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Anomalies can be defined as any non-random structure which deviates from normality. Anomaly detection methods reported in the literature are numerous and diverse, as what is considered anomalous usually varies depending on particular…

Many important data analysis applications present with severely imbalanced datasets with respect to the target variable. A typical example is medical image analysis, where positive samples are scarce, while performance is commonly estimated…

Large language models (LLMs) have achieved remarkable performance in various evaluation benchmarks. However, concerns are raised about potential data contamination in their considerable volume of training corpus. Moreover, the static nature…

Generalized linear models (GLMs) -- such as logistic regression, Poisson regression, and robust regression -- provide interpretable models for diverse data types. Probabilistic approaches, particularly Bayesian ones, allow coherent…

Generalized linear models are flexible tools for the analysis of diverse datasets, but the classical formulation requires that the parametric component is correctly specified and the data contain no atypical observations. To address these…

Deep Learning Gaussian Processes (DL-GP) are proposed as a methodology for analyzing (approximating) computer models that produce heteroskedastic and high-dimensional output. Computer simulation models have many areas of applications,…

Developing efficient time series anomaly detection techniques is important to maintain service quality and provide early alarms. Generative neural network methods are one class of the unsupervised approaches that are achieving increasing…

We characterize the sample size required for accurate graphical model selection from non-stationary samples. The observed data is modeled as a vector-valued zero-mean Gaussian random process whose samples are uncorrelated but have different…

Holistic linear regression extends the classical best subset selection problem by adding additional constraints designed to improve the model quality. These constraints include sparsity-inducing constraints, sign-coherence constraints and…

There exist multiple methods to detect outliers in multivariate data in the literature, but most of them require to estimate the covariance matrix. The higher the dimension, the more complex the estimation of the matrix becoming impossible…

Gaussian process (GP) is a Bayesian model which provides several advantages for regression tasks in machine learning such as reliable quantitation of uncertainty and improved interpretability. Their adoption has been precluded by their…

The analysis of longitudinal data gives the chance to observe how unit behaviors change over time, but it also poses a series of issues. These have been the focus of an extensive literature in the context of linear and generalized linear…

Motivation: Mendelian randomization (MR) infers causal relationships between exposures and outcomes using genetic variants as instrumental variables. Typically, MR considers only a pair of exposure and outcome at a time, limiting its…

Large Language Models (LLMs) frequently generate plausible but non-factual content, a phenomenon known as hallucination. While existing detection methods typically rely on computationally expensive sampling-based consistency checks or…

A popular technique for selecting and tuning machine learning estimators is cross-validation. Cross-validation evaluates overall model fit, usually in terms of predictive accuracy. In causal inference, the optimal choice of estimator…

Gaussian processes (GPs) are widely used as distributions of random effects in linear mixed models, which are fit using the restricted likelihood or the closely-related Bayesian analysis. This article addresses two problems. First, we…

In this paper, we explore various statistical techniques for anomaly detection in conjunction with the popular Long Short-Term Memory (LSTM) deep learning model for transportation networks. We obtain the prediction errors from an LSTM…

This paper introduces the generalized Hausman test as a novel method for detecting non-normality of the latent variable distribution of unidimensional Item Response Theory (IRT) models for binary data. The test utilizes the pairwise maximum…

We present GLEAM (Galaxy Line Emission & Absorption Modeling), a Python tool for fitting Gaussian models to emission and absorption lines in large samples of 1D extragalactic spectra. GLEAM is tailored to work well in batch mode without…

Identifying anomalous patterns in real-world data is essential for understanding where, when, and how systems deviate from their expected dynamics. Yet methods that separately consider the anomalousness of each individual data point have…