相关论文: Multidimensional two-component Gaussian mixtures d…

We study the problem of detection of a p-dimensional sparse vector of parameters in the linear regression model with Gaussian noise. We establish the detection boundary, i.e., the necessary and sufficient conditions for the possibility of…

Gaussian mixture filters for nonlinear systems usually rely on severe approximations when calculating mixtures in the prediction and filtering step. Thus, offline approximations of noise densities by Gaussian mixture densities to reduce the…

Density deconvolution is the task of estimating a probability density function given only noise-corrupted samples. We can fit a Gaussian mixture model to the underlying density by maximum likelihood if the noise is normally distributed, but…

We consider the problem of detecting sparse heterogeneous mixtures in a two-sample setting from a nonparametric perspective, where the effect manifests itself as a positive shift. We suggest a two-sample higher criticism test, and show that…

The study of mixture models constitutes a large domain of research in statistics. In the first part of this work, we present phi-divergences and the existing methods which produce robust estimators. We are more particularly interested in…

We resolve one of the major outstanding problems in robust statistics. In particular, if $X$ is an evenly weighted mixture of two arbitrary $d$-dimensional Gaussians, we devise a polynomial time algorithm that given access to samples from…

We consider the classification problem of a high-dimensional mixture of two Gaussians with general covariance matrices. Using the replica method from statistical physics, we investigate the asymptotic behavior of a general class of…

This paper studies the problem of discriminating two multivariate Gaussian distributions in a distributed manner. Specifically, it characterizes in a special case the optimal typeII error exponent as a function of the available…

We investigate the problem of jointly testing two hypotheses and estimating a random parameter based on data that is observed sequentially by sensors in a distributed network. In particular, we assume the data to be drawn from a Gaussian…

A new method is proposed to get image features' geometric information. Using Gaussian as an input signal, a theoretical optimal solution to calculate feature's affine shape is proposed. Based on analytic result of a feature model, the…

We present a new subspace-based method to construct probabilistic models for high-dimensional data and highlight its use in anomaly detection. The approach is based on a statistical estimation of probability density using densities of…

In this paper we present a method for learning the parameters of a mixture of $k$ identical spherical Gaussians in $n$-dimensional space with an arbitrarily small separation between the components. Our algorithm is polynomial in all…

Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions. A key challenge, especially in high-dimensional settings, is to determine the mixture order and estimate the…

Estimating the number of components is a fundamental challenge in unsupervised learning, particularly when dealing with high-dimensional data with many components or severely imbalanced component sizes. This paper addresses this challenge…

In this paper we consider the uniformity testing problem for high-dimensional discrete distributions (multinomials) under sparse alternatives. More precisely, we derive sharp detection thresholds for testing, based on $n$ samples, whether a…

We present a self-consistent framework to perform the wavelet analysis of two-dimensional statistical distributions. The analysis targets the 2D probability density function (p.d.f.) of an input sample, in which each object is characterized…

Given i.i.d samples from some unknown continuous density on hyper-rectangle $[0, 1]^d$, we attempt to learn a piecewise constant function that approximates this underlying density non-parametrically. Our density estimate is defined on a…

When modeling the distribution of a set of data by a mixture of Gaussians, there are two possibilities: i) the classical one is using a set of parameters which are the proportions, the means and the variances; ii) the second is to consider…

Gaussian mixture models are widely used in Statistics. A fundamental aspect of these distributions is the study of the local maxima of the density, or modes. In particular, it is not known how many modes a mixture of $k$ Gaussians in $d$…

The microscopic approach to the description of the phase behaviour and critical phenomena in binary fluid mixtures is proposed. It is based on the method of collective variables with a reference system. The physical nature of the order…