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The Lasso method is known to exhibit instability in the presence of highly correlated features, often leading to an arbitrary selection of predictors. This issue manifests itself in two primary error types: the erroneous omission of…

Forecasting the evolution of complex systems is one of the grand challenges of modern data science. The fundamental difficulty lies in understanding the structure of the observed stochastic process. In this paper, we show that every…

Structural change detection problems are often encountered in analytics and econometrics, where the performance of a model can be significantly affected by unforeseen changes in the underlying relationships. Although these problems have a…

Many econometric analyses involve spatio--temporal data. A considerable amount of literature has addressed spatio--temporal models, with Spatial Dynamic Panel Data (SDPD) being widely investigated and applied. In real data applications,…

In this article, it is described how to use statistical data analysis to obtain models directly from data. The focus is put on finding nonlinearities within a generalized additive model. These models are found by the means of backfitting…

In real data analysis with structural equation modeling, data are unlikely to be exactly normally distributed. If we ignore the non-normality reality, the parameter estimates, standard error estimates, and model fit statistics from normal…

Astronomical time series from large-scale surveys like LSST are often irregularly sampled and incomplete, posing challenges for classification and anomaly detection. We introduce a new framework based on Neural Stochastic Delay Differential…

This article introduces a novel nonparametric methodology for Generalized Linear Models which combines the strengths of the binary regression and latent variable formulations for categorical data, while overcoming their disadvantages.…

Time series autoregression (AR) is a classical tool for modeling auto-correlations and periodic structures in real-world systems. We revisit this model from an interpretable machine learning perspective by introducing sparse autoregression…

This paper investigates the applicability of a recently-proposed nonlinear sparse Bayesian learning (NSBL) algorithm to identify and estimate the complex aerodynamics of limit cycle oscillations. NSBL provides a semi-analytical framework…

A new method for analyzing high-dimensional categorical data, Linear Latent Structure (LLS) analysis, is presented. LLS models belong to the family of latent structure models, which are mixture distribution models constrained to satisfy the…

Nonlinear dimension reduction (NLDR) techniques such as tSNE, and UMAP provide a low-dimensional representation of high-dimensional data ($p\text{-}D$) by applying a nonlinear transformation. NLDR often exaggerates random patterns. But NLDR…

Time Series forecasting is critical in diverse domains such as weather forecasting, financial investment, and traffic management. While traditional numerical metrics like mean squared error (MSE) can quantify point-wise accuracy, they fail…

Stochastic computing (SC) has emerged as an efficient low-power alternative for deploying neural networks (NNs) in resource-limited scenarios, such as the Internet of Things (IoT). By encoding values as serial bitstreams, SC significantly…

Analog forecasting is a nonparametric technique introduced by Lorenz in 1969 which predicts the evolution of states of a dynamical system (or observables defined on the states) by following the evolution of the sample in a historical record…

Estimation of Markov Random Field and covariance models from high-dimensional data represents a canonical problem that has received a lot of attention in the literature. A key assumption, widely employed, is that of {\em sparsity} of the…

We propose non-parametric estimators for the average run length (ARL) and average detection delay (ADD) in quickest changepoint detection (QCD) under finite and irregular sequence lengths. Although ARL and ADD are widely used as optimality…

We address the problem of uncertainty quantification in time series forecasting by exploiting observations at correlated sequences. Relational deep learning methods leveraging graph representations are among the most effective tools for…

We develop theory for nonlinear dimensionality reduction (NLDR). A number of NLDR methods have been developed, but there is limited understanding of how these methods work and the relationships between them. There is limited basis for using…

This paper addresses a gap in the current state of the art by providing a solution for modeling causal relationships that evolve over time and occur at different time scales. Specifically, we introduce the multiscale non-stationary directed…