2020/05/04 by Sándor Szedmák, Anna Cichońska, Szedmak, Sandor +7 · 1 citation
Computer Science · Mathematics · #Advanced Neural Network Applications #Computational Physics and Python Applications #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Algorithms #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.2005.01538
openalex publication_date 2020/05/04 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
This paper proposes a novel method for learning highly nonlinear,\nmultivariate functions from examples. Our method takes advantage of the\nproperty that continuous functions can be approximated by polynomials, which in\nturn are representable by tensors. Hence the function learning problem is\ntransformed into a tensor reconstruction problem, an inverse problem of the\ntensor decomposition. Our method incrementally builds up the unknown tensor\nfrom rank-one terms, which lets us control the complexity of the learned model\nand reduce the chance of overfitting. For learning the models, we present an\nefficient gradient-based algorithm that can be implemented in linear time in\nthe sample size, order, rank of the tensor and the dimension of the input. In\naddition to regression, we present extensions to classification, multi-view\nlearning and vector-valued output as well as a multi-layered formulation. The\nmethod can work in an online fashion via processing mini-batches of the data\nwith constant memory complexity. Consequently, it can fit into systems equipped\nonly with limited resources such as embedded systems or mobile phones. Our\nexperiments demonstrate a favorable accuracy and running time compared to\ncompeting methods.\n