Randomized smoothing has emerged as a scalable technique for certifying the adversarial robustness of classifiers. However, its application to regression remains under-explored and faces unique challenges. Existing regression certificates rely on probabilistic acceptance regions and fail to exploit the local geometry of the function. In this work, we present a novel framework for certified robust regression that addresses these limitations. We derive a prediction-centered certificate that guarantees the stability of the smoothed model's prediction and ensures practical computability at test time. We investigate several alternatives for constructing these certificates by explicitly incorporating means, variances, and gradients. In particular, we demonstrate on the MNIST rotation task that utilizing gradient information yields significantly tighter robustness certificates compared to the current state-of-the-art, alpha-smoothing.
We consider the problem of learning from a single finite trajectory of an ergodic stochastic dynamical system. More precisely, we study discrete-time autonomous stochastic systems defining time-homogeneous Markov processes. We first focus on estimating the optimal one-step predic…
Density modes provide a localized and interpretable summary of multimodal distributions, but their estimation under rigorous differential privacy constraints remains largely unexplored. We study differentially private recovery of density modes for multivariate distributions under…
An initial high-recall stage in an empirical pipeline decides which items pass to later review, labelling, or modelling, and relevant items it misses are lost to every subsequent stage. We study how many audit labels are needed to certify, with finite-sample validity, that this m…
We study the expected improvement (EI) policy for minimizing a deterministic objective function $f$ on a nonempty compact set $\mathcal X \subset\mathbb R^d$. We assume that $f$ belongs to the RKHS $\mathcal H_k$ of a continuous positive-semidefinite kernel $k$ on $\mathcal X$. F…
Double Machine Learning (DML) is a popular approach for treatment effect estimation in various settings, which allows a wide range of flexible machine learning methods to be used for nuisance parameter estimation while preserving valid inference. In practice, however, applied res…
Organizations increasingly rely on sequential experimentation to improve decision-making. While the multi-armed bandit literature has developed algorithms with strong asymptotic regret guarantees, many practical applications operate over finite and externally imposed horizons. Mo…