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Accounting for the complexity of psychological theories requires methods that can predict not only changes in the means of latent variables -- such as personality factors, creativity, or intelligence -- but also changes in their variances.…

We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a…

Linear Least Squares is a very well known technique for parameter estimation, which is used even when sub-optimal, because of its very low computational requirements and the fact that exact knowledge of the noise statistics is not required.…

In this paper, we propose a certified reduced basis (RB) method for quasilinear elliptic problems together with its application to nonlinear magnetostatics equations, where the later model permanent magnet synchronous motors (PMSM). The…

Predictive modeling involving simulation and sensor data at the same time, is a growing challenge in computational science. Even with large-scale finite element models, a mismatch to the sensor data often remains, which can be attributed to…

We use asymptotically optimal \emph{adaptive} numerical methods (here specifically a wavelet scheme) for snapshot computations within the offline phase of the Reduced Basis Method (RBM). The resulting discretizations for each snapshot…

We study the problem of identifying change points in high-dimensional generalized linear models, and propose an approach based on sample-weighted empirical risk minimization. Our method, Weighted ERM, encodes priors on the change points via…

Understanding the results of deep neural networks is an essential step towards wider acceptance of deep learning algorithms. Many approaches address the issue of interpreting artificial neural networks, but often provide divergent…

In the era of Model-as-a-Service, organizations increasingly rely on third-party AI models for rapid deployment. However, the dynamic nature of emerging AI applications, the continual introduction of new datasets, and the growing number of…

This paper examines the use of a residual bootstrap for bias correction in machine learning regression methods. Accounting for bias is an important obstacle in recent efforts to develop statistical inference for machine learning methods. We…

Expectation maximisation (EM) is an unsupervised learning method for estimating the parameters of a finite mixture distribution. It works by introducing "hidden" or "latent" variables via Baum's auxiliary function $Q$ that allow the joint…

Quantifying the complexity and irregularity of time series data is a primary pursuit across various data-scientific disciplines. Sample entropy (SampEn) is a widely adopted metric for this purpose, but its reliability is sensitive to the…

This work proposes a machine-learning framework for constructing statistical models of errors incurred by approximate solutions to parameterized systems of nonlinear equations. These approximate solutions may arise from early termination of…

Regularized system identification has become a significant complement to more classical system identification. It has been numerically shown that kernel-based regularized estimators often perform better than the maximum likelihood estimator…

In this study, we consider the problem of variable selection and estimation in high-dimensional linear regression models when the complete data are not accessible, but only certain marginal information or summary statistics are available.…

Many applications of generalised linear models (GLMs) can be improved by applying constraints that impose assumptions on the associations or improve consistency of the estimators. Yet, there are still barriers to the implementation and…

Optimizing machine learning algorithms that are used to solve the objective function has been of great interest. Several approaches to optimize common algorithms, such as gradient descent and stochastic gradient descent, were explored. One…

The paradigm of Multimodal Large Language Models (MLLMs) offers a promising blueprint for advancing the electromagnetic (EM) domain. However, prevailing approaches often deviate from the native MLLM paradigm, instead using task-specific or…

Extreme learning machine (ELM) as an emerging branch of shallow networks has shown its excellent generalization and fast learning speed. However, for blended data, the robustness of ELM is weak because its weights and biases of hidden nodes…

Selecting artificial intelligence (AI) models, such as large language models (LLMs), from multiple candidates requires accurate performance estimation. This is ideally achieved through empirical evaluations involving abundant real-world…