Related papers: Maximum likelihood estimation in the sparse Rasch …
The $\ell_0$-constrained empirical risk minimization ($\ell_0$-ERM) is a promising tool for high-dimensional statistical estimation. The existing analysis of $\ell_0$-ERM estimator is mostly on parameter estimation and support recovery…
Maximum Likelihood Estimators (MLE) has many good properties. For example, the asymptotic variance of MLE solution attains equality of the asymptotic Cram{\'e}r-Rao lower bound (efficiency bound), which is the minimum possible variance for…
We introduce a very general method for sparse and large-scale variable selection. The large-scale regression settings is such that both the number of parameters and the number of samples are extremely large. The proposed method is based on…
Since Rendle and Krichene argued that commonly used sampling-based evaluation metrics are "inconsistent" with respect to the global metrics (even in expectation), there have been a few studies on the sampling-based recommender system…
This study focuses on the estimation of the Emax dose-response model, a widely utilized framework in clinical trials, agriculture, and environmental experiments. Existing challenges in obtaining maximum likelihood estimates (MLE) for model…
We propose a method for obtaining maximum likelihood estimates in a model with continuous and binary outcomes. Combinations of left and right censored observations are also naturally modeled in this framework. The model and estimation…
Maximum entropy models provide the least constrained probability distributions that reproduce statistical properties of experimental datasets. In this work we characterize the learning dynamics that maximizes the log-likelihood in the case…
We consider the problem of estimating the parameters of a multivariate Bernoulli process with auto-regressive feedback in the high-dimensional setting where the number of samples available is much less than the number of parameters. This…
Logistic regression is a classical model for describing the probabilistic dependence of binary responses to multivariate covariates. We consider the predictive performance of the maximum likelihood estimator (MLE) for logistic regression,…
We develop a likelihood methodology which can be used to search for evidence of burst repetition in the BATSE catalog, and to study the properties of the repetition signal. We use a simplified model of burst repetition in which a number…
We consider the famous Rasch model, which is applied to psychometric surveys when n persons under test answer m questions. The score is given by a realization of a random binary (n,m)-matrix. Its (j,k)th component indicates whether or not…
Many decision-making processes involve evaluating and then selecting items; examples include scientific peer review, job hiring, school admissions, and investment decisions. The eventual selection is performed by applying rules or…
Over the last decades, the family of $\alpha$-stale distributions has proven to be useful for modelling in telecommunication systems. Particularly, in the case of radar applications, finding a fast and accurate estimation for the amplitude…
Item Response Theory (IRT) models have received growing interest in health science for analyzing latent constructs such as depression, anxiety, quality of life, or cognitive functioning from the information provided by each individual's…
The existence and consistency of a maximum likelihood estimator for the joint probability distribution of random parameters in discrete-time abstract parabolic systems are established by taking a nonparametric approach in the context of a…
While globally optimal empirical risk minimization (ERM) decision trees have become computationally feasible and empirically successful, rigorous theoretical guarantees for their statistical performance remain limited. In this work, we…
We propose a class of Item Response Theory models for items with ordinal polytomous responses, which extends an existing class of multidimensional models for dichotomously-scored items measuring more than one latent trait. In the proposed…
In this paper we develop rate--optimal estimation procedures in the problem of estimating the $L_p$--norm, $p\in (0, \infty)$ of a probability density from independent observations. The density is assumed to be defined on $R^d$, $d\geq 1$…
Maximum entropy method is a constructive criterion for setting up a probability distribution maximally non-committal to missing information on the basis of partial knowledge, usually stated as constrains on expectation values of some…
In many estimation problems, e.g. linear and logistic regression, we wish to minimize an unknown objective given only unbiased samples of the objective function. Furthermore, we aim to achieve this using as few samples as possible. In the…