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Multivariate time series (MTS) have become increasingly common in healthcare domains where human vital signs and laboratory results are collected for predictive diagnosis. Recently, there have been increasing efforts to visualize healthcare…

A task of interest in machine learning (ML) is that of ascribing explanations to the predictions made by ML models. Furthermore, in domains deemed high risk, the rigor of explanations is paramount. Indeed, incorrect explanations can and…

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…

Dimensionality reduction and clustering techniques are frequently used to analyze complex data sets, but their results are often not easy to interpret. We consider how to support users in interpreting apparent cluster structure on scatter…

We consider high-dimensional generalized linear models when the covariates are contaminated by measurement error. Estimates from errors-in-variables regression models are well-known to be biased in traditional low-dimensional settings if…

Dimensionality reduction techniques play important roles in the analysis of big data. Traditional dimensionality reduction approaches, such as principal component analysis (PCA) and linear discriminant analysis (LDA), have been studied…

This paper demonstrates RAGE, an interactive tool for explaining Large Language Models (LLMs) augmented with retrieval capabilities; i.e., able to query external sources and pull relevant information into their input context. Our…

The advent of modern technology, permitting the measurement of thousands of characteristics simultaneously, has given rise to floods of data characterized by many large or even huge datasets. This new paradigm presents extraordinary…

The statistical analysis of functional data is a growing need in many research areas. In particular, a robust methodology is important to study curves, which are the output of experiments in applied statistics. In this paper we study some…

Fitting linear regression models can be computationally very expensive in large-scale data analysis tasks if the sample size and the number of variables are very large. Random projections are extensively used as a dimension reduction tool…

A set of curves or images of similar shape is an increasingly common functional data set collected in the sciences. Principal Component Analysis (PCA) is the most widely used technique to decompose variation in functional data. However, the…

Principal component analysis continues to be a powerful tool in dimension reduction of high dimensional data. We assume a variance-diverging model and use the high-dimension, low-sample-size asymptotics to show that even though the…

Conventional visualization tools such as phase diagrams and convex hulls are ill-suited to visualize multiple principal element alloys (MPEAs) due to their large compositional space that cannot be easily projected onto two dimensions. Here,…

One of the central issues of several machine learning applications on real data is the choice of the input features. Ideally, the designer should select only the relevant, non-redundant features to preserve the complete information…

Visualisation is an effective way to facilitate the analysis and understanding of multivariate data. In the context of multi-objective optimisation, comparing to quantitative performance metrics, visualisation is, in principle, able to…

The ever-increasing quantity of multivariate process data is driving a need for skilled engineers to analyze, interpret, and build models from such data. Multivariate data analytics relies heavily on linear algebra, optimization, and…

Rule sets are often used in Machine Learning (ML) as a way to communicate the model logic in settings where transparency and intelligibility are necessary. Rule sets are typically presented as a text-based list of logical statements…

The practical impact of deep learning on complex supervised learning problems has been significant, so much so that almost every Artificial Intelligence problem, or at least a portion thereof, has been somehow recast as a deep learning…

Many data problems contain some reference or normal conditions, upon which to compare newly collected data. This scenario occurs in data collected as part of clinical trials to detect adverse events, or for measuring climate change against…

Rationale is defined as a subset of input features that best explains or supports the prediction by machine learning models. Rationale identification has improved the generalizability and interpretability of neural networks on vision and…