Related papers: FEMDA: a unified framework for discriminant analys…
Fisher's linear discriminant analysis is a classical method for classification, yet it is limited to capturing linear features only. Kernel discriminant analysis as an extension is known to successfully alleviate the limitation through a…
The recently developed semi-parametric generalized linear model (SPGLM) offers more flexibility as compared to the classical GLM by including the baseline or reference distribution of the response as an additional parameter in the model.…
Estimation-of-distribution algorithms (EDAs) are general metaheuristics used in optimization that represent a more recent alternative to classical approaches like evolutionary algorithms. In a nutshell, EDAs typically do not directly evolve…
This article carries out a large dimensional analysis of standard regularized discriminant analysis classifiers designed on the assumption that data arise from a Gaussian mixture model with different means and covariances. The analysis…
Copulas provide a modular parameterization of multivariate distributions that decouples the modeling of marginals from the dependencies between them. Gaussian Mixture Copula Model (GMCM) is a highly flexible copula that can model many kinds…
Flexible systems are linear systems of inclusions in which the elements of the coefficient matrix are external numbers in the sense of nonstandard analysis. External numbers represent real numbers with small, individual error terms. Using…
Functional linear discriminant analysis (FLDA) is a powerful tool that extends LDA-mediated multiclass classification and dimension reduction to univariate time-series functions. However, in the age of large multivariate and incomplete…
The adoption of probabilistic models for the best individuals found so far is a powerful approach for evolutionary computation. Increasingly more complex models have been used by estimation of distribution algorithms (EDAs), which often…
A new method for analyzing high-dimensional categorical data, Linear Latent Structure (LLS) analysis, is presented. LLS models belong to the family of latent structure models, which are mixture distribution models constrained to satisfy the…
In the typical analysis of a data set, a single method is selected for statistical reporting even when equally applicable methods yield very different results. Examples of equally applicable methods can correspond to those of different…
In many applications it is desirable to infer coarse-grained models from observational data. The observed process often corresponds only to a few selected degrees of freedom of a high-dimensional dynamical system with multiple time scales.…
This article addresses the problem of classification method based on both labeled and unlabeled data, where we assume that a density function for labeled data is different from that for unlabeled data. We propose a semi-supervised logistic…
This paper develops a novel hybrid approach for estimating the mixture model of $t$-factor analyzers (MtFA) that employs multivariate $t$-distribution and factor model to cluster and characterize grouped data. The traditional estimation…
In high-dimensional statistics, the Lasso is a cornerstone method for simultaneous variable selection and parameter estimation. However, its reliance on the squared loss function renders it highly sensitive to outliers and heavy-tailed…
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.…
We present a novel algorithm aimed at identifying peaks within a uniformly sampled time series affected by uncorrelated Gaussian noise. The algorithm, called "MEPSA" (multiple excess peak search algorithm), essentially scans the time series…
This work performs a non-asymptotic analysis of the generalized Lasso under the assumption of sub-exponential data. Our main results continue recent research on the benchmark case of (sub-)Gaussian sample distributions and thereby explore…
In this article the issues are discussed with the Bayesian approach, least-square fits, and most-likely fits. Trying to counter these issues, a method, based on weighted confidence, is proposed for estimating probabilities and other…
Linear discriminant analysis (LDA) is an important classification tool in statistics and machine learning. This paper investigates the varying coefficient LDA model for dynamic data, with Bayes' discriminant direction being a function of…
By distributing the training process, local approximation reduces the cost of the standard Gaussian Process. An ensemble technique combines local predictions from Gaussian experts trained on different partitions of the data. Ensemble…