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This summary is machine-generated.

This study presents a new supervised learning method using B-splines to approximate complex functions. This approach efficiently handles regression and classification tasks by leveraging low-rank tensor decomposition.

Keywords:
B-splinescanonical polyadic decompositionclassificationgauss-newtonregressionsupervised learningtensor decompositions

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Area of Science:

  • Machine Learning
  • Numerical Analysis
  • Functional Approximation

Background:

  • Supervised learning often requires approximating complex target functions.
  • Representing functions as sums of separable terms can simplify approximation.
  • B-splines offer a flexible basis for function approximation.

Purpose of the Study:

  • To develop a supervised learning framework for functions approximated by sums of separable terms.
  • To utilize B-splines for approximating component functions within this framework.
  • To leverage low-rank tensor decomposition for efficient representation.

Main Methods:

  • Approximating component functions using B-splines.
  • Employing a low-rank polyadic decomposition for the coefficient tensor.
  • Exploiting multilinear structure and B-spline sparsity.
  • Training parameters using the Gauss-Newton algorithm.

Main Results:

  • The proposed framework effectively approximates target functions.
  • The method is well-suited for both regression and classification tasks.
  • Numerical examples demonstrate the approach's effectiveness.

Conclusions:

  • The B-spline-based, low-rank tensor decomposition framework provides an efficient supervised learning method.
  • This approach offers a powerful tool for complex function approximation in machine learning.
  • The Gauss-Newton algorithm effectively trains the model parameters.