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The article attempts to find an algebraic formula describing the correlation coefficients between random variables and the principal components representing them. As a result of the analysis, starting from selected statistics relating to…
Despite their simplicity, linear models perform well at time series forecasting, even when pitted against deeper and more expensive models. A number of variations to the linear model have been proposed, often including some form of feature…
Linear regression is perhaps one of the most popular statistical concepts, which permeates almost every scientific field of study. Due to the technical simplicity and wide applicability of linear regression, attention is almost always…
A new method is proposed for variable screening, variable selection and prediction in linear regression problems where the number of predictors can be much larger than the number of observations. The method involves minimizing a penalized…
It is increasingly common to evaluate the same coreference resolution (CR) model on multiple datasets. Do these multi-dataset evaluations allow us to draw meaningful conclusions about model generalization? Or, do they rather reflect the…
In the present paper, we propose and analyze a novel method for estimating a univariate regression function of bounded variation. The underpinning idea is to combine two classical tools in nonparametric statistics, namely isotonic…
Multivariate time series analysis is a vital but challenging task, with multidisciplinary applicability, tackling the characterization of multiple interconnected variables over time and their dependencies. Traditional methodologies often…
This paper develops a new framework, called modular regression, to utilize auxiliary information -- such as variables other than the original features or additional data sets -- in the training process of linear models. At a high level, our…
The rapid development of high-throughput technologies has enabled the generation of data from biological or disease processes that span multiple layers, like genomic, proteomic or metabolomic data, and further pertain to multiple sources,…
A new multivariate concept of quantile, based on a directional version of Koenker and Bassett's traditional regression quantiles, is introduced for multivariate location and multiple-output regression problems. In their empirical version,…
We study a model where one target variable Y is correlated with a vector X:=(X_1,...,X_d) of predictor variables being potential causes of Y. We describe a method that infers to what extent the statistical dependences between X and Y are…
Learning curves provide insight into the dependence of a learner's generalization performance on the training set size. This important tool can be used for model selection, to predict the effect of more training data, and to reduce the…
This paper explores the generalization loss of linear regression in variably parameterized families of models, both under-parameterized and over-parameterized. We show that the generalization curve can have an arbitrary number of peaks, and…
Distributed learning provides an attractive framework for scaling the learning task by sharing the computational load over multiple nodes in a network. Here, we investigate the performance of distributed learning for large-scale linear…
With the increasing interplay between experimental and computational approaches at multiple length scales, new research directions are emerging in materials science and computational mechanics. Such cooperative interactions find many…
This paper describes a generalizable model evaluation method that can be adapted to evaluate AI/ML models across multiple criteria including core scientific principles and more practical outcomes. Emerging from prediction competitions in…
Distributed statistical learning problems arise commonly when dealing with large datasets. In this setup, datasets are partitioned over machines, which compute locally, and communicate short messages. Communication is often the bottleneck.…
A connection between the General Linear Model (GLM) in combination with classical statistical inference and the machine learning (MLE)-based inference is described in this paper. Firstly, the estimation of the GLM parameters is expressed as…
This paper considers the problem of estimation in the generalized semiparametric model for longitudinal data when the number of parameters diverges with the sample size. A penalization type of generalized estimating equation method is…
Graph-structured data is a type of data to be obtained associated with a graph structure where vertices and edges describe some kind of data correlation. This paper proposes a regression method on graph-structured data, which is based on…