Related papers: On Correlation and Prediction Interval Reduction

Principal Component Analysis (PCA) is a well known procedure to reduce intrinsic complexity of a dataset, essentially through simplifying the covariance structure or the correlation structure. We introduce a novel algebraic, model-based…

Probabilistic models are often used to make predictions in regions of the data space where no observations are available, but it is not always clear whether such predictions are well-informed by previously seen data. In this paper, we…

Pairwise likelihood is a useful approximation to the full likelihood function for covariance estimation in high-dimensional context. It simplifies high-dimensional dependencies by combining marginal bivariate likelihood objects, thus making…

In this work we present a statistical approach to distinguish and interpret the complex relationship between several predictors and a response variable at the small area level, in the presence of i) high correlation between the predictors…

To infer a function value on a specific point $x$, it is essential to assign higher weights to the points closer to $x$, which is called local polynomial / multivariable regression. In many practical cases, a limited sample size may ruin…

We study inference with a small labeled sample, a large unlabeled sample, and high-quality predictions from an external model. We link prediction-powered inference with empirical likelihood by stacking supervised estimating equations based…

Sparse recovery in linear systems underpins applications from signal processing to high-dimensional regression. Sparse Bayesian Learning, grounded in the principle of automatic relevance determination (ARD), offers a practical Bayesian…

The Conway-Maxwell-Poisson (CMP) or COM-Poison regression is a popular model for count data due to its ability to capture both under dispersion and over dispersion. However, CMP regression is limited when dealing with complex nonlinear…

dentifying associations among biological variables is a major challenge in modern quantitative biological research, particularly given the systemic and statistical noise endemic to biological systems. Drug sensitivity data has proven to be…

The Partial Information Decomposition (PID) framework has emerged as a powerful tool for analyzing high-order interdependencies in complex network systems. However, its application to dynamic processes remains challenging due to the…

The partial correlation coefficient is a commonly used measure to assess the conditional dependence between two random variables. We provide a thorough explanation of the partial copula, which is a natural generalization of the partial…

The accurate classification of galaxies in large-sample astrophysical databases of galaxy clusters depends sensitively on the ability to distinguish between morphological types, especially at higher redshifts. This capability can be…

Probabilistic modeling is cyclical: we specify a model, infer its posterior, and evaluate its performance. Evaluation drives the cycle, as we revise our model based on how it performs. This requires a metric. Traditionally, predictive…

We revisit the index leverage effect, that can be decomposed into a volatility effect and a correlation effect. We investigate the latter using a matrix regression analysis, that we call `Principal Regression Analysis' (PRA) and for which…

Confidence intervals (CIs) are instrumental in statistical analysis, providing a range estimate of the parameters. In modern statistics, selective inference is common, where only certain parameters are highlighted. However, this selective…

This paper proposes a novel loss function, called 'Tube Loss', for simultaneous estimation of bounds of a Prediction Interval (PI) in the regression setup. The PIs obtained by minimizing the empirical risk based on the Tube Loss are shown…

Sparse linear discriminant analysis via penalized optimal scoring is a successful tool for classification in high-dimensional settings. While the variable selection consistency of sparse optimal scoring has been established, the…

We propose new methods for multivariate linear regression when the regression coefficient matrix is sparse and the error covariance matrix is dense. We assume that the error covariance matrix has equicorrelation across the response…

We consider the scenario where the parameters of a probabilistic model are expected to vary over time. We construct a novel prior distribution that promotes sparsity and adapts the strength of correlation between parameters at successive…

Detecting dependence between two random variables is a fundamental problem. Although the Pearson correlation is effective for capturing linear dependency, it can be entirely powerless for detecting nonlinear and/or heteroscedastic patterns.…