Related papers: A Block Minorization--Maximization Algorithm for H…
Theoretical guarantees are established for a standard estimator in a semi-parametric finite mixture model, where each component density is modeled as a product of univariate densities under a conditional independence assumption. The focus…
Block majorization-minimization (BMM) is a simple iterative algorithm for constrained nonconvex optimization that sequentially minimizes majorizing surrogates of the objective function in each block while the others are held fixed. BMM…
We consider the problem of efficiently computing the maximum likelihood estimator in Generalized Linear Models (GLMs) when the number of observations is much larger than the number of coefficients ($n \gg p \gg 1$). In this regime,…
Linear mixed models (LMMs), which incorporate fixed and random effects, are key tools for analyzing heterogeneous data, such as in personalized medicine. Nowadays, this type of data is increasingly wide, sometimes containing thousands of…
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…
Parameter estimation in logistic regression is a well-studied problem with the Newton-Raphson method being one of the most prominent optimization techniques used in practice. A number of monotone optimization methods including…
Heteroscedastic regression models a Gaussian variable's mean and variance as a function of covariates. Parametric methods that employ neural networks for these parameter maps can capture complex relationships in the data. Yet, optimizing…
The principle of majorization-minimization (MM) provides a general framework for eliciting effective algorithms to solve optimization problems. However, they often suffer from slow convergence, especially in large-scale and high-dimensional…
Relative error estimation has been recently used in regression analysis. A crucial issue of the existing relative error estimation procedures is that they are sensitive to outliers. To address this issue, we employ the $\gamma$-likelihood…
Accelerated algorithms for maximum likelihood image reconstruction are essential for emerging applications such as 3D tomography, dynamic tomographic imaging, and other high dimensional inverse problems. In this paper, we introduce and…
The performance of a modulation classifier is highly sensitive to channel signal-to-noise ratio (SNR). In this paper, we focus on amplitude-phase modulations and propose a modulation classification framework based on centralized data fusion…
The expectation-maximization (EM) algorithm is an iterative method for finding maximum likelihood estimates when data are incomplete or are treated as being incomplete. The EM algorithm and its variants are commonly used for parameter…
Block majorization-minimization (BMM) is a simple iterative algorithm for nonconvex optimization that sequentially minimizes a majorizing surrogate of the objective function in each block coordinate while the other block coordinates are…
Constrained approaches to maximum likelihood estimation in the context of finite mixtures of normals have been presented in the literature. A fully data-dependent constrained method for maximum likelihood estimation of clusterwise linear…
Maximum-likelihood estimation (MLE) is arguably the most important tool for statisticians, and many methods have been developed to find the MLE. We present a new inequality involving posterior distributions of a latent variable that holds…
Huber's criterion can be used for robust joint estimation of regression and scale parameters in the linear model. Huber's (Huber, 1981) motivation for introducing the criterion stemmed from non-convexity of the joint maximum likelihood…
We propose a nonconvex estimator for joint multivariate regression and precision matrix estimation in the high dimensional regime, under sparsity constraints. A gradient descent algorithm with hard thresholding is developed to solve the…
Mixed linear regression (MLR) model is among the most exemplary statistical tools for modeling non-linear distributions using a mixture of linear models. When the additive noise in MLR model is Gaussian, Expectation-Maximization (EM)…
Traditional MCMC algorithms are computationally intensive and do not scale well to large data. In particular, the Metropolis-Hastings (MH) algorithm requires passing over the entire dataset to evaluate the likelihood ratio in each…
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…