Related papers: Maximum lilkelihood estimation in the $\beta$-mode…
The missing data problem has been broadly studied in the last few decades and has various applications in different areas such as statistics or bioinformatics. Even though many methods have been developed to tackle this challenge, most of…
We study the consistency and optimality of the maximum marginal likelihood estimate (MMLE) in the hyperparameter inference for large-degree-of-freedom models. We perform main analyses within the exponential family, where the natural…
Determinantal point processes (DPPs) have wide-ranging applications in machine learning, where they are used to enforce the notion of diversity in subset selection problems. Many estimators have been proposed, but surprisingly the basic…
The methods of statistical physics are widely used for modelling complex networks. Building on the recently proposed Equilibrium Expectation approach, we derive a simple and efficient algorithm for maximum likelihood estimation (MLE) of…
We suggest an iterative approach to computing K-step maximum likelihood estimates (MLE) of the parametric components in semiparametric models based on their profile likelihoods. The higher order convergence rate of K-step MLE mainly depends…
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…
Implicit probabilistic models are models defined naturally in terms of a sampling procedure and often induces a likelihood function that cannot be expressed explicitly. We develop a simple method for estimating parameters in implicit models…
We present both offline and online maximum likelihood estimation (MLE) techniques for inferring the static parameters of a multiple target tracking (MTT) model with linear Gaussian dynamics. We present the batch and online versions of the…
This paper develops a quasi-maximum likelihood estimator for genuinely unbalanced dynamic network panel data models with individual fixed effects. We propose a model that accommodates contemporaneous and lagged network spillovers, temporal…
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…
The assumption of log-concavity is a flexible and appealing nonparametric shape constraint in distribution modelling. In this work, we study the log-concave maximum likelihood estimator (MLE) of a probability mass function (pmf). We show…
We study the uniform convergence rate of the nonparametric maximum likelihood estimator (MLE) for the sub-distribution functions in the current status data with competing risks model. It is known that the MLE have $L^2$-norm convergence…
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…
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)…
The paper offers a novel unified approach to studying the accuracy of parameter estimation by the quasi likelihood method. Important features of the approach are: (1) The underlying model {is not assumed to be parametric}. (2) No conditions…
We study holonomic gradient decent for maximum likelihood estimation of exponential-polynomial distribution, whose density is the exponential function of a polynomial in the random variable. We first consider the case that the support of…
For many diseases, logistic and other constraints often render large incidence studies difficult, if not impossible, to carry out. This becomes a drawback, particularly when a new incidence study is needed each time the disease incidence…
Maximum likelihood estimation (MLE) of latent variable models is often recast as the minimization of a free energy functional over an extended space of parameters and probability distributions. This perspective was recently combined with…
The Maximum Likelihood Estimator (MLE) serves an important role in statistics and machine learning. In this article, for i.i.d. variables, we obtain constant-specified and sharp concentration inequalities and oracle inequalities for the MLE…
For regression model selection via maximum likelihood estimation, we adopt a vector representation of candidate models and study the likelihood ratio confidence region for the regression parameter vector of a full model. We show that when…