Related papers: Maximum Likelihood for Dual Varieties
The density ratio model (DRM) provides a flexible and useful platform for combining information from multiple sources. In this paper, we consider statistical inference under two-sample DRMs with additional parameters defined through and/or…
Works, briefly surveyed here, are concerned with two basic methods: Maximum Probability and Bayesian Maximum Probability; as well as with their asymptotic instances: Relative Entropy Maximization and Maximum Non-parametric Likelihood.…
Pseudo log-likelihood is a type of maximum likelihood estimation (MLE) method used in various fields including contextual bandits, influence maximization of social networks, and causal bandits. However, in previous literature…
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 present new results for consistency of maximum likelihood estimators with a focus on multivariate mixed models. Our theory builds on the idea of using subsets of the full data to establish consistency of estimators based on the full…
There have been many applications of deep neural networks to detector calibrations and a growing number of studies that propose deep generative models as automated fast detector simulators. We show that these two tasks can be unified by…
Maximum likelihood estimation (MLE) is the most common approach to quantum state tomography. In this letter, we investigate whether it is also optimal in any sense. We show that MLE is an inadmissible estimator for most of the commonly used…
A fundamental problem with nonlinear models is that maximum likelihood estimates are not guaranteed to exist. Though nonexistence is a well known problem in the binary response model literature, it presents significant challenges for other…
The log-concave maximum likelihood estimator (MLE) problem answers: for a set of points $X_1,...X_n \in \mathbb R^d$, which log-concave density maximizes their likelihood? We present a characterization of the log-concave MLE that leads to…
Distributed statistical inference has recently attracted immense attention. The asymptotic efficiency of the maximum likelihood estimator (MLE), the one-step MLE, and the aggregated estimating equation estimator are established for…
The stationary distribution of allele frequencies under a variety of Wright--Fisher $k$-allele models with selection and parent independent mutation is well studied. However, the statistical properties of maximum likelihood estimates of…
The idea of maximizing the likelihood of the observed range for a set of jointly realized counts has been employed in a variety of contexts. The applicability of the MLE introduced in [1] has been extended to the general case of a…
Multivariate normal mixtures provide a flexible model for high-dimensional data. They are widely used in statistical genetics, statistical finance, and other disciplines. Due to the unboundedness of the likelihood function, classical…
The maximum likelihood amplitude estimation algorithm (MLAE) is a practical solution to the quantum amplitude estimation problem with Heisenberg limit error convergence. We improve MLAE by using random depths to avoid the so-called critical…
Maximum likelihood estimators (MLE) and control variate estimators (CVE) have been used in conjunction with known information across sketching algorithms and applications in machine learning. We prove that under certain conditions in an…
Mixed linear regression (MLR) is a powerful model for characterizing nonlinear relationships by utilizing a mixture of linear regression sub-models. The identification of MLR is a fundamental problem, where most of the existing results…
This paper revisits the classical inference results for profile quasi maximum likelihood estimators (profile MLE) in the semiparametric estimation problem. We mainly focus on two prominent theorems: the Wilks phenomenon and Fisher expansion…
Accurately estimating high quantiles beyond the largest observed value is crucial for risk assessment and devising effective adaptation strategies to prevent a greater disaster. The generalized extreme value distribution is widely used for…
In a mixture of linear regression model, the regression coefficients are treated as random vectors that may follow either a continuous or discrete distribution. We propose two Expectation-Maximization (EM) algorithms to estimate this prior…
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…