Related papers: The Maximum Likelihood Degree of Toric Models is M…

We study the maximum likelihood degree (ML degree) of toric varieties, known as discrete exponential models in statistics. By introducing scaling coefficients to the monomial parameterization of the toric variety, one can change the ML…

We express the maximum likelihood (ML) degrees of a family toric varieties in terms of Mobius invariants of matroids. The family of interest are those parametrized by monomial maps given by Lawrence lifts of totally unimodular matrices with…

Given a statistical model, the maximum likelihood degree is the number of complex solutions to the likelihood equations for generic data. We consider discrete algebraic statistical models and study the solutions to the likelihood equations…

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 study multivariate Gaussian models that are described by linear conditions on the concentration matrix. We compute the maximum likelihood (ML) degrees of these models. That is, we count the critical points of the likelihood function over…

We study the maximum likelihood (ML) degree of discrete exponential independence models and models defined by the second hypersimplex. For models with two independent variables, we show that the ML degree is an invariant of a matroid…

In this paper we revisit the likelihood geometry of Gaussian graphical models. We give a detailed proof that the ML-degree behaves monotonically on induced subgraphs. Furthermore, we complete a missing argument that the ML-degree of the…

Maximum likelihood estimation (MLE) is a fundamental problem in statistics. Characteristics of the MLE problem for discrete algebraic statistical models are reflected in the geometry of the $\textit{likelihood correspondence}$, a variety…

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…

We study the maximum likelihood (ML) degree of linear concentration models in algebraic statistics. We relate it to an intersection problem on the variety of complete quadrics. This allows us to provide an explicit, basic, albeit of high…

For general data, the number of complex solutions to the likelihood equations is constant and this number is called the (maximum likelihood) ML-degree of the model. In this article, we describe the special locus of data for which the…

Maximum likelihood estimation in statistics leads to the problem of maximizing a product of powers of polynomials. We study the algebraic degree of the critical equations of this optimization problem. This degree is related to the number of…

The maximum likelihood degree of a statistical model refers to the number of solutions, where the derivative of the log-likelihood function is zero, over the complex field. This paper examines the maximum likelihood degree of the parameter…

This paper considers maximum likelihood (ML) estimation in a large class of models with hidden Markov regimes. We investigate consistency of the ML estimator and local asymptotic normality for the models under general conditions which allow…

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…

Maximum likelihood estimation is a fundamental computational problem in statistics. In this note, we give a bound for the maximum likelihood degree of algebraic statistical models for discrete data. As usual, such models are identified with…

We settle a conjecture by Bik and Marigliano stating that the degree of a one-dimensional discrete model with rational maximum likelihood estimator is bounded above by a linear function in the size of its support, therefore showing that…

Relational models for contingency tables are generalizations of log-linear models, allowing effects associated with arbitrary subsets of cells in a possibly incomplete table, and not necessarily containing the overall effect. In this…

In algebraic statistics, the maximum likelihood degree of a statistical model is the number of complex critical points of its log-likelihood function. A priori knowledge of this number is useful for applying techniques of numerical…

We give an explicit formula for the reciprocal maximum likelihood degree of Brownian motion tree models. To achieve this, we connect them to certain toric (or log-linear) models, and express the Brownian motion tree model of an arbitrary…