相关论文: The maximum likelihood degree of Fermat hypersurfa…

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…

Let X be a projective geometrically irreducible non-singular algebraic curve defined over a finite field F of order $q^2$. If the number of F-rational points of X satisfies the Hasse-Weil upper bound, then X is said to be F-maximal. For a…

Statistical models with latent structure have a history going back to the 1950s and have seen widespread use in the social sciences and, more recently, in computational biology and in machine learning. Here we study the basic latent class…

Three steps in the development of the maximum likelihood (ML) method are presented. At first, the application of the ML method and Fisher information notion in the model selection analysis is described (Chapter 1). The fundamentals of…

We consider 1-dimensional location estimation, where we estimate a parameter $\lambda$ from $n$ samples $\lambda + \eta_i$, with each $\eta_i$ drawn i.i.d. from a known distribution $f$. For fixed $f$ the maximum-likelihood estimate (MLE)…

It is well-known that there is a positive relationship between the maximal multiplicity and the length of the associated virtual 1-parameter subgroup of a projective hypersurface. In this paper, we will define the multiplicity classes of…

We study the optimization of ergodic averages for multi-valued dynamical systems, i.e. where points may have multiple different forward orbits. Under upper semi-continuity assumptions, we show that the maximum space average with respect to…

Motivated by recent works on the high-dimensional logistic regression, we establish that the existence of the maximum likelihood estimate exhibits a phase transition for a wide range of generalized linear models with binary outcome and…

In this paper, we study sample size thresholds for maximum likelihood estimation for tensor normal models. Given the model parameters and the number of samples, we determine whether, almost surely, (1) the likelihood function is bounded…

This work introduces a method for fitting to the degree distributions of complex network datasets, such that the most appropriate distribution from a set of candidate distributions is chosen while maximizing the portion of the distribution…

Maximum regularized likelihood estimators (MRLEs) are arguably the most established class of estimators in high-dimensional statistics. In this paper, we derive guarantees for MRLEs in Kullback-Leibler divergence, a general measure of…

Theoretical guarantees are established for a standard estimator in a semi-parametric finite mixture model, where each component density is modeled as a product of univariate densities under a conditional independence assumption. The focus…

We study structured optimization problems with polynomial objective function and polynomial equality constraints. The structure comes from a multi-grading on the polynomial ring in several variables. For fixed multi-degrees we determine the…

Peak estimation of hybrid systems aims to upper bound extreme values of a state function along trajectories, where this state function could be different in each subsystem. This finite-dimensional but nonconvex problem may be lifted into an…

Predicting the value of a function $f$ at a new point given its values at old points is an ubiquitous scientific endeavor, somewhat less developed when $f$ produces multiple values that depend on one another, e.g. when it outputs…

In the context of the Integer Quantum Hall plateau transitions, we formulate a specific map from random landscape potentials onto 2D discrete random surfaces. Critical points of the potential, namely maxima, minima and saddle points…

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…

Fisher's Method of Maximum Likelihood is shown to be a procedure for the construction of likelihood intervals or regions, instead of a procedure of point estimation. Based on Fisher's articles and books it is justified that by estimation…

We study hypersurfaces with fractional mean curvature in N-dimensional Euclidean space. These hypersurfaces are critical points of the fractional perimeter under a volume constraint. We use local inversion arguments to prove existence of…

Supertree methods are tree reconstruction techniques that combine several smaller gene trees (possibly on different sets of species) to build a larger species tree. The question of interest is whether the reconstructed supertree converges…