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Accurate models are essential for design, performance prediction, control, and diagnostics in complex engineering systems. Physics-based models excel during the design phase but often become outdated during system deployment due to changing…

While interpretability is crucial for machine learning applications in safety-critical domains and for regulatory compliance, existing tabular foundation models like TabPFN lack transparency. Generalized Additive Models (GAMs) provide the…

We investigate the use of models from the theory of regularity structures as features in machine learning tasks. A model is a polynomial function of a space-time signal designed to well-approximate solutions to partial differential…

We present a novel, generalised formulation to treat coupled structural integrity problems by combining phase field and multi-physics modelling. The approach exploits the versatility of the heat transfer equation and is therefore well…

Feature-importance methods show promise in transforming machine learning models from predictive engines into tools for scientific discovery. However, due to data sampling and algorithmic stochasticity, expressive models can be unstable,…

A methodology is developed for the adjustment of the covariance matrices underlying a multivariate constant time series dynamic linear model. The covariance matrices are embedded in a distribution-free inner-product space of matrix objects…

This work focuses on the mixed membership models for multivariate categorical data widely used for analyzing survey responses and population genetics data. These grade of membership (GoM) models offer rich modeling power but present…

Traditional time series models are task-specific and often depend on dataset-specific training and extensive feature engineering. While Transformer-based architectures have improved scalability, foundation models, commonplace in text,…

We combine high-dimensional factor models with fractional integration methods and derive models where nonstationary, potentially cointegrated data of different persistence is modelled as a function of common fractionally integrated factors.…

Spatial processes with nonstationary and anisotropic covariance structure are often used when modelling, analysing and predicting complex environmental phenomena. Such processes may often be expressed as ones that have stationary and…

Generalized Additive Models (GAMs) have recently experienced a resurgence in popularity due to their interpretability, which arises from expressing the target value as a sum of non-linear transformations of the features. Despite the current…

Predictive analytics aims to build machine learning models to predict behavior patterns and use predictions to guide decision-making. Predictive analytics is human involved, thus the machine learning model is preferred to be interpretable.…

This paper studies the inference of the regression coefficient matrix under multivariate response linear regressions in the presence of hidden variables. A novel procedure for constructing confidence intervals of entries of the coefficient…

FeFETs hold strong potential for advancing memory and logic technologies, but their inherent randomness arising from both operational cycling and fabrication variability poses significant challenges for accurate and reliable modeling.…

Gaussian Process (GP) models are a powerful tool in probabilistic machine learning with a solid theoretical foundation. Thanks to current advances, modeling complex data with GPs is becoming increasingly feasible, which makes them an…

Gaussian process (GP) models that combine both categorical and continuous input variables have found use in analysis of longitudinal data and computer experiments. However, standard inference for these models has the typical cubic scaling,…

Numerical homogenization and multiscale finite element methods construct effective properties on a coarse grid by solving local problems and extracting the average effective properties from these local solutions. In some cases, the…

Despite the versatility of generalized linear mixed models in handling complex experimental designs, they often suffer from misspecification and convergence problems. This makes inference on the values of coefficients problematic. To…

Undirected graphical models are a key component in the analysis of complex observational data in a large variety of disciplines. In many of these applications one is interested in estimating the undirected graphical model underlying a…

Understanding the decisions of deep learning (DL) models is essential for the acceptance of DL to risk-sensitive applications. Although methods, like class activation maps (CAMs), give a glimpse into the black box, they do miss some crucial…