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Activity Number:
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145
- Trend Filtering and Related Regression Methods
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Type:
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Invited
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Date/Time:
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Tuesday, August 10, 2021 : 10:00 AM to 11:50 AM
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Sponsor:
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IMS
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Abstract #316869
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Title:
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MARS via LASSO
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Author(s):
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Dohyeong Ki and Billy Fang and Adityanand Guntuboyina*
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Companies:
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and Google and UC Berkeley
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Keywords:
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Nonparametric regression;
trend filtering;
bounded mixed derivative;
curse of dimensionality;
piecewise constant fitting
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Abstract:
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We propose and study a natural LASSO variant of the MARS method for regression. Our method is based on least squares estimation over a convex class of functions obtained by considering infinite dimensional linear combinations of functions in the MARS basis and putting a variation based complexity constraint. We show that this method can be computed via finite-dimensional convex optimization and that it can be viewed as a multivariate generalization of trend filtering. Under natural design assumptions, we prove that our estimator achieves a rate of convergence that depends only logarithmically on dimension and thus avoids the usual curse of dimensionality to some extent.
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Authors who are presenting talks have a * after their name.
