Specialized Session 3: Nonparametric Inference and Prediction

High-quality environmental data are scarce and costly, while low-quality reanalysis data are more abundant but less reliable. Wind speed, a key predictor in air quality models, often lacks the necessary resolution and accuracy. We propose a new multi-fidelity Gaussian process model leveraging a tailored Vecchia approximation to efficiently fuse large spatio-temporal datasets. Our method improves predictive accuracy, particularly in regions with sparse high-quality data, while supporting non-stationary integration of multiple fidelity levels. Results show a superior representation of wind speed’s mean level and local variability, making this approach a valuable tool for generating high-resolution environmental predictors.

Conformal prediction is a nonparametric method widely applied in regression, classification, and outlier detection, providing valid predictive inference with finite-sample coverage guarantees. Marginal coverage, in particular, is a fundamental objective in conformal inference, ensuring that prediction sets contain the correct label for a predefined proportion of future test points. However, these guarantees rely on the assumption of data exchangeability, which is often violated in real-world applications due to distribution shifts, outliers, and label noise. In this work, we address the limitations of conformal classification in the presence of label contamination and propose novel adaptive methodologies that automatically adjust for noise to restore marginal coverage. Our approach builds on results from empirical process theory to derive correction factors that account for the inflation of coverage caused by label noise. The proposed adaptive calibration methods ensure nominal marginal coverage while maintaining informative prediction sets, even in challenging classification tasks with a large number of classes or severe class imbalance. The effectiveness of our approach is demonstrated through extensive experiments on synthetic and real-world datasets, including CIFAR-10H and BigEarthNet. Our findings highlight the importance of accounting for label contamination in conformal classification and provide a robust framework for reliable and informative predictive inference in noisy settings.

We address the problem of testing hypotheses on functional data defined over a manifold domain. This work aims to perform local hypothesis testing by providing a p-value function, $\tilde{p}(s)$, that allows testing a null hypothesis against an alternative hypothesis at every location on the manifold. In particular, the p-value function must be adjusted for multiplicity while accounting for the structure of the manifold. We present three methods for this adjustment: (i) an adjusted p-value function controlling the functional false discovery rate, (ii) an adjusted p-value function controlling the ball-wise error rate, and (iii) an adjusted e-value function that is ball-wise e-valid.