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Statistical Relational Learning (SRL) models have attracted significant attention due to their ability to model complex data while handling uncertainty. However, most of these models have been limited to discrete domains due to their…
Graphical tests assess whether a function of interest departs from an envelope of functions generated under a simulated null distribution. This approach originated in spatial statistics, but has recently gained some popularity in functional…
Hypothesis testing results often rely on simple, yet important assumptions about the behaviour of the distribution of p-values under the null and the alternative. We examine tests for one dimensional parameters of interest that converge to…
While Supervised Fine-Tuning (SFT) and Rejection Sampling Fine-Tuning (RFT) are standard for LLM alignment, they either rely on costly expert data or discard valuable negative samples, leading to data inefficiency. To address this, we…
Persistent homology is a vital tool for topological data analysis. Previous work has developed some statistical estimators for characteristics of collections of persistence diagrams. However, tools that provide statistical inference for…
Reliable inference for spatial regression remains challenging because it requires the correct specification of the spatial dependence structure, the mean trend, and the error distribution. Existing parametric testing methods rely on…
Many testing problems are readily amenable to randomised tests such as those employing data splitting. However despite their usefulness in principle, randomised tests have obvious drawbacks. Firstly, two analyses of the same dataset may…
We introduce a new approach to probabilistic unsupervised learning based on the recognition-parametrised model (RPM): a normalised semi-parametric hypothesis class for joint distributions over observed and latent variables. Under the key…
The complex nature of artificial neural networks raises concerns on their reliability, trustworthiness, and fairness in real-world scenarios. The Shapley value -- a solution concept from game theory -- is one of the most popular explanation…
Random Effects analysis has been introduced into fMRI research in order to generalize findings from the study group to the whole population. Generalizing findings is obviously harder than detecting activation in the study group since in…
Machine learning (ML) algorithms become increasingly important in the analysis of astronomical data. However, since most ML algorithms are not designed to take data uncertainties into account, ML based studies are mostly restricted to data…
In meta analysis, multiple hypothesis testing and many other methods, p-values are utilized as inputs and assumed to be uniformly distributed over the unit interval under the null hypotheses. If data used to generate p-values have discrete…
We present a general nonparametric approach for testing whether a statistical parameter defined through conditional distributions is constant across the conditioning variables. Such hypotheses arise naturally in problems such as assessing…
Neural Radiance Field (NeRF) research has attracted significant attention recently, with 3D modelling, virtual/augmented reality, and visual effects driving its application. While current NeRF implementations can produce high quality visual…
Saliency Maps (SMs) have been extensively used to interpret deep learning models decision by highlighting the features deemed relevant by the model. They are used on highly nonlinear problems, where linear feature selection (FS) methods…
Understanding how deep learning architectures work is a central scientific problem. Recently, a correspondence between neural networks (NNs) and Euclidean quantum field theories (QFTs) has been proposed. This work investigates this…
Value-function approximation methods that operate in batch mode have foundational importance to reinforcement learning (RL). Finite sample guarantees for these methods often crucially rely on two types of assumptions: (1) mild distribution…
Foundation models (FMs), large neural networks pretrained on extensive and diverse datasets, have revolutionized artificial intelligence and shown significant promise in medical imaging by enabling robust performance with limited labeled…
Random feature mapping (RFM) is a popular method for speeding up kernel methods at the cost of losing a little accuracy. We study kernel ridge regression with random feature mapping (RFM-KRR) and establish novel out-of-sample error upper…
Brain mapping analyzes the wavelengths of brain signals and outputs them in a map, which is then analyzed by a radiologist. Introducing Machine Learning (ML) into the brain mapping process reduces the variable of human error in reading such…