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Morten Hjorth-Jensen
2023-09-11 06:08:52 +02:00
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doc/src/week37/exercisesweek37.do.txt
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@@ -8,7 +8,7 @@ DATE: Deadline is Sunday September 17 at midnight
This exercise deals with various mean values and variances in linear regression method (here it may be useful to look up chapter 3, equation (3.8) of "Trevor Hastie, Robert Tibshirani, Jerome H. Friedman, The Elements of Statistical Learning, Springer":"https://www.springer.com/gp/book/9780387848570"). The exercise is also a part of project 1 and can be reused in the theory part of the project.
For more discussions on Ridge regression and calculation of expectation values, "Wessel van Wieringen's":"https://arxiv.org/abs/1509.09169" article is highly recommended.
The assumption we have made is
doc/src/week37/week37.do.txt
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* Exercise for week 37
* Work on project 1
* See also additional note on scaling (jupyter-notebook) sent separately. This will be discussed during the first hour of each session.
* For more discussions of Ridge regression and calculation of averages, "Wessel van Wieringen's":"https://arxiv.org/abs/1509.09169" article is highly recommended.
!eblock
!bblock Material for the lecture on Thursday September 7
* Statistical interpretation of Ridge and Lasso regression
* Resampling techniques, Bootstrap and cross validation and bias-variance tradeoff
* Recommended Reading:
o Lectures on Resampling methods (these lectures)
o Bishop 1.3 (cross-validation) and 3.2 (bias-variance tradeoff)
* Reads and Videos:
o Hastie et al Chapter 7, here we recommend 7.1-7.5 and 7.10 (cross-validation) and 7.11 (bootstrap).
* "Video on cross validation":"https://www.youtube.com/watch?v=fSytzGwwBVw"
* "Video on bias-variance tradeoff":"https://www.youtube.com/watch?v=EuBBz3bI-aA"
o "Video on cross validation":"https://www.youtube.com/watch?v=fSytzGwwBVw"
o "Video on bias-variance tradeoff":"https://www.youtube.com/watch?v=EuBBz3bI-aA"
!eblock
@@ -201,6 +200,7 @@ The difference is non-negative definite since each component of the
matrix product is non-negative definite.
This means the variance we obtain with the standard OLS will always for $\lambda > 0$ be larger than the variance of $\bm{\beta}$ obtained with the Ridge estimator. This has interesting consequences when we discuss the so-called bias-variance trade-off below.
For more discussions of Ridge regression and calculation of averages, "Wessel van Wieringen's":"https://arxiv.org/abs/1509.09169" article is highly recommended.
!split