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We propose a new method for feature learning and function estimation in supervised learning via regularised empirical risk minimisation. Our approach considers functions as expectations of Sobolev functions over all possible one-dimensional…

Recently there has been a great deal of interest surrounding the calibration of quantum sensors using machine learning techniques. In this work, we explore the use of regression to infer a machine-learned point estimate of an unknown…

In online Inverse Reinforcement Learning (IRL), the learner can collect samples about the dynamics of the environment to improve its estimate of the reward function. Since IRL suffers from identifiability issues, many theoretical works on…

Subspace recycling iterative methods and other subspace augmentation schemes are a successful extension to Krylov subspace methods in which a Krylov subspace is augmented with a fixed subspace spanned by vectors deemed to be helpful in…

The K-means algorithm is among the most commonly used data clustering methods. However, the regular K-means can only be applied in the input space and it is applicable when clusters are linearly separable. The kernel K-means, which extends…

Large Language Models (LLMs) heavily rely on high-quality training data, making data valuation crucial for optimizing model performance, especially when working within a limited budget. In this work, we aim to offer a third-party data…

One well adopted power grid simulation methodology is to factorize matrix once and perform only backward forward substitution with a deliberately chosen step size along the simulation. Since the required simulation time is usually long for…

Ellipsoid fitting is of general interest in machine vision, such as object detection and shape approximation. Most existing approaches rely on the least-squares fitting of quadrics, minimizing the algebraic or geometric distances, with…

Wildlife conservation using continuous monitoring of environmental factors and biomedical classification, which generate a vast amount of sensor data, is a challenge due to limited bandwidth in the case of remote monitoring. It becomes…

While most approaches to the problem of Inverse Reinforcement Learning (IRL) focus on estimating a reward function that best explains an expert agent's policy or demonstrated behavior on a control task, it is often the case that such…

The Fisher information matrix (FIM) has long been of interest in statistics and other areas. It is widely used to measure the amount of information and calculate the lower bound for the variance for maximum likelihood estimation (MLE). In…

The linear-chain Conditional Random Field (CRF) model is one of the most widely-used neural sequence labeling approaches. Exact probabilistic inference algorithms such as the forward-backward and Viterbi algorithms are typically applied in…

Multivariable parametric models are essential for optimizing the performance of high-tech systems. The main objective of this paper is to develop an identification strategy that provides accurate parametric models for complex multivariable…

The rapid growth of microcontroller-based IoT devices has opened up numerous applications, from smart manufacturing to personalized healthcare. Despite the widespread adoption of energy-efficient microcontroller units (MCUs) in the Tiny…

We study the estimation and prediction of functional autoregressive~(FAR) processes, a statistical tool for modeling functional time series data. Due to the infinite-dimensional nature of FAR processes, the existing literature addresses its…

Autoregressive moving average (ARMA) models are widely used for analyzing time series data. However, standard likelihood-based inference methodology for ARMA models has avoidable limitations. We show that currently accepted standards for…

Three steps in the development of the maximum likelihood (ML) method are presented. At first, the application of the ML method and Fisher information notion in the model selection analysis is described (Chapter 1). The fundamentals of…

The FEAST eigenvalue algorithm is a subspace iteration algorithm that uses contour integration in the complex plane to obtain the eigenvectors of a matrix for the eigenvalues that are located in any user-defined search interval. By…

With the emergence of mixed precision capabilities in hardware, iterative refinement schemes for solving linear systems $Ax=b$ have recently been revisited and reanalyzed in the context of three or more precisions. These new analyses show…

This paper adds to the growing literature of reinforcement learning (RL) for healthcare by proposing a novel paradigm: augmenting any predictor with Rule-based RL Layer (RRLL) that corrects the model's physiologically impossible…