Learning a function from input and output data pairs is one of the most fundamental tasks in machine learning. In this talk, we propose a generalization of the Canonical Polyadic Decomposition (CPD) from tensors to multivariate functions of continuous variables, and show how it can be applied to supervised learning. We approximate a compactly supported multivariate function using a tensor of truncated multidimensional Fourier series coefficients and propose a hidden tensor factorization formulation for learning a low-rank CPD model of the Fourier coefficients tensor. In contrast to prior work, our method is quite general as it can model any compactly supported multivariate function that can be well-approximated by a finite multidimensional Fourier series, and under certain conditions it guarantees that the unknown function is uniquely characterized by the given input-output data. Furthermore, our model naturally allows stochastic gradient updates allowing it to scale to larger datasets. We develop two optimization algorithms and demonstrate promising results on synthetic and real multivariate regression tasks.
Reference: https://ieeexplore.ieee.org/abstract/document/9340610
Bio: N. Sidiropoulos earned his Ph.D. in Electrical Engineering from the University of Maryland College Park, in 1992. He has served on the faculty of the University of Virginia, University of Minnesota, and the Technical University of Crete, Greece, prior to his current appointment as Chair of ECE at UVA. His research interests are in signal processing, communications, optimization, tensor decomposition, and factor analysis, with applications in machine learning and communications. He received the NSF/CAREER award in 1998, the IEEE Signal Processing Society (SPS) Best Paper Award in 2001, 2007, and 2011, served as IEEE SPS Distinguished Lecturer (2008-2009), and as Vice President - Membership of IEEE SPS (2017-2019). He received the 2010 IEEE Signal Processing Society Meritorious Service Award, and the 2013 Distinguished Alumni Award from the University of Maryland, Dept. of ECE. He is a Fellow of IEEE (2009) and a Fellow of EURASIP (2014).
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