GMRA Regression

Project Summary

We present a framework for high-dimensional regression using the GMRA data structure. In analogy to a classical wavelet decomposition of function spaces, a GMRA is a tree-based decomposition of a data set into local linear projections.

Themes and Categories
David Lawlor

Moreover, for new points, GMRA admits a fast algorithm for computing the projection coefficients on the already-learned dictionary. Within each node of the tree one can also assign regression coefficients in any manner; here we study the simple case of weighted linear regression. We explore the performance of the method using synthetic data as well as galactic spectra from the Sloan Digital Sky Survey, and compare against other methods for regression in high dimensions.

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Project Lead: Amy Schmid

Project Manager: Andrew. Soborowski

Image credit: Tonner, P.D., Darnell, C.L., Bushell, F.M.L., Lund, P.A., Schmid, A.K.*, Schmidler, S.C. 2020. A Bayesian non-parametric mixed-Effects model of microbial growth curves. PLoS Comp Biol. 16(10): e1008366.

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Project Manager: Anita Silver