Statistics

This dissertation presents a general framework for changepoint detection based on L0 model selection. The core method, Iteratively Reweighted Fused Lasso (IRFL), improves upon the generalized lasso by adaptively reweighting penalties to…

Comparative judgement studies elicit quality assessments through pairwise comparisons, typically analysed using the Bradley-Terry model. A challenge in these studies is experimental design, specifically, determining the optimal pairs to…

Estimators in statistics and machine learning must typically trade off between efficiency, having low variance for a fixed target, and distributional robustness, such as multiaccuracy, or having low bias over a range of possible targets. In…

Efficient design of genomic perturbation experiments is crucial for accelerating drug discovery and therapeutic target identification, yet exhaustive perturbation of the human genome remains infeasible due to the vast search space of…

Mobile health (mHealth) leverages digital technologies, such as mobile phones, to capture objective, frequent, and real-world digital phenotypes from individuals, enabling the delivery of tailored interventions to accommodate substantial…

Monitoring for changes in a predictive relationship represented by a fitted supervised learning model (i.e., concept drift detection) is a widespread problem in modern data-driven applications. A general and powerful Fisher score-based…

We propose using Probabilistic Cellular Automata (PCA) to address inverse problems with the Bayesian approach. In particular, we use PCA to sample from an approximation of the posterior distribution. The peculiar feature of PCA is their…

Traditional Reinforcement Learning from Human Feedback (RLHF) often relies on reward models, frequently assuming preference structures like the Bradley--Terry model, which may not accurately capture the complexities of real human…

Gaussian processes are a powerful class of non-linear models, but have limited applicability for larger datasets due to their high computational complexity. In such cases, approximate methods are required, for example, the recently…

Causal inference literature has extensively focused on binary treatments, with relatively fewer methods developed for multi-valued treatments. In particular, methods for multiple simultaneously assigned treatments remain understudied…

We study the problem of linear feature selection when features are highly correlated. Such settings pose two fundamental challenges. First, how should model similarity be defined? Simply counting features in common can be misleading: two…

Spontaneous reporting system databases are key resources for post-marketing surveillance, providing real-world evidence (RWE) on the adverse events (AEs) of regulated drugs or other medical products. Various statistical methods have been…

In this paper, we study the problem of multivariate shuffled linear regression, where the correspondence between predictors and responses in a linear model is obfuscated by a latent permutation. Specifically, we investigate the model…

Decision makers routinely use constrained optimization technology to plan and operate complex systems like global supply chains or power grids. In this context, practitioners must assess how close a computed solution is to optimality in…

Over the past decades, the increasing dimensionality of data has increased the need for effective data decomposition methods. Existing approaches, however, often rely on linear models or lack sufficient interpretability or flexibility. To…

We consider statistical learning problems in which data are observed as a set of probability measures. Optimal transport (OT) is a popular tool to compare and manipulate such objects, but its computational cost becomes prohibitive when the…

Quantifying causal effects in the presence of complex and multivariate outcomes remains a key challenge in treatment evaluation. For hierarchical multivariate outcomes, the FDA recommends the Win Ratio and Generalized Pairwise Comparisons…

Verifying the provenance of content is crucial to the functioning of many organizations, e.g., educational institutions, social media platforms, and firms. This problem is becoming increasingly challenging as text generated by Large…

We derive explicit formulas for Kendall's tau and Spearman's rho for two broad classes of asymmetric copulas: normal location-scale mixture copulas and skew-normal scale mixture copulas. These classes encompass widely used specifications,…

Regression models have a substantial impact on interpretation of treatments, genetic characteristics and other potential risk factors in survival analysis. In many applications, the description of censoring and survival curve reveals the…