Related papers: Maximum likelihood thresholds of generic linear co…
Consider a parametrized family of general hidden Markov models, where both the observed and unobserved components take values in a complete separable metric space. We prove that the maximum likelihood estimator (MLE) of the parameter is…
Consider a random graph G in G(n,p) and the graph property: G contains a copy of a specific graph H. (Note: H depends on n; a motivating example: H is a Hamiltonian cycle.) Let q be the minimal value for which the expected number of copies…
I consider two problems in machine learning and statistics: the problem of estimating the joint probability density of a collection of random variables, known as density estimation, and the problem of inferring model parameters when their…
Mixture of autoregressions (MoAR) models provide a model-based approach to the clustering of time series data. The maximum likelihood (ML) estimation of MoAR models requires the evaluation of products of large numbers of densities of normal…
Estimating the matrix of connections probabilities is one of the key questions when studying sparse networks. In this work, we consider networks generated under the sparse graphon model and the in-homogeneous random graph model with missing…
In a finite mixture of location-scale distributions maximum likelihood estimator does not exist because of the unboundedness of the likelihood function when the scale parameter of some mixture component approaches zero. In order to study…
The controlled branching process is a generalization of the classical Bienaym\'e-Galton-Watson branching process. It is a useful model for describing the evolution of populations in which the population size at each generation needs to be…
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…
The epidemic threshold is probably the most studied quantity in the modelling of epidemics on networks. For a large class of networks and dynamics the epidemic threshold is well studied and understood. However, it is less so for clustered…
With generalizing the Brody distribution to include the Poisson, GOE and GUE limits and with employing the maximum likelihood estimation technique, the spectral statistics of different sequences were considered in the nearest neighbor…
The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models.…
The asymptotic variance of the maximum likelihood estimate is proved to decrease when the maximization is restricted to a subspace that contains the true parameter value. Maximum likelihood estimation allows a systematic fitting of…
We consider maximum likelihood estimation of finite mixture of uniform distributions. We prove that maximum likelihood estimator is strongly consistent, if the scale parameters of the component uniform distributions are restricted from…
We present a maximum-likelihood method for parameter estimation in terahertz time-domain spectroscopy. We derive the likelihood function for a parameterized frequency response function, given a pair of time-domain waveforms with known…
Maximum likelihood estimation is one of the most used methods in quantum state tomography, where the aim is to reconstruct the density matrix of a physical system from measurement results. One strategy to deal with positivity and unit trace…
Learning and compression are driven by the common aim of identifying and exploiting statistical regularities in data, which opens the door for fertile collaboration between these areas. A promising group of compression techniques for…
In this paper, we study the maximum likelihood estimation of the parameters of the multivariate and matrix variate symmetric Laplace distributions through group actions. The multivariate and matrix variate symmetric Laplace distributions…
We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…
Estimation of generalized linear mixed models (GLMMs) with non-nested random effects structures requires approximation of high-dimensional integrals. Many existing methods are tailored to the low-dimensional integrals produced by nested…
In this paper we consider Poisson loglinear models with linear constraints (LMLC) on the expected table counts. Multinomial and product multinomial loglinear models can be obtained by considering that some marginal totals (linear…