Related papers: Estimation of Gaussian mixtures in small sample st…
In this paper, we first consider the parameter estimation of a multivariate random process distribution using multivariate Gaussian mixture law. The labels of the mixture are allowed to have a general probability law which gives the…
In this paper, we propose a regularized mixture probabilistic model to cluster matrix data and apply it to brain signals. The approach is able to capture the sparsity (low rank, small/zero values) of the original signals by introducing…
Problems of probabilistic inference and decision making under uncertainty commonly involve continuous random variables. Often these are discretized to a few points, to simplify assessments and computations. An alternative approximation is…
The generalized estimating equation (GEE) method is a popular tool for longitudinal data analysis. However, GEE produces biased estimates when the outcome of interest is associated with cluster size, a phenomenon known as informative…
We consider efficient estimation of flexible transformation models with interval-censored data. To reduce the dimension of semi-parametric models, the unknown monotone transformation function is approximated via monotone splines. A…
A penalized maximum likelihood estimation approach is proposed for discrete-time hidden Markov models where covariates affect the observed responses and serial dependence is considered. The proposed penalized maximum likelihood method…
We consider the problem of Gaussian mixture clustering in the high-dimensional limit where the data consists of $m$ points in $n$ dimensions, $n,m \rightarrow \infty$ and $\alpha = m/n$ stays finite. Using exact but non-rigorous methods…
Maximum likelihood estimation in logistic regression with mixed effects is known to often result in estimates on the boundary of the parameter space. Such estimates, which include infinite values for fixed effects and singular or infinite…
The mixture model is undoubtedly one of the greatest contributions to clustering. For continuous data, Gaussian models are often used and the Expectation-Maximization (EM) algorithm is particularly suitable for estimating parameters from…
For data with high-dimensional covariates but small to moderate sample sizes, the analysis of single datasets often generates unsatisfactory results. The integrative analysis of multiple independent datasets provides an effective way of…
We study a framework of regularized $K$-means methods based on direct penalization of the size of the cluster centers. Different penalization strategies are considered and compared through simulation and theoretical analysis. Based on the…
We address the new problem of estimating a piece-wise constant signal with the purpose of detecting its change points and the levels of clusters. Our approach is to model it as a nonparametric penalized least square model selection on a…
In sparse Bayesian learning (SBL), Gaussian scale mixtures (GSMs) have been used to model sparsity-inducing priors that realize a class of concave penalty functions for the regression task in real-valued signal models. Motivated by the…
Training the parameters of statistical models to describe a given data set is a central task in the field of data mining and machine learning. A very popular and powerful way of parameter estimation is the method of maximum likelihood…
Channel estimation in quantized systems is challenging, particularly in low-resolution systems. In this work, we propose to leverage a Gaussian mixture model (GMM) as generative prior, capturing the channel distribution of the propagation…
We develop a method for estimating well-conditioned and sparse covariance and inverse covariance matrices from a sample of vectors drawn from a sub-gaussian distribution in high dimensional setting. The proposed estimators are obtained by…
This paper studies the partial estimation of Gaussian graphical models from high-dimensional empirical observations. We derive a convex formulation for this problem using $\ell_1$-regularized maximum-likelihood estimation, which can be…
Clustering is a widely used technique with a long and rich history in a variety of areas. However, most existing algorithms do not scale well to large datasets, or are missing theoretical guarantees of convergence. This paper introduces a…
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…
We study the problem of estimating a $p$-dimensional $s$-sparse vector in a linear model with Gaussian design and additive noise. In the case where the labels are contaminated by at most $o$ adversarial outliers, we prove that the…