Related papers: Higher-Order Partial Least Squares (HOPLS): A Gene…
Recently, tensor data (or multidimensional array) have been generated in many modern applications, such as functional magnetic resonance imaging (fMRI) in neuroscience and videos in video analysis. Many efforts are made in recent years to…
Contingency tables are a fundamental representation of multivariate categorical data. As the size of the contingency table grows exponentially with the number of variables, even a moderate number of variables, each with a moderate number of…
Higher-Order Hypergraph Learning (HOHL) was recently introduced as a principled alternative to classical hypergraph regularization, enforcing higher-order smoothness via powers of multiscale Laplacians induced by the hypergraph structure.…
Data-driven deep learning methods like neural operators have advanced in solving nonlinear temporal partial differential equations (PDEs). However, these methods require large quantities of solution pairs\u2014the solution functions and…
This paper considers the approximation of partial differential equations with a point collocation framework based on high-order local maximum-entropy schemes (HOLMES). In this approach, smooth basis functions are computed through an…
In this article, the parameters of a hybrid log-linear model (log-Poisson) are estimated using the fuzzy least-squares (FLS) procedures (Celmi\c{n}\v{s}, 987a,b, D'Urso and Gastaldi, 2000, DUrso and Gastaldi, 2001). A goodness of fit have…
We propose a new scalable algorithm for holistic linear regression building on Bertsimas & King (2016). Specifically, we develop new theory to model significance and multicollinearity as lazy constraints rather than checking the conditions…
Sorted $\ell_1$ Penalized Estimator (SLOPE) is a relatively new convex regularization method for fitting high-dimensional regression models. SLOPE allows to reduce the model dimension by shrinking some estimates of the regression…
We present a new finite-time analysis of the estimation error of the Ordinary Least Squares (OLS) estimator for stable linear time-invariant systems. We characterize the number of observed samples (the length of the observed trajectory)…
Ordinary least squares (OLS) linear regression is one of the most basic statistical techniques for data analysis. In the main stream literature and the statistical education, the study of linear regression is typically restricted to the…
Recurrent Neural Networks (RNNs) have been widely used in sequence analysis and modeling. However, when processing high-dimensional data, RNNs typically require very large model sizes, thereby bringing a series of deployment challenges.…
Hierarchical data analysis is crucial in various fields for making discoveries. The linear mixed model is often used for training hierarchical data, but its parameter estimation is computationally expensive, especially with big data.…
Sensor networks increasingly govern modern infrastructure, yet the data they lose are rarely missing in the uniform-random patterns assumed by standard imputation benchmarks. Loop detectors go offline during calibration, roadside cabinets…
In many applications throughout science and engineering, model reduction plays an important role replacing expensive large-scale linear dynamical systems by inexpensive reduced order models that capture key features of the original, full…
Partial Least Squares (PLS) methods have been heavily exploited to analyse the association between two blocs of data. These powerful approaches can be applied to data sets where the number of variables is greater than the number of…
In statistics, series of ordinary least squares problems (OLS) are used to study the linear correlation among sets of variables of interest; in many studies, the number of such variables is at least in the millions, and the corresponding…
Here we propose an algorithm, named generalized orthogonal components regression (GOCRE), to explore the relationship between a categorical outcome and a set of massive variables. A set of orthogonal components are sequentially constructed…
Tensor data represents a multidimensional array. Regression methods based on low-rank tensor decomposition leverage structural information to reduce the parameter count. Multilinear logistic regression serves as a powerful tool for the…
Regression analysis is an important instrument to determine the effect of the explanatory variables on response variables. When outliers and bias errors are present, the standard weighted least squares estimator may perform poorly. For this…
Demanding sparsity in estimated models has become a routine practice in statistics. In many situations, we wish to require that the sparsity patterns attained honor certain problem-specific constraints. Hierarchical sparse modeling (HSM)…