Related papers: Eigenstructure of Maximum Likelihood from Counts D…

This paper rigorously establishes that the existence of the maximum likelihood estimate (MLE) in high-dimensional logistic regression models with Gaussian covariates undergoes a sharp `phase transition'. We introduce an explicit boundary…

In this paper, a new mixture family of multivariate normal distributions, formed by mixing multivariate normal distribution and skewed distribution, is constructed. Some properties of this family, such as characteristic function, moment…

Finite mixture models are widely used in econometric analyses to capture unobserved heterogeneity. This paper shows that maximum likelihood estimation of finite mixtures of parametric densities can suffer from substantial finite-sample bias…

We propose a technique for calculating and understanding the eigenvalue distribution of sums of random matrices from the known distribution of the summands. The exact problem is formidably hard. One extreme approximation to the true density…

An implicit goal in works on deep generative models is that such models should be able to generate novel examples that were not previously seen in the training data. In this paper, we investigate to what extent this property holds for…

Conventional methods for computing maximum-likelihood estimators (MLE) often converge slowly in practical situations, leading to a search for simplifying methods that rely on additional assumptions for their validity. In this work, we…

Network structure provides critical information for understanding the dynamic behavior of networks. However, the complete structure of real-world networks is often unavailable, thus it is crucially important to develop approaches to infer a…

We reinvigorate maximum likelihood estimation (MLE) for macroeconomic density forecasting through a novel neural network architecture with dedicated mean and variance hemispheres. Our architecture features several key ingredients making MLE…

The marginal likelihood is a well established model selection criterion in Bayesian statistics. It also allows to efficiently calculate the marginal posterior model probabilities that can be used for Bayesian model averaging of quantities…

Heterogeneous porous materials play a crucial role in various engineering systems. Microstructure characterization and reconstruction provide effective means for modeling these materials, which are critical for conducting physical property…

In computational mechanics, multiple models are often present to describe a physical system. While Bayesian model selection is a helpful tool to compare these models using measurement data, it requires the computationally expensive…

Probabilistic graphical models that encode an underlying Markov random field are fundamental building blocks of generative modeling to learn latent representations in modern multivariate data sets with complex dependency structures. Among…

Variational Autoencoders (VAEs) typically rely on a probabilistic decoder with a predefined likelihood, most commonly an isotropic Gaussian, to model the data conditional on latent variables. While convenient for optimization, this choice…

We study the nonparametric maximum likelihood estimator $\widehat{\pi}$ for Gaussian location mixtures in one dimension. It has been known since (Lindsay, 1983) that given an $n$-point dataset, this estimator always returns a mixture with…

Although there are a few works reported in the literature considering loss tomography in the general topology, there is few well established result since all of them rely either on simulations or on experiments that have many random factors…

With the growth of interest in network data across fields, the Exponential Random Graph Model (ERGM) has emerged as the leading approach to the statistical analysis of network data. ERGM parameter estimation requires the approximation of an…

The choice of free parameters in network models is subjective, since it depends on what topological properties are being monitored. However, we show that the Maximum Likelihood (ML) principle indicates a unique, statistically rigorous…

The robust improper maximum likelihood estimator (RIMLE) is a new method for robust multivariate clustering finding approximately Gaussian clusters. It maximizes a pseudo-likelihood defined by adding a component with improper constant…

Large-scale networks are commonly encountered in practice (e.g., Facebook and Twitter) by researchers. In order to study the network interaction between different nodes of large-scale networks, the spatial autoregressive (SAR) model has…

In the Admixture Model, the probability of an individual having a certain number of alleles at a specific marker depends on the allele frequencies in $K$ ancestral populations and the fraction of the individual's genome originating from…