A0698
Title: On the multivariate Fourier integral theorem: Statistical and methodological perspectives
Authors: Nhat Pham Minh Ho - University of Texas, Austin (United States) [presenting]
Abstract: The focus is on overcoming the inferential and interpretability challenges of deep neural networks by use of the Fourier integral theorem, a remarkable result from mathematics. We first demonstrate that the Fourier integral theorem provides natural Monte Carlo estimators in many machine learning and data science problems, such as multivariate density estimation. Then, leveraging our insight from these estimators, we propose a novel generative model based on sequentially sampling each feature of new data from a martingale sequence of conditional distribution estimators. The proposed generative model paves the way for developing uncertainty quantification and predictive inference procedures. Our key finding and idea on which this proposal is dependent are that the combination of the Fourier integral theorem, Monte Carlo methods for direct estimation of quantities of interest, and sampling-based approaches to statistical and machine learning, such as generative models, provide a natural and perfect synergy both from a mathematical and practical perspective. If time permitted, we also briefly discuss applications of the multivariate Fourier integral Theorem to improve Transformer-based language models and Graph Neural Networks.
