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Histogram-valued variables are a particular kind of variables studied in Symbolic Data Analysis where to each entity under analysis corresponds a distribution that may be represented by a histogram or by a quantile function. Linear…
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…
This paper studies the subspace segmentation problem which aims to segment data drawn from a union of multiple linear subspaces. Recent works by using sparse representation, low rank representation and their extensions attract much…
The effectiveness of non-parametric, kernel-based methods for function estimation comes at the price of high computational complexity, which hinders their applicability in adaptive, model-based control. Motivated by approximation techniques…
The analytic characterization of the high-dimensional behavior of optimization for Generalized Linear Models (GLMs) with Gaussian data has been a central focus in statistics and probability in recent years. While convex cases, such as the…
Spatial-temporal estimation of signals on graph edges is challenging because most conventional Graph Signal Processing techniques are defined on the graph nodes. Leveraging the Line Graph transform, the Line Graph Least Mean Square (LGLMS)…
Regression adjustment is broadly applied in randomized trials under the premise that it usually improves the precision of a treatment effect estimator. However, previous work has shown that this is not always true. To further understand…
Performance of regularized least-squares estimation in noisy compressed sensing is analyzed in the limit when the dimensions of the measurement matrix grow large. The sensing matrix is considered to be from a class of random ensembles that…
The LMS algorithm is one of the most successful adaptive filtering algorithms. It uses the instantaneous value of the square of the error signal as an estimate of the mean-square error (MSE). The LMS algorithm changes (adapts) the filter…
Sparse linear regression, which entails finding a sparse solution to an underdetermined system of linear equations, can formally be expressed as an $l_0$-constrained least-squares problem. The Orthogonal Least-Squares (OLS) algorithm…
Uncovering genuine relationships between a response variable of interest and a large collection of covariates is a fundamental and practically important problem. In the context of Gaussian linear models, both the Bayesian and non-Bayesian…
Presented is a new algorithm for estimating the frequency of a single-tone noisy signal using linear least squares (LLS). Frequency estimation is a nonlinear problem, and typically, methods such as Nonlinear Least Squares (NLS) (batch) or a…
We study the task of conducting structured reasoning as generating a reasoning graph from natural language input using large language models (LLMs). Previous approaches have explored various prompting schemes, yet they suffer from error…
Randomized experiments are the gold standard for causal inference, and justify simple comparisons across treatment groups. Regression adjustment provides a convenient way to incorporate covariate information for additional efficiency. This…
Many problems in statistics and machine learning can be formulated as model selection problems, where the goal is to choose an optimal parsimonious model among a set of candidate models. It is typical to conduct model selection by…
In this paper we analyze, for a model of linear regression with gaussian covariates, the performance of a Bayesian estimator given by the mean of a log-concave posterior distribution with gaussian prior, in the high-dimensional limit where…
We explore the usage of the Levenberg-Marquardt (LM) algorithm for regression (non-linear least squares) and classification (generalized Gauss-Newton methods) tasks in neural networks. We compare the performance of the LM method with other…
We address component-based regularisation of a multivariate Generalized Linear Mixed Model. A set of random responses Y is modelled by a GLMM, using a set X of explanatory variables and a set T of additional covariates. Variables in X are…
It is well known that in the presence of heteroscedasticity ordinary least squares estimator is not efficient. I propose a generalized automatic least squares estimator (GALS) that makes partial correction of heteroscedasticity based on a…
Linear regression is arguably the most widely used statistical method. With fixed regressors and correlated errors, the conventional wisdom is to modify the variance-covariance estimator to accommodate the known correlation structure of the…