<ul data-eligibleForWebStory="true"><li>Schmidt-Hieber (2020) showed the minimax optimality of deep neural networks with ReLu activation for least-square regression estimation.</li><li>The paper extends these results by considering dependent data, removing the i.i.d. assumption.</li><li>Observations are now allowed to be a Markov chain with a non-null pseudo-spectral gap.</li><li>A more general class of machine learning problems, including least-square and logistic regression, is studied.</li><li>The study uses PAC-Bayes oracle inequalities and a version of Bernstein inequality by Paulin (2015) to derive upper bounds on estimation risk for a generalized Bayesian estimator.</li><li>For least-square regression, the bound matches Schmidt-Hieber's lower bound up to a logarithmic factor.</li><li>The paper establishes a lower bound for classification with logistic loss and proves the optimality of the proposed deep neural network estimator in a minimax sense.</li></ul>

Minimax optimality of deep neural networks on dependent data via PAC-Bayes bounds

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