Abstract: We consider the Error-in-Operator (EiO) problem of recovering the source x signal from the noise observation Y given by the equation Y = A x + ε in the situation when the operator A is not precisely known. Instead, a pilot estimate \hat{A} is available. The study is motivated by Hoffmann & Reiss (2008), Trabs (2018) and by recent results on high dimensional regression with random design; see e.g., Tsigler, Bartlett (2020) (Benign overfitting in ridge regression; arXiv:2009.14286) Cheng, and Montanari (2022) (Dimension free ridge regression; arXiv:2210.08571), among many others. Examples of EiO include regression with error-in-variables and instrumental regression, stochastic diffusion, Markov time series, interacting particle…

Abstract: In this talk, we revisit classical results in the theory of statistical aggregation, focusing on the transition from global complexity to a more manageable local one. The goal of aggregation is to combine several base predictors to achieve a prediction nearly as accurate as the best one, without assumptions on the class structure or target. Though studied in both sequential and statistical settings, they traditionally use the same "global" complexity measure. We highlight the lesser-known PAC-Bayes localization enabling us…

Abstract: In 1948, Shannon used a probabilistic argument to prove the existence of codes achieving channel capacity. In 1954, Muller and Reed introduced a simple deterministic code construction, conjectured shortly after to achieve channel capacity. Major progress was made towards establishing this conjecture over the last decades, with various branches of discrete mathematics involved. In particular, the special case of the erasure channel was settled in 2015 by Kudekar at al., relying on Bourgain-Kalai's sharp threshold theorem for symmetric monotone…

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