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In geostatistics, and also in other applications in science and engineering, we are now performing updates on Gaussian process models with many thousands or even millions of components. These large-scale inferences involve computational…

Metric data plays an important role in various settings such as metric-based indexing, clustering, classification, and approximation algorithms in general. Due to measurement error, noise, or an inability to completely gather all the data,…

Anomaly detection in medical imaging is essential for identifying rare pathological conditions, particularly when annotated abnormal samples are limited. We propose a hybrid anomaly detection framework that integrates self-supervised…

For many machine learning algorithms such as $k$-Nearest Neighbor ($k$-NN) classifiers and $ k $-means clustering, often their success heavily depends on the metric used to calculate distances between different data points. An effective…

We present a method for simultaneous Bayesian learning of the correlation matrix and graphical model of a multivariate dataset, along with uncertainties in each, to subsequently compute distance between the learnt graphical models of a pair…

Categorical data does not have an intrinsic definition of distance or order, and therefore, established visualization techniques for categorical data only allow for a set-based or frequency-based analysis, e.g., through Euler diagrams or…

Dimensionality reduction is often used as an initial step in data exploration, either as preprocessing for classification or regression or for visualization. Most dimensionality reduction techniques to date are unsupervised; they do not…

Reliable anomaly detection is essential for ensuring the safety of autonomous robots, particularly when conventional detection systems based on vision or LiDAR become unreliable in adverse or unpredictable conditions. In such scenarios,…

Validation metrics are key for the reliable tracking of scientific progress and for bridging the current chasm between artificial intelligence (AI) research and its translation into practice. However, increasing evidence shows that…

Matrix-variate data of high dimensions are frequently observed in finance and economics, spanning extended time periods, such as the long-term data on international trade flows among numerous countries. To address potential structural…

Human mobility similarity comparison plays a critical role in mobility estimation/prediction model evaluation, mobility clustering and mobility matching, which exerts an enormous impact on improving urban mobility, accessibility, and…

In meta-analysis with continuous outcomes, the use of effect sizes based on the means is the most common. It is often found, however, that only the quantile summary measures are reported in some studies, and in certain scenarios, a…

Visual analytics now plays a central role in decision-making across diverse disciplines, but it can be unreliable: the knowledge or insights derived from the analysis may not accurately reflect the underlying data. In this dissertation, we…

Geodesic distance serves as a reliable means of measuring distance in nonlinear spaces, and such nonlinear manifolds are prevalent in the current multimodal learning. In these scenarios, some samples may exhibit high similarity, yet they…

Repeated-measure designs allow comparisons within a group as well as between groups, and are commonly referred to as split-plot designs. While originating in agricultural experiments, they are now widely used in medical research,…

Cross-domain visual data matching is one of the fundamental problems in many real-world vision tasks, e.g., matching persons across ID photos and surveillance videos. Conventional approaches to this problem usually involves two steps: i)…

We propose a likelihood ratio test framework for testing normal mean vectors in high-dimensional data under two common scenarios: the one-sample test and the two-sample test with equal covariance matrices. We derive the test statistics…

In recent years, there has been a surge in the prevalence of high- and multi-dimensional temporal data across various scientific disciplines. These datasets are characterized by their vast size and challenging potential for analysis. Such…

This paper surveys visual methods of explainability of Machine Learning (ML) with focus on moving from quasi-explanations that dominate in ML to domain-specific explanation supported by granular visuals. ML interpretation is fundamentally a…

With the increasing volume of astronomical data generated by modern survey telescopes, automated pipelines and machine learning techniques have become crucial for analyzing and extracting knowledge from these datasets. Anomaly detection,…