectation-maximization (EM) and Monte Carlo EM (MCEM) algorithms. We…

Softmax mixture models (SMMs) are discrete $K$-mixtures introduced to model the probability of choosing an attribute $x_j \in \RR^L$ from $p$ candidates, in heterogeneous populations. They have been known as mixed multinomial logits in the…

This paper considers an approximate dynamic matrix factor model that accounts for the time series nature of the data by explicitly modelling the time evolution of the factors. We study estimation of the model parameters based on the…

We consider the problem of spherical Gaussian Mixture models with $k \geq 3$ components when the components are well separated. A fundamental previous result established that separation of $\Omega(\sqrt{\log k})$ is necessary and sufficient…

The testing problem for the order of finite mixture models has a long history and remains an active research topic. Since Ghosh and Sen (1985) revealed the hard-to-manage asymptotic properties of the likelihood ratio test, there has been…

In this paper, we firstly give a brief introduction of expectation maximization (EM) algorithm, and then discuss the initial value sensitivity of expectation maximization algorithm. Subsequently, we give a short proof of EM's convergence.…

Many statistical estimators are defined as the fixed point of a data-dependent operator, with estimators based on minimizing a cost function being an important special case. The limiting performance of such estimators depends on the…

Mixed linear regression (MLR) model is among the most exemplary statistical tools for modeling non-linear distributions using a mixture of linear models. When the additive noise in MLR model is Gaussian, Expectation-Maximization (EM)…

A weighted likelihood technique for robust estimation of a multivariate Wrapped Normal distribution for data points scattered on a p-dimensional torus is proposed. The occurrence of outliers in the sample at hand can badly compromise…

Regime shifts in high-dimensional time series arise naturally in many applications, from neuroimaging to finance. This problem has received considerable attention in low-dimensional settings, with both Bayesian and frequentist methods used…

Estimating dynamic discrete choice models with unobserved heterogeneity is computationally costly because it requires repeatedly solving fixed-point equations for all unobserved types. We develop the EM-NPL(q) framework that combines the…