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Iterative Construction of Sparse Polynomial Approximations

We present an iterative algorithm for nonlinear regression based on construction of sparse polynomials. Polynomials are built sequentially from lower to higher order. Selection of new terms is accomplished using a novel look-ahead approach that predicts whether a variable contributes to the remaining error. The algorithm is based on the tree-growing heuristic in LMS Trees which we have extended to approximation of arbitrary polynomials of the input features. In addition, we provide a new theoretical justification for this heuristic approach. The algorithm is shown to discover a known polynomial from samples, and to make accurate estimates of pixel values in an image processing task.

Citation

T. Sanger, R. Sutton, C. Matheus. "Iterative Construction of Sparse Polynomial Approximations". Neural Information Processing Systems (NIPS), Denver, CO, USA, December 1992.

Keywords: sparse, polynomials, pixel values
Category: In Conference

BibTeX

@incollection{Sanger+al:NIPS92,
  author = {T.D. Sanger and Richard S. Sutton and C.J. Matheus},
  title = {Iterative Construction of Sparse Polynomial Approximations},
  booktitle = {Neural Information Processing Systems (NIPS)},
  year = 1992,
}

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