Related papers: An Efficient Algorithm for High-Dimensional Log-Co…
Motivated by studies in biological sciences to detect differentially expressed genes, a semiparametric two-component mixture model with one known component is being studied in this paper. Assuming the density of the unknown component to be…
We consider the problem of estimating a regularization parameter, or a shrinkage coefficient $\alpha \in (0,1)$ for Regularized Tyler's M-estimator (RTME). In particular, we propose to estimate an optimal shrinkage coefficient by setting…
Filtering and parameter estimation under partial information for multiscale problems is studied in this paper. After proving mean square convergence of the nonlinear filter to a filter of reduced dimension, we establish that the conditional…
In this paper, we study the nonparametric maximum likelihood estimator (MLE) of a convex hazard function. We show that the MLE is consistent and converges at a local rate of $n^{2/5}$ at points $x_0$ where the true hazard function is…
Training the parameters of statistical models to describe a given data set is a central task in the field of data mining and machine learning. A very popular and powerful way of parameter estimation is the method of maximum likelihood…
The L1-regularized Gaussian maximum likelihood estimator (MLE) has been shown to have strong statistical guarantees in recovering a sparse inverse covariance matrix, or alternatively the underlying graph structure of a Gaussian Markov…
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…
Maximum likelihood estimation (MLE) is a fundamental computational problem in statistics. The problem is to maximize the likelihood function with respect to given data on a statistical model. An algebraic approach to this problem is to…
This paper rigorously establishes that the existence of the maximum likelihood estimate (MLE) in high-dimensional logistic regression models with Gaussian covariates undergoes a sharp `phase transition'. We introduce an explicit boundary…
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…
We consider the system identification problem of estimating a dynamical parameter of a Markovian quantum open system (the atom maser), by performing continuous time measurements in the system's output (outgoing atoms). Two estimation…
In computational mechanics, multiple models are often present to describe a physical system. While Bayesian model selection is a helpful tool to compare these models using measurement data, it requires the computationally expensive…
Maximum-likelihood (ML) decoding for arbitrary block codes remains fundamentally hard, with worst-case time complexity-measured by the total number of multiplications-being no better than straightforward exhaustive search, which requires…
Monte Carlo maximum likelihood (MCML) provides an elegant approach to find maximum likelihood estimators (MLEs) for latent variable models. However, MCML algorithms are computationally expensive when the latent variables are…
We show that the maximum likelihood estimator (MLE) is an effective tool for mitigating non-flow effects in flow analysis. To this end, one constructs two toy models that simulate non-flow contributions corresponding to particle decay and…
We consider two connected aspects of maximum likelihood estimation of the parameter for high-dimensional discrete graphical models: the existence of the maximum likelihood estimate (mle) and its computation. When the data is sparse, there…
In this article, we revisit the problem of fitting a mixture model under the assumption that the mixture components are symmetric and log-concave. To this end, we first study the nonparametric maximum likelihood estimation (NPMLE) of a…
Log-concave distributions are an attractive choice for modeling and inference, for several reasons: The class of log-concave distributions contains most of the commonly used parametric distributions and thus is a rich and flexible…
We analyze four different approaches to estimate a multivariate probability density (or the log-density) and its first and second order derivatives. Two methods, local log-likelihood and local Hyv\"arinen score estimation, are in terms of…
Distributed statistical inference has recently attracted immense attention. The asymptotic efficiency of the maximum likelihood estimator (MLE), the one-step MLE, and the aggregated estimating equation estimator are established for…