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1 | 1 | #+TITLE: Machine Learning with Linear Models - a demo |
2 | 2 |
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| 3 | +[[file:img/example_results.png]] |
| 4 | + |
3 | 5 | * Table of Contents :TOC_4_gh:noexport: |
4 | 6 | - [[#description][Description]] |
5 | 7 | - [[#usage][Usage]] |
6 | 8 |
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7 | 9 | * Description |
8 | | - |
9 | 10 | This is a small demo meant to showcase a few simple but different linear |
10 | | - models for mapping X to Y. Different assumptions about the data can lead to |
11 | | - (sometimes drastically) different levels of performance. For instance, when |
12 | | - the mapping from X to Y is low rank (i.e., an information 'bottleneck'), a |
13 | | - technique called reduced rank regression (RRR) can outperform standard |
14 | | - multivariate linear regression (LR). When the mapping from X to Y is time |
15 | | - dependent and based on an underlying linear dynamical system, applying a |
16 | | - system identification technique (SUBID) can result in big gains over LR. |
| 11 | + models for mapping vectors of observations X to vectors of outcomes Y. |
| 12 | + Different assumptions about the data can lead to different levels of |
| 13 | + performance -- sometimes drastically. |
| 14 | + |
| 15 | + For instance, when the mapping from X to Y is low rank (i.e., an information |
| 16 | + 'bottleneck'), a technique called reduced rank regression |
| 17 | + (~reduced_rank_regressor.py~) can outperform standard multivariate linear |
| 18 | + regression (~multivariate_regressor.py~). When the mapping from X to Y is |
| 19 | + time dependent and based on an underlying linear dynamical system, applying a |
| 20 | + system identification technique (~system_identifier.py~) can result in big |
| 21 | + gains over both. |
17 | 22 |
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18 | 23 | My Ph.D. supervisor Dr. Michael Bowling introduced me to RRR; Dr. Tijl De Bie |
19 | 24 | gave a great talk on subspace system identification in 2005 that I modeled my |
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