Publications [#363233] of Hau-Tieng Wu

Papers Published

1. Liu, GR; Sheu, YC; Wu, HT, Asymptotic Analysis of higher-order scattering transform of Gaussian processes, Electronic Journal of Probability, vol. 27 (January, 2022) [doi]
   (last updated on 2024/04/24)

   Abstract:
   We analyze the scattering transform with the quadratic nonlinearity (STQN) of Gaussian processes without depth limitation. STQN is a nonlinear transform that involves a sequential interlacing convolution and nonlinear operators, which is motivated to model the deep convolutional neural network. We prove that with a proper normalization, the output of STQN converges to a chi-square process with one degree of freedom in the finite dimensional distribution sense, and we provide a total variation distance control of this convergence at each time that converges to zero at an exponential rate. To show these, we derive a recursive formula to represent the intricate nonlinearity of STQN by a linear combination of Wiener chaos, and then apply the Malliavin calculus and Stein’s method to achieve the goal.