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Knowing when a trained segmentation model is encountering data that is different to its training data is important. Understanding and mitigating the effects of this play an important part in their application from a performance and…
This article focuses on the problem of studying shared- and individual-specific structure in replicated networks or graph-valued data. In particular, the observed data consist of $n$ graphs, $G_i, i=1,\ldots,n$, with each graph consisting…
Inferring a binary connectivity graph from resting-state fMRI data for a single subject requires making several methodological choices and assumptions that can significantly affect the results. In this study, we investigate the robustness…
Brain structural networks are often represented as discrete adjacency matrices with elements summarizing the connectivity between pairs of regions of interest (ROIs). These ROIs are typically determined a-priori using a brain atlas. The…
An important task in image processing and neuroimaging is to extract quantitative information from the acquired images in order to make observations about the presence of disease or markers of development in populations. Having a…
This paper introduces a novel approach to statistics and data analysis, departing from the conventional assumption of data residing in Euclidean space to consider a Riemannian Manifold. The challenge lies in the absence of vector space…
In this paper, a novel Bayesian nonparametric test for assessing multivariate normal models is presented. While there are extensive frequentist and graphical methods for testing multivariate normality, it is challenging to find Bayesian…
ANOVA decomposition of function with random input variables provides ANOVA functionals (AFs), which contain information about the contributions of the input variables on the output variable(s). By embedding AFs into an appropriate…
While the manifold hypothesis is widely adopted in modern machine learning, complex data is often better modeled as stratified spaces -- unions of manifolds (strata) of varying dimensions. Stratified learning is challenging due to varying…
Upon a consistent topological statistical theory the application of structural statistics requires a quantification of the proximity structure of model spaces. An important tool to study these structures are Pseudo-Riemannian metrices,…
Novelty detection aims to automatically identify out-of-distribution (OOD) data, without any prior knowledge of them. It is a critical step in data monitoring, behavior analysis and other applications, helping enable continual learning in…
The manifold hypothesis says that natural high-dimensional data lie on or around a low-dimensional manifold. The recent success of statistical and learning-based methods in very high dimensions empirically supports this hypothesis,…
Many statistical analyses involve the comparison of multiple data sets collected under different conditions in order to identify the difference in the underlying distributions. A common challenge in multi-sample comparison is the presence…
Deep learning methods have boosted the adoption of NLP systems in real-life applications. However, they turn out to be vulnerable to distribution shifts over time which may cause severe dysfunctions in production systems, urging…
Wide accessibility of imaging and profile sensors in modern industrial systems created an abundance of high-dimensional sensing variables. This led to a a growing interest in the research of high-dimensional process monitoring. However,…
The Manifold Hypothesis is a widely accepted tenet of Machine Learning which asserts that nominally high-dimensional data are in fact concentrated near a low-dimensional manifold, embedded in high-dimensional space. This phenomenon is…
We introduce a manifold analysis technique for neural network representations. Normalized Space Alignment (NSA) compares pairwise distances between two point clouds derived from the same source and having the same size, while potentially…
The normality assumption for random errors is fundamental in the analysis of variance (ANOVA) models. However, it is rarely subjected to formal testing in practice, and theoretically justified procedures are largely unavailable, especially…
In recent years, the crucial importance of metrics in machine learning algorithms has led to an increasing interest for optimizing distance and similarity functions. Most of the state of the art focus on learning Mahalanobis distances…
Neural networks may naturally favor distance-based representations, where smaller activations indicate closer proximity to learned prototypes. This contrasts with intensity-based approaches, which rely on activation magnitudes. To test this…