Related papers: Maximum Likelihood Estimation in Latent Class Mode…
Temporal Point Processes (TPP) with partial likelihoods involving a latent structure often entail an intractable marginalization, thus making inference hard. We propose a novel approach to Maximum Likelihood Estimation (MLE) involving…
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…
The Expectation-Maximization (EM) algorithm is routinely used for the maximum likelihood estimation in the latent class analysis. However, the EM algorithm comes with no guarantees of reaching the global optimum. We study the geometry of…
There has been considerable recent interest in Bayesian modeling of high-dimensional networks via latent space approaches. When the number of nodes increases, estimation based on Markov Chain Monte Carlo can be extremely slow and show poor…
Spatial-temporal linear model and the corresponding likelihood-based statistical inference are important tools for the analysis of spatial-temporal lattice data. In this paper, we study the asymptotic properties of maximum likelihood…
A very popular class of models for networks posits that each node is represented by a point in a continuous latent space, and that the probability of an edge between nodes is a decreasing function of the distance between them in this latent…
Every student in statistics or data science learns early on that when the sample size largely exceeds the number of variables, fitting a logistic model produces estimates that are approximately unbiased. Every student also learns that there…
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.…
Stephen Fienberg's affinity for contingency table problems and reinterpreting models with a fresh look gave rise to a new approach for hypothesis testing of network models that are linear exponential families. We outline his vision and…
This article is an exposition on some recent theoretical advances in learning latent structured models, with a primary focus on the fundamental roles that optimal transport distances play in the statistical theory. We aim at what may be the…
A new statistical technique for constructing linear latent structure (LLS) models from available data, supported by well established theoretical results and an efficient algorithm, is presented. The method reduces the problem of estimating…
Deep directed generative models have attracted much attention recently due to their expressive representation power and the ability of ancestral sampling. One major difficulty of learning directed models with many latent variables is the…
Latent class model (LCM), which is a finite mixture of different categorical distributions, is one of the most widely used models in statistics and machine learning fields. Because of its non-continuous nature and the flexibility in shape,…
Latent space models (LSM) for network data were introduced by Hoff et al. (2002) under the basic assumption that each node of the network has an unknown position in a D-dimensional Euclidean latent space: generally the smaller the distance…
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…
Most statistical software packages implement numerical strategies for computation of maximum likelihood estimates in random effects models. Little is known, however, about the algebraic complexity of this problem. For the one-way layout…
Joint models (JMs) for longitudinal and time-to-event data are an important class of biostatistical models in health and medical research. When the study population consists of heterogeneous subgroups, the standard JM may be inadequate and…
Unsupervised estimation of latent variable models is a fundamental problem central to numerous applications of machine learning and statistics. This work presents a principled approach for estimating broad classes of such models, including…
We revisit the problem of the existence of the maximum likelihood estimate for multi-class logistic regression. We show that one method of ensuring its existence is by assigning positive probability to every class in the sample dataset. The…
Hierarchical learning models, such as mixture models and Bayesian networks, are widely employed for unsupervised learning tasks, such as clustering analysis. They consist of observable and hidden variables, which represent the given data…