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In this article, we propose a new method for calculating the mixed correlation coefficient (Pearson, polyserial and polychoric) matrix and its covariance matrix based on the GMM framework. We build moment equations for each coefficient and…

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,…

We present an asymptotic analysis of Viterbi Training (VT) and contrast it with a more conventional Maximum Likelihood (ML) approach to parameter estimation in Hidden Markov Models. While ML estimator works by (locally) maximizing the…

In this work, we study non-parametric estimation of joint probabilities of a given set of discrete and continuous random variables from their (empirically estimated) 2D marginals, under the assumption that the joint probability could be…

The recent emergence of deep learning has led to a great deal of work on designing supervised deep semantic segmentation algorithms. As in many tasks sufficient pixel-level labels are very difficult to obtain, we propose a method which…

Gaussian mixtures are a powerful and widely used tool to model non-Gaussian estimation problems. They are able to describe measurement errors that follow arbitrary distributions and can represent ambiguity in assignment tasks like point set…

Conventional methods for computing maximum-likelihood estimators (MLE) often converge slowly in practical situations, leading to a search for simplifying methods that rely on additional assumptions for their validity. In this work, we…

Several recently developed methods have the potential to harness machine learning in the pursuit of target quantities inspired by causal inference, including inverse weighting, doubly robust estimating equations and substitution estimators…

Our main interest in this paper is to study some approximation problems for classes of functions with mixed smoothness. We use technique, based on a combination of results from hyperbolic cross approximation, which were obtained in 1980s --…

Large language models (LLMs) have been widely adopted in mathematical optimization in scientific scenarios for their extensive knowledge and advanced reasoning capabilities. Existing methods mainly focus on utilizing LLMs to solve…

Downsampling or under-sampling is a technique that is utilized in the context of large and highly imbalanced classification models. We study optimal downsampling for imbalanced classification using generalized linear models (GLMs). We…

Stochastic gradient descent type methods are ubiquitous in machine learning, but they are only applicable to the optimization of differentiable functions. Proximal algorithms are more general and applicable to nonsmooth functions. We…

Mixtures of generalized normal distributions (MGND) have gained popularity for modelling datasets with complex statistical behaviours. However, the estimation of the shape parameter within the maximum likelihood framework is quite complex,…

Highly robust and efficient estimators for the generalized linear model with a dispersion parameter are proposed. The estimators are based on three steps. In the first step the maximum rank correlation estimator is used to consistently…

The linear coefficient in a partially linear model with confounding variables can be estimated using double machine learning (DML). However, this DML estimator has a two-stage least squares (TSLS) interpretation and may produce overly wide…

We consider inference in models defined by approximate moment conditions. We show that near-optimal confidence intervals (CIs) can be formed by taking a generalized method of moments (GMM) estimator, and adding and subtracting the standard…

We propose an inexact variable-metric proximal point algorithm to accelerate gradient-based optimization algorithms. The proposed scheme, called QNing can be notably applied to incremental first-order methods such as the stochastic…

Probabilistic inference is a fundamental task in modern machine learning. Recent advances in tensor network (TN) contraction algorithms have enabled the development of better exact inference methods. However, many common inference tasks in…

We propose a fast algorithm for computing the GMM estimator in the BLP demand model (Berry, Levinsohn, and Pakes, 1995). Inspired by nested pseudo-likelihood methods for dynamic discrete choice models, our approach avoids repeatedly solving…

We study maximum likelihood estimation for spatial generalized linear mixed models with Gaussian process approximations using a stochastic Newton-Raphson algorithm. We consider two Gaussian Process approximations in this context: spectral…