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#+TITLE: Machine Learning with Linear Models - a demo
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[[file:img/example_results.png]]
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* Table of Contents :TOC_4_gh:noexport:
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- [[#description][Description]]
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- [[#usage][Usage]]
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* Description
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This is a small demo meant to showcase a few simple but different linear
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models for mapping X to Y. Different assumptions about the data can lead to
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(sometimes drastically) different levels of performance. For instance, when
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the mapping from X to Y is low rank (i.e., an information 'bottleneck'), a
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technique called reduced rank regression (RRR) can outperform standard
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multivariate linear regression (LR). When the mapping from X to Y is time
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dependent and based on an underlying linear dynamical system, applying a
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system identification technique (SUBID) can result in big gains over LR.
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models for mapping vectors of observations X to vectors of outcomes Y.
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Different assumptions about the data can lead to different levels of
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performance -- sometimes drastically.
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For instance, when the mapping from X to Y is low rank (i.e., an information
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'bottleneck'), a technique called reduced rank regression
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(~reduced_rank_regressor.py~) can outperform standard multivariate linear
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regression (~multivariate_regressor.py~). When the mapping from X to Y is
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time dependent and based on an underlying linear dynamical system, applying a
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system identification technique (~system_identifier.py~) can result in big
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gains over both.
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My Ph.D. supervisor Dr. Michael Bowling introduced me to RRR; Dr. Tijl De Bie
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gave a great talk on subspace system identification in 2005 that I modeled my

img/example_results.png

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