Related papers: Maximum likelihood degree of Fermat hypersurfaces …
Computing all critical points of a monomial on a very affine variety is a fundamental task in algebraic statistics, particle physics and other fields. The number of critical points is known as the maximum likelihood (ML) degree. When the…
With any \emph{surjective rational map} $f: \mathbb{P}^n \dashrightarrow \mathbb{P}^n$ of the projective space we associate a numerical invariant (\emph{ML degree}) and compute it in terms of a naturally defined vector bundle $E_f…
We study probability density functions that are log-concave. Despite the space of all such densities being infinite-dimensional, the maximum likelihood estimate is the exponential of a piecewise linear function determined by finitely many…
We stratify families of projective and very affine hypersurfaces according to their topological Euler characteristic. Our new algorithms compute all strata using algebro-geometric techniques. For very affine hypersurfaces, we investigate…
In this article, we investigate Maximum Likelihood Estimation with tools from Tropical Geometry and Bernstein--Sato theory. We investigate the critical points of very affine varieties and study their asymptotic behavior. We relate these…
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…
Given a model in algebraic statistics and some data, the likelihood function is a rational function on a projective variety. Algebraic algorithms are presented for computing all critical points of this function, with the aim of identifying…
The maximum likelihood degree (ML degree) measures the algebraic complexity of a fundamental optimization problem in statistics: maximum likelihood estimation. In this problem, one maximizes the likelihood function over a statistical model.…
We present a statistically and computationally efficient spectral-domain maximum-likelihood procedure to solve for the structure of Gaussian spatial random fields within the Matern covariance hyperclass. For univariate, stationary, and…
We give a numerical algorithm computing Euler obstruction functions using maximum likelihood degrees. The maximum likelihood degree is a well-studied property of a variety in algebraic statistics and computational algebraic geometry. In…
We study ``forms of the Fermat equation'' over an arbitrary field $k$, i.e. homogenous equations of degree $m$ in $n$ unknowns that can be transformed into the Fermat equation $X_1^m+...+X_n^m$ by a suitable linear change of variables over…
In exploratory factor analysis, model parameters are usually estimated by maximum likelihood method. The maximum likelihood estimate is obtained by solving a complicated multivariate algebraic equation. Since the solution to the equation is…
The method of maximum likelihood estimation (MLE) is a widely used statistical approach for estimating the values of one or more unknown parameters of a probabilistic model based on observed data. In this tutorial, I briefly review the…
The degree of a projective subscheme has an upper bound in term of the codimension and the reduction number. If a projective variety has an almost maximal degree, that is, the degree equals to the upper bound minus one, then its Betti table…
The maximum likelihood threshold of a graph is the smallest number of data points that guarantees that maximum likelihood estimates exist almost surely in the Gaussian graphical model associated to the graph. We show that this graph…
This article focuses on the study of toric algebraic statistical models which correspond to toric Del Pezzo surfaces with Du Val singularities. A closed-form for the Maximum Likelihood Estimate of algebraic statistical models which…
As is the case for many curved exponential families, the computation of maximum likelihood estimates in a multivariate normal model with a Kronecker covariance structure is typically carried out with an iterative algorithm, specifically, a…
The minimum number of observations such that the maximum likelihood estimator in a Gaussian graphical model exists with probability one is called the maximum likelihood threshold of the underlying graph G. The natural algebraic relaxation…
Maximum likelihood estimation (MLE) is a fundamental computational problem in statistics. In this paper, MLE for statistical models with discrete data is studied from an algebraic statistics viewpoint. A reformulation of the MLE problem in…
We study the problem of maximum likelihood (ML) estimation for statistical models defined by reflexive polytopes. Our focus is on the maximum likelihood degree of these models as an algebraic measure of complexity of the corresponding…