Related papers: The Maximum Likelihood Degree of Toric Varieties
Toric geometry provides a bridge between the theory of polytopes and algebraic geometry: one can associate to each lattice polytope a polarized toric variety. In this paper we explore this correspondence to classify smooth lattice polytopes…
The maximum likelihood threshold of a statistical model is the minimum number of datapoints required to fit the model via maximum likelihood estimation. In this paper we determine the maximum likelihood thresholds of generic linear…
For the tree topology, previous studies show the maximum likelihood estimate (MLE) of a link/path takes a polynomial form with a degree that is one less than the number of descendants connected to the link/path. Since then, the main concern…
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…
Restricted maximum likelihood (REML) estimation is a widely accepted and frequently used method for fitting linear mixed models, with its principal advantage being that it produces less biased estimates of the variance components. However,…
The aim of this paper is to use Maximum Likelihood (ML) Classification on multispectral data by means of qualitative and quantitative approaches. Maximum Likelihood is a supervised classification algorithm which is based on the Classical…
One of the fundamental invariants connecting algebra and geometry is the degree of an ideal. In this paper we derive the probabilistic behavior of degree with respect to the versatile Erd\H{o}s-R\'enyi-type model for random monomial ideals…
Targeted maximum likelihood estimation (TMLE) is a general method for estimating parameters in semiparametric and nonparametric models. Each iteration of TMLE involves fitting a parametric submodel that targets the parameter of interest. We…
Multivariate extreme value statistical analysis is concerned with observations on several variables which are thought to possess some degree of tail-dependence. In areas such as the modeling of financial and insurance risks, or as the…
We propose a novel Continuation Multi Level Monte Carlo (CMLMC) algorithm for weak approximation of stochastic models. The CMLMC algorithm solves the given approximation problem for a sequence of decreasing tolerances, ending when the…
We study statistical model checking of continuous-time stochastic hybrid systems. The challenge in applying statistical model checking to these systems is that one cannot simulate such systems exactly. We employ the multilevel Monte Carlo…
In coherent imaging, speckle is statistically modeled as multiplicative noise, posing a fundamental challenge for image reconstruction. While maximum likelihood estimation (MLE) provides a principled framework for speckle mitigation, its…
An important question in statistical network analysis is how to estimate models of discrete and dependent network data with intractable likelihood functions, without sacrificing computational scalability and statistical guarantees. We…
Maximum likelihood degree of a projective variety is the number of critical points of a general likelihood function. In this note, we compute the Maximum likelihood degree of Fermat hypersurfaces. We give a formula of the Maximum likelihood…
In this paper, we study the log-likelihood function and Maximum Likelihood Estimate (MLE) for the matrix normal model for both real and complex models. We describe the exact number of samples needed to achieve (almost surely) three…
We study the critical points of monomial functions over an algebraic subset of the probability simplex. The number of critical points on the Zariski closure is a topological invariant of that embedded projective variety, known as its…
We show that the height of a toric variety with respect to a toric metrized line bundle can be expressed as the integral over a polytope of a certain adelic family of concave functions. To state and prove this result, we study the Arakelov…
This paper considers the maximum likelihood estimation of factor models of high dimension, where the number of variables (N) is comparable with or even greater than the number of observations (T). An inferential theory is developed. We…
A simple formula computing the multiplier ideal of a monomial ideal on an arbitrary affine toric variety is given. Variants for the multiplier module and test ideals are also treated.
The $p$-tensor Ising model is a one-parameter discrete exponential family for modeling dependent binary data, where the sufficient statistic is a multi-linear form of degree $p \geq 2$. This is a natural generalization of the matrix Ising…