Nandan Tumu

Conformal prediction is a statistical tool for producing prediction regions for machine learning models that are valid with high probability. A key component of conformal prediction algorithms is a non-conformity score function that quantifies how different a model’s prediction is from the unknown ground truth value. Essentially, these functions determine the shape and the size of the conformal prediction regions. However, little work has gone into finding non-conformity score functions that produce prediction regions that are multi-modal and practical, i.e., that can efficiently be used in engineering applications. We propose a method that optimizes parameterized shape template functions over calibration data, which results in non-conformity score functions that produce prediction regions with minimum volume. Our approach results in prediction regions that are multi-modal, so they can properly capture residuals of distributions that have multiple modes, and practical, so each region is convex and can be easily incorporated into downstream tasks, such as a motion planner using conformal prediction regions. Our method applies to general supervised learning tasks, while we illustrate its use in time-series prediction. We provide a toolbox and present illustrative case studies of F16 fighter jets and autonomous vehicles, showing an up to 68% reduction in prediction region area.

We present the Social Influence Game (SIG), a framework for modeling adversarial persuasion in social net- works with an arbitrary number of competing players. Our goal is to provide a tractable and interpretable model of contested influence that scales to large systems while capturing the struc- tural leverage points of networks. Each player allocates influence from a fixed budget to steer opinions that evolve under DeGroot dynamics, and we prove that the resulting optimization problem is a difference-of-convex program. To enable scalability, we develop an Iterated Linear (IL) solver that approximates player objectives with linear programs. In experiments on random and archetypical networks, IL achieves solutions within 7% of nonlinear solvers while being over 10x faster, scaling to large social networks. This paper lays a foundation for asymptotic analysis of contested influence in complex networks.

Rigorous uncertainty quantification is essential for the safe deployment of autonomous systems in unconstrained environments. Conformal Prediction (CP) provides a distribution-free framework for this task, yet its standard formulations rely on exchangeability assumptions that are violated by the distribution shifts inherent in real-world robotics. Existing online CP methods maintain target coverage by adaptively scaling the conformal threshold, but typically employ a static nonconformity score function. We show that this fixed geometry leads to highly conservative, volume-inefficient prediction regions when environments undergo structural shifts. To address this, we propose \textbfAdaptNC, a framework for the joint online adaptation of both the nonconformity score parameters and the conformal threshold. AdaptNC leverages an adaptive reweighting scheme to optimize score functions, and introduces a replay buffer mechanism to mitigate the coverage instability that occurs during score transitions. We evaluate AdaptNC on diverse robotic benchmarks involving multi-agent policy changes, environmental changes and sensor degradation. Our results demonstrate that AdaptNC significantly reduces prediction region volume compared to state-of-the-art threshold-only baselines while maintaining target coverage levels.