相关论文: Existence of maximum likelihood estimates in expon…
Bayesian inference with empirical likelihood faces a challenge as the posterior domain is a proper subset of the original parameter space due to the convex hull constraint. We propose a regularized exponentially tilted empirical likelihood…
The maximum likelihood method offers a standard way to estimate the three parameters of a generalized extreme value (GEV) distribution. Combined with the block maxima method, it is often used in practice to assess the extreme value index…
We develop a new methodology for model-based clustering. Optimizing the log-likelihood provides a principled statistical framework for clustering, with solutions found via the EM algorithm. However, because the log-likelihood is nonconvex,…
We investigate convergence of the expectation maximization algorithm by representing it as a generalized proximal method. Convergence of iterates and not just in value is investigated under natural hypotheses such as definability of the…
The maximum likelihood principle is widely used in statistics, and the associated estimators often display good properties. indeed maximum likelihood estimators are guaranteed to be asymptotically efficient under mild conditions. However in…
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)…
We propose a family of statistical models for social network evolution over time, which represents an extension of Exponential Random Graph Models (ERGMs). Many of the methods for ERGMs are readily adapted for these models, including…
We consider the problem of model selection type aggregation in the context of density estimation. We first show that empirical risk minimization is sub-optimal for this problem and it shares this property with the exponential weights…
Maximization of the entropy rate is an important issue to design diffusion processes aiming at a well-mixed state. We demonstrate that it is possible to construct maximal-entropy random walks with only local information on the graph…
This paper develops several interesting, significant, and interconnected approaches to nonparametric or semi-parametric statistical inferences. The overwhelmingly favoured maximum likelihood estimator (MLE) under parametric model is…
We develop a maximum-likelihood based method for regression in a setting where the dependent variable is a random graph and covariates are available on a graph-level. The model generalizes the well-known $\beta$-model for random graphs by…
We introduce a method for the comparison of some extremal eigenvalue statistics of random matrices. For example, it allows one to compare the maximal eigenvalue gap in the bulk of two generalized Wigner ensembles, provided that the first…
We establish the validity of bootstrap methods for empirical likelihood (EL) inference under the density ratio model (DRM). In particular, we prove that the bootstrap maximum EL estimators share the same limiting distribution as their…
Maximum likelihood estimation of energy-based models is a challenging problem due to the intractability of the log-likelihood gradient. In this work, we propose learning both the energy function and an amortized approximate sampling…
Spectral learning recently generated lots of excitement in machine learning, largely because it is the first known method to produce consistent estimates (under suitable conditions) for several latent variable models. In contrast, maximum…
In this paper, we obtain a precise estimate of the probability that the sparse binomial random graph contains a large number of vertices in a triangle. The estimate of log of this probability is correct up to second order, and enables us to…
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…
When an expert operates a perilous dynamic system, ideal constraint information is tacitly contained in their demonstrated trajectories and controls. The likelihood of these demonstrations can be computed, given the system dynamics and task…
The maximum-likelihood estimator of nonlinear panel data models with fixed effects is consistent but asymptotically-biased under rectangular-array asymptotics. The literature has thus far concentrated its effort on devising methods to…
The exponential random graph model (ERGM) is a central object in the study of clustering properties in social networks as well as canonical ensembles in statistical physics. Despite some breakthrough works in the mathematical understanding…