TL;DR
An intrinsic geometric failure of kernel-embedding-based descriptions is identified, whose enclosing balls can admit arbitrarily dispersed distributions and produce infinite worst-case costs.
This paper introduces a data-driven Distributionally Robust Optimization (DRO) framework to identify risk-averse Hamiltonian cycles in non-stationary stochastic networks subject to severe probabilistic uncertainty. Rather than relying on static nominal travel times, which suffer heavily from the optimizer's curse, we c...
This work studies robust score estimation under Wasserstein perturbations of a reference distribution of Ornstein--Uhlenbeck diffusion and characterize how finite data, intrinsic dimension, and distribution shift affect the robustness of score-based diffusion models.
Decisions that weigh several reward signals against each other require the joint distribution of the return vector. Categorical critics scale exponentially in the reward dimension, and quantiles have no canonical multivariate analogue. Multivariate distributional critics therefore represent each return distribution by...
The probability smoothing problem seeks estimators that assign positive probability to all categories, including those unobserved in a finite sample. In our previous work, we established that the estimator derived from distributionally robust optimization (DRO) with a $q$-norm ambiguity set ($q$-DRO) satisfies the axio...
Distribution regression seeks to learn mappings from probability distributions to response variables and has emerged as a unifying framework for kernel methods, multi-instance learning, and set-valued learning. Despite its success, kernel-based distribution regression remains computationally expensive and sensitive to...
Bilevel data selection is a fundamental task with numerous applications in machine learning and statistics. A common strategy for tackling this problem is to relax the original bilevel combinatorial optimization into a continuous one. However, existing methods, including 0-1 relaxation and probabilistic relaxation, sti...
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