Related papers: Robust estimation of mixing measures in finite mix…
In this paper, we introduce a robust nonparametric density estimator combining the popular Kernel Density Estimation method and the Median-of-Means principle (MoM-KDE). This estimator is shown to achieve robustness to any kind of anomalous…
Mixtures of Linear Regressions (MLR) is an important mixture model with many applications. In this model, each observation is generated from one of the several unknown linear regression components, where the identity of the generated…
Kernel density estimation on a finite interval poses an outstanding challenge because of the well-recognized bias at the boundaries of the interval. Motivated by an application in cancer research, we consider a boundary constraint linking…
A nonparametric kernel density estimator for directional-linear data is introduced. The proposal is based on a product kernel accounting for the different nature of both (directional and linear) components of the random vector. Expressions…
Kernel embeddings have emerged as a powerful tool for representing probability measures in a variety of statistical inference problems. By mapping probability measures into a reproducing kernel Hilbert space (RKHS), kernel embeddings enable…
Identifying pure components in mixtures is a common yet challenging problem. The associated unmixing process requires the pure components, also known as endmembers, to be sufficiently spectrally distinct. Even with this requirement met,…
Semi- and non-parametric mixture of regressions are a very useful flexible class of mixture of regressions in which some or all of the parameters are non-parametric functions of the covariates. These models are, however, based on the…
Kernel methods, being supported by a well-developed theory and coming with efficient algorithms, are among the most popular and successful machine learning techniques. From a mathematical point of view, these methods rest on the concept of…
We consider a finite mixture model with varying mixing probabilities. Linear regression models are assumed for observed variables with coefficients depending on the mixture component the observed subject belongs to. A modification of the…
We provide a general and rigorous proof for the strong consistency of maximum likelihood estimators of the cumulative distribution function of the mixing distribution and structural parameter under finite mixtures of location-scale…
Finite Mixture of Regressions (FMR) models are among the most widely used approaches in dealing with the heterogeneity among the observations in regression problems. One of the limitations of current approaches is their inability to…
Nonparametric kernel density and local polynomial regression estimators are very popular in Statistics, Economics, and many other disciplines. They are routinely employed in applied work, either as part of the main empirical analysis or as…
The paper introduces a new kernel-based Maximum Mean Discrepancy (MMD) statistic for measuring the distance between two distributions given finitely-many multivariate samples. When the distributions are locally low-dimensional, the proposed…
Kernel ridge regression is used to approximate the kinetic energy of non-interacting fermions in a one-dimensional box as a functional of their density. The properties of different kernels and methods of cross-validation are explored, and…
Mixture models are widely used in modeling heterogeneous data populations. A standard approach of mixture modeling assumes that the mixture component takes a parametric kernel form. In many applications, making parametric assumptions on the…
Mixture distributions provide a versatile and widely used framework for modeling random phenomena, and are particularly well-suited to the analysis of geoscientific processes and their attendant risks to society. For continuous mixtures of…
For many machine learning problem settings, particularly with structured inputs such as sequences or sets of objects, a distance measure between inputs can be specified more naturally than a feature representation. However, most standard…
Many modern datasets are collected automatically and are thus easily contaminated by outliers. This led to a regain of interest in robust estimation, including new notions of robustness such as robustness to adversarial contamination of the…
Kernel density estimation is a convenient way to estimate the probability density of a distribution given the sample of data points. However, it has certain drawbacks: proper description of the density using narrow kernels needs large data…
In this study, we establish a basis for selecting similarity measures when applying machine learning techniques to solve materials science problems. This selection is considered with an emphasis on the distinctiveness between materials that…