Consistency in deep learning for non-stationary strong mixing processes

Deep learning has demonstrated remarkable success in various applications, but its theoretical foundations for handling non-stationary and dependent data remain challenging. This paper investigates the consistency of deep learning models when applied to non-stationary strong mixing processes, which are widely encountered in real-world scenarios such as financial time series, climate modelling, and sequential decision-making. Under some appropriate assumptions, the asymptotic learning rate achieves O(n−1/2log2⁡n) for non-stationary strong mixing processes. Some simulation results and two applications to the real data are provided to support the theoretical results.