B1388
Title: Designing neural network layers for functional data analysis
Authors: Cedric Beaulac - Universite Du Quebec a Montreal (Canada) [presenting]
Abstract: The aim is to discuss the main contributions of my research group toward the goal of integrating neural networks and machine learning models in the analysis of functional data. First, a novel neural network layer architecture is proposed, designed for the prediction of a functional response; a novel functional output layer for neural networks of any kind is proposed. In the proposed solution, the second-to-last layer is designed to output basis coefficients that are combined in the last layer with associated basis functions in order to output a functional response. A roughness penalty is also designed that can be integrated into the optimization process of the proposed functional neural network as a regularizer. Second, a novel functional input layer is proposed. This time, inspired by the continuous convolution operator, an adjustable smooth convolution functional input layer is proposed. It is proposed first to smooth the data and then extract a variable number of points along the smooth representation, given the nature of the problem. Consequently, the collection of layers proposed bridges the gap between the discrete and the continuous convolution operators. Both the input and output layers are appropriate for irregularly spaced data. Together, these layers allow researchers to process functional data in any machine learning pipeline either as input or output. It is concluded by showcasing possible applications of these models using real data.
