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Spatial time series (STS) data are fundamental to climate science, yet conventional approaches often conflate temporal co-evolution with genuine spatial dependence, obscuring subtle but critical climatic anomalies. We introduce a Random…
Uncertainty quantification is necessary for developers, physicians, and regulatory agencies to build trust in machine learning predictors and improve patient care. Beyond measuring uncertainty, it is crucial to express it in clinically…
Model-based approaches to the verification of non-terminating Cyber-Physical Systems (CPSs) usually rely on numerical simulation of the System Under Verification (SUV) model under input scenarios of possibly varying duration, chosen among…
Symmetry plays a central role in the sciences, machine learning, and statistics. While statistical tests for the presence of distributional invariance with respect to groups have a long history, tests for conditional symmetry in the form of…
How can we monitor, in real time, whether one uncertain prospect has any upside over another? To answer this question, we develop a novel family of sequential, anytime-valid tests for stochastic dominance (SD; also known as stochastic…
Reliable uncertainty quantification at unobserved spatial locations, especially in the presence of complex and heterogeneous datasets, remains a core challenge in spatial statistics. Traditional approaches like Kriging rely heavily on…
We present a novel neural RGB-D Simultaneous Localization And Mapping (SLAM) system that learns an implicit map of the scene in real time. For the first time, we explore the use of Scene Coordinate Regression (SCR) as the core implicit map…
Quantum measurements under realistic conditions reveal only partial information about a system. Yet, by performing sequential measurements on the same system, additional information can be accessed. We investigate this problem in the…
In scientific disciplines such as neuroimaging, climatology, and cosmology it is useful to study the uncertainty of excursion sets of imaging data. While the case of imaging data obtained from a single study condition has already been…
Reliable uncertainty quantification is essential for deploying machine learning systems in high-stakes domains. Conformal prediction provides distribution-free coverage guarantees but often produces overly large prediction sets, limiting…
Distinguishing two candidate models is a fundamental and practically important statistical problem. Error rate control is crucial to the testing logic but, in complex nonparametric settings, can be difficult to achieve, especially when the…
Randomized smoothing (RS) is one of the prominent techniques to ensure the correctness of machine learning models, where point-wise robustness certificates can be derived analytically. While RS is well understood for classification, its…
In dynamic MRI, sufficient time resolution can often only be obtained using imaging protocols which produce undersampled data for each image in the time series. This has led to the popularity of compressed sensing (CS) based image…
Real-world road networks have an approximate scale-invariance property; can one devise mathematical models of random networks whose distributions are {\em exactly} invariant under Euclidean scaling? This requires working in the continuum…
The size of large, geo-located datasets has reached scales where visualization of all data points is inefficient. Random sampling is a method to reduce the size of a dataset, yet it can introduce unwanted errors. We describe a method for…
The continuous random energy model (CREM) is a toy model of spin glasses on $\{0,1\}^N$ that, in the limit, exhibits an infinitely hierarchical correlation structure. We give two polynomial-time algorithms to approximately sample from the…
Regionalization aims to partition a spatial domain into contiguous regions that share similar characteristics, enabling more effective spatial analysis, policy making, and resource management. Existing approaches for spatial regionalization…
We discuss two important techniques, series expansion and Monte Carlo simulation, for random sequential adsorption study. Random sequential adsorption is an idealization for surface deposition where the time scale of particle relaxation is…
Relative survival represents the preferred framework for the analysis of population cancer survival data. The aim is to model the survival probability associated to cancer in the absence of information about the cause of death. Recent data…
We study fundamental theoretical aspects of probabilistic roadmaps (PRM) in the finite time (non-asymptotic) regime. In particular, we investigate how completeness and optimality guarantees of the approach are influenced by the underlying…