Related papers: Maximal Invariants For Lorentz Wishart Models
This thesis consists of two independent parts: random matrices, which form the first one-third of this thesis, and machine learning, which constitutes the remaining part. The main results of this thesis are as follows: a necessary and…
The objective of this paper is to study the characteristics (geometric and otherwise) of very large attribute based undirected networks. Real-world networks are often very large and fast evolving. Their analysis and understanding present a…
The Dirichlet distribution, also known as multivariate beta, is the most used to analyse frequencies or proportions data. Maximum likelihood is widespread for estimation of Dirichlet's parameters. However, for small sample sizes, the…
This article considers exponential families of truncated multivariate normal distributions with one-sided truncation for some or all coordinates. We observe that if all components are one-sided truncated then this family is not full. The…
We discuss an application of the random matrix theory in the context of estimating the bipartite entanglement of a quantum system. We discuss how the Wishart ensemble (the earliest studied random matrix ensemble) appears in this quantum…
This paper focuses on the non-asymptotic concentration of the heteroskedastic Wishart-type matrices. Suppose $Z$ is a $p_1$-by-$p_2$ random matrix and $Z_{ij} \sim N(0,\sigma_{ij}^2)$ independently, we prove the expected spectral norm of…
We give an overview of statistical models and likelihood, together with two of its variants: penalized and hierarchical likelihood. The Kullback-Leibler divergence is referred to repeatedly, for defining the misspecification risk of a…
Testing covariance structure is of importance in many areas of statistical analysis, such as microarray analysis and signal processing. Conventional tests for finite-dimensional covariance cannot be applied to high-dimensional data in…
We introduce a natural definition of Riesz measures and Wishart laws associated to an $\Omega$-positive (virtual) quadratic map, where $\Omega \subset \real^n$ is a regular open convex cone. We give a general formula for moments of the…
We derive the class of covariant measurements which are optimal according to the maximum likelihood criterion. The optimization problem is fully resolved in the case of pure input states, under the physically meaningful hypotheses of…
We study stochastic optimization problems with chance and risk constraints, where in the latter, risk is quantified in terms of the conditional value-at-risk (CVaR). We consider the distributionally robust versions of these problems, where…
We investigate the problem of semi-parametric maximum likelihood under constraints on summary statistics. Such a procedure results in a discrete probability distribution that maximises the likelihood among all such distributions under the…
We consider the structural change in a class of discrete valued time series that the conditional distribution follows a one-parameter exponential family. We propose a change-point test based on the maximum likelihood estimator of the…
Maximum likelihood estimation is a common method of estimating the parameters of the probability distribution from a given sample. This paper aims to introduce the maximum likelihood estimation in the framework of sublinear expectation. We…
The paper proves several limit theorems for linear eigenvalue statistics of overlapping Wigner and sample covariance matrices. It is shown that the covariance of the limiting multivariate Gaussian distribution is diagonalized by choosing…
We prove the existence and uniqueness of a quasi-stationary distribution for three stochastic processes derived from the model of Muller's ratchet. This model was invented with the aim of evaluating the limitations of an asexual…
In the propositional setting, the marginal problem is to find a (maximum-entropy) distribution that has some given marginals. We study this problem in a relational setting and make the following contributions. First, we compare two…
In this work, we consider the weighted difference of two independent complex Wishart matrices and derive the joint probability density function of the corresponding eigenvalues in a finite-dimension scenario using two distinct approaches.…
We consider random walks on the cone of $m \times m$ positive definite matrices, where the underlying random matrices have orthogonally invariant distributions on the cone and the Riemannian metric is the measure of distance on the cone. By…
Consider bivariate observations $(X_1,Y_1), \ldots, (X_n,Y_n) \in \mathbb{R}\times \mathbb{R}$ with unknown conditional distributions $Q_x$ of $Y$, given that $X = x$. The goal is to estimate these distributions under the sole assumption…