Related papers: Revisiting the Conceptualization of Multiple Linea…
We consider a finite mixture model with varying mixing probabilities. Linear regression models are assumed for observed variables with coefficients depending on the mixture component the observed subject belongs to. A modification of the…
Machine learning (ML) applications have automated numerous real-life tasks, improving both private and public life. However, the black-box nature of many state-of-the-art models poses the challenge of model verification; how can one be sure…
Multiple Sclerosis is a degenerative condition of the central nervous system that affects nearly 2.5 million of individuals in terms of their physical, cognitive, psychological and social capabilities. Researchers are currently…
Many mechanical engineering applications call for multiscale computational modeling and simulation. However, solving for complex multiscale systems remains computationally onerous due to the high dimensionality of the solution space.…
Collinearity and near-collinearity of predictors cause difficulties when doing regression. In these cases, variable selection becomes untenable because of mathematical issues concerning the existence and numerical stability of the…
Model multiplicity is a well-known but poorly understood phenomenon that undermines the generalisation guarantees of machine learning models. It appears when two models with similar training-time performance differ in their predictions and…
In statistical learning, many problem formulations have been proposed so far, such as multi-class learning, complementarily labeled learning, multi-label learning, multi-task learning, which provide theoretical models for various real-world…
ML models have errors when used for predictions. The errors are unknown but can be quantified by model uncertainty. When multiple ML models are trained using the same training points, their model uncertainties may be statistically…
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…
Accurate forecasting of multivariate time series data is important in many engineering and scientific applications. Recent state-of-the-art works ignore the inter-relations between variates, using their model on each variate independently.…
Multi-label learning is a rapidly growing research area that aims to predict multiple labels from a single input data point. In the era of big data, tasks involving multi-label classification (MLC) or ranking present significant and…
Functional linear regression analysis aims to model regression relations which include a functional predictor. The analog of the regression parameter vector or matrix in conventional multivariate or multiple-response linear regression…
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…
We consider the on-line predictive version of the standard problem of linear regression; the goal is to predict each consecutive response given the corresponding explanatory variables and all the previous observations. The standard…
A fundamental aspect of relational data, such as from a social network, is the possibility of dependence among the relations. In particular, the relations between members of one pair of nodes may have an effect on the relations between…
Multiple linear regression is a basic statistical tool, yielding a prediction formula with the input variables, slopes, and an intercept. But is it really easy to see which terms have the largest effect, or to explain why the prediction of…
Model uncertainty is a crucial issue in statistics, econometrics and machine learning, yet its definition remains ambiguous and is subject to various interpretations in the literature. So far, there has not been a universally accepted…
This paper tackles the challenge of detecting unreliable behavior in regression algorithms, which may arise from intrinsic variability (e.g., aleatoric uncertainty) or modeling errors (e.g., model uncertainty). First, we formally introduce…
We reexamine the classical linear regression model when the model is subject to two types of uncertainty: (i) some of covariates are either missing or completely inaccessible, and (ii) the variance of the measurement error is undetermined…
Determinant formulas are presented for: a certain positive semidefinite, hermitian matrix; the loss value of multilinear regression; the multiple linear regression coefficient.