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
Year
Contact
David Lawlor
Mathematics
djl@math.duke.edu

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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The goal of this Data+ project is to apply and extend custom analytics solutions to understand and predict microbial population growth. An explosion of data has resulted from tracking the growth of bacteria in high throughput devices. These data were generated to understand how microbes grow. Better models that fit and predict these growth data are needed for better treatment of pathogenic bacterial infections, food safety, beer and bread fermentation, and understanding stress resilience of the microbiome. Using nonparametric statistical models to analyze how microbes grow under stress, the Schmid research lab at Duke has made important discoveries in these areas. These studies generated large data sets and developed statistical models to track and predict how microbes grow and change their gene expression when faced with extreme stress. We built a web application called phenom to make these models accessible to the broader community. In this Data+ project, students will beta test the web app and make improvements, including data visualization, extending the underlying statistical model, and analyzing data using the app.

 

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. https://doi.org/10.1371/journal.pcbi.1008366

A team of students led by Biomedical Engineering professor Lingchong You will predict pattern formation of bacterial colonies by integrating experimental results with both mechanistic modelling and machine learning methods. Bacterial colonies have the capability to self-organize into beautiful and intricate patterns. Students will contribute to a method for controlling the outcome of colony spatial patterning, which is an important challenge facing the field of synthetic biology.

 

Project Lead: Lingchong You

Project Manager: Anita Silver