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  1. ; ; ; ( , Proceedings of Machine Learning Research)
    We rigorously quantify the improvement in the sample complexity of variational divergence estimations for group-invariant distributions. In the cases of the Wasserstein-1 metric and the Lipschitz-regularized 𝛼 -divergences, the reduction of sample complexity is proportional to an ambient-dimension-dependent power of the group size. For the maximum mean discrepancy (MMD), the improvement of sample complexity is more nuanced, as it depends on not only the group size but also the choice of kernel. Numerical simulations verify our theories. 
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    Free, publicly-accessible full text available July 3, 2024
  2. ; ; ; ; ( , ICLR 2023 Conference Proceedings)
    Accepted Manuscript Full Text Available
  3. ; ; ; ( , SIAM/ASA Journal on Uncertainty Quantification)
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  4. ; ; ( , IEEE Transactions on Information Theory)
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  5. ; ; ; ( , Proceedings of Machine Learning Research)
    Accepted Manuscript Full Text Available
  6. ; ; ; ; ( , IEEE Transactions on Neural Networks and Learning Systems)
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  7. ; ; ; ; ( , Journal of machine learning research)
    Accepted Manuscript Full Text Available
  8. ; ; ; ( , Journal of Computational Physics)
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  9. ; ; ( , ESAIM: Mathematical Modelling and Numerical Analysis)
    Quantifying the impact of parametric and model-form uncertainty on the predictions of stochastic models is a key challenge in many applications. Previous work has shown that the relative entropy rate is an effective tool for deriving path-space uncertainty quantification (UQ) bounds on ergodic averages. In this work we identify appropriate information-theoretic objects for a wider range of quantities of interest on path-space, such as hitting times and exponentially discounted observables, and develop the corresponding UQ bounds. In addition, our method yields tighter UQ bounds, even in cases where previous relative-entropy-based methods also apply, e.g. , for ergodic averages. We illustrate these results with examples from option pricing, non-reversible diffusion processes, stochastic control, semi-Markov queueing models, and expectations and distributions of hitting times. 
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  10. ; ; ; ; ( , SIAM Journal on Mathematics of Data Science)
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