Related papers: FEMDA: a unified framework for discriminant analys…
Expectation maximization (EM) algorithm is to find maximum likelihood solution for models having latent variables. A typical example is Gaussian Mixture Model (GMM) which requires Gaussian assumption, however, natural images are highly…
Graphical model has been widely used to investigate the complex dependence structure of high-dimensional data, and it is common to assume that observed data follow a homogeneous graphical model. However, observations usually come from…
With the recent growth in data availability and complexity, and the associated outburst of elaborate modelling approaches, model selection tools have become a lifeline, providing objective criteria to deal with this increasingly challenging…
This paper introduces the Trimmed Functional Empirical Process (TFEP) as a robust framework for statistical inference when dealing with heavy-tailed or skewed distributions, where classical moments such as the mean or variance may be…
This paper introduces a novel theoretically sound approach for the celebrated CMA-ES algorithm. Assuming the parameters of the multi variate normal distribution for the minimum follow a conjugate prior distribution, we derive their optimal…
Recent studies in the literature have paid much attention to the sparsity in linear classification tasks. One motivation of imposing sparsity assumption on the linear discriminant direction is to rule out the noninformative features, making…
The Bayesian approach to inference stands out for naturally allowing borrowing information across heterogeneous populations, with different samples possibly sharing the same distribution. A popular Bayesian nonparametric model for…
Clustering is essential in data analysis and machine learning, but traditional algorithms like $k$-means and Gaussian Mixture Models (GMM) often fail with nonconvex clusters. To address the challenge, we introduce the Flexible Bivariate…
Clustering analysis is one of the most widely used statistical tools in many emerging areas such as microarray data analysis. For microarray and other high-dimensional data, the presence of many noise variables may mask underlying…
Linear Discriminant Analysis (LDA) is a well-known method for dimensionality reduction and classification. Previous studies have also extended the binary-class case into multi-classes. However, many applications, such as object detection…
We consider the problem of inference in a linear regression model in which the relative ordering of the input features and output labels is not known. Such datasets naturally arise from experiments in which the samples are shuffled or…
Classical discriminant analysis (DA) is based on the mean and empirical covariance matrix of each class, both of which are sensitive to outliers in the data. In the past the focus was on casewise outliers, that is, datapoints that lie far…
In numerous instances, the generalized exponential distribution can be used as an alternative to the most widely used non-regular family of distributions: Weibull, gamma, lognormal with three-parameters when analyzing lifetime or any skewed…
We consider maximum likelihood estimation for Gaussian Mixture Models (Gmms). This task is almost invariably solved (in theory and practice) via the Expectation Maximization (EM) algorithm. EM owes its success to various factors, of which…
A new, coordinate-free (geometric) approach to multivariate statistical analysis. General multivariate linear models and linear hypotheses are defined in geometric form. A method of constructing statistical criteria is defined for linear…
Non linear mixed effect models are classical tools to analyze non linear longitudinal data in many fields such as population Pharmacokinetic. Groups of observations are usually compared by introducing the group affiliations as binary…
This article proposes a new class of Real Elliptically Skewed (RESK) distributions and associated clustering algorithms that allow for integrating robustness and skewness into a single unified cluster analysis framework. Non-symmetrically…
Gaussian empirical Bayes methods usually maintain a precision independence assumption: The unknown parameters of interest are independent from the known standard errors of the estimates. This assumption is often theoretically questionable…
In many social, economical, biological and medical studies, one objective is to classify a subject into one of several classes based on a set of variables observed from the subject. Because the probability distribution of the variables is…
Various regularized linear discriminant analysis (LDA) methods have been proposed to address the problems of the classic methods in high-dimensional settings. Asymptotic optimality has been established for some of these methods in high…