Statistical Properties of Deep Neural Networks with Dependent Data
Read the original on arXiv Machine Learning →The paper develops theory for deep neural network (DNN) estimators under dependent data. It establishes nonasymptotic probability bounds on the theoretical and empirical ∼2-errors of nonparametric sieve estimators for a general class of estimation problems with possibly nonstationary β-mixing data in unbounded sets. The theory is then applied to fully connected and convolutional DNN estimators without weight bounds or sparsity restrictions, deriving results for H"older smooth functions under nonstationary, subgaussian, β-mixing data with exponential or polynomial decay, and achieving the nonparametric minimax rate up to logarithmic factors in several regression settings.
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