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This paper proposes a novel method for learning highly nonlinear,multivariate functions from examples. Our method takes advantage of theproperty that continuous functions can be approximated by polynomials, which inturn are representable by tensors. Hence the function learning problem istransformed into a tensor reconstruction problem, an inverse problem of thetensor decomposition. Our method incrementally builds up the unknown tensorfrom rank-one terms, which lets us control the complexity of the learned modeland reduce the chance of overfitting. For learning the models, we present anefficient gradient-based algorithm that can be implemented in linear time inthe sample size, order, rank of the tensor and the dimension of the input. Inaddition to regression, we present extensions to classification, multi-viewlearning and vector-valued output as well as a multi-layered formulation. Themethod can work in an online fashion via processing mini-batches of the datawith constant memory complexity. Consequently, it can fit into systems equippedonly with limited resources such as embedded systems or mobile phones. Ourexperiments demonstrate a favorable accuracy and running time compared tocompeting methods.

A Solution for Large Scale Nonlinear Regression with High Rank and Degree at Constant Memory Complexity via Latent Tensor Reconstruction