Week 37: Summary of Ridge and Lasso Regression and Resampling Methods
Contents
Plans for week 37
Thursday September 16, Summary of Ridge and Lasso Regression and start Resampling methods
Deriving OLS from a probability distribution
Independent and Identically Distrubuted (iid)
Maximum Likelihood Estimation (MLE)
A new Cost Function
Bayes' Theorem
Interpretations of Bayes' Theorem
Test Function for what happens with OLS, Ridge and Lasso
Rerunning the above code
Invoking Bayes' theorem
Ridge and Bayes
Lasso and Bayes
Why resampling methods
Resampling methods
Resampling approaches can be computationally expensive
Why resampling methods ?
Statistical analysis
Resampling methods
Resampling methods: Jackknife and Bootstrap
Resampling methods: Jackknife
Jackknife code example
Resampling methods: Bootstrap
The Central Limit Theorem
Finding the Limit
Rewriting the \( \delta \)-function
Identifying Terms
Wrapping it up
Confidence Intervals
Standard Approach based on the Normal Distribution
Resampling methods: Bootstrap background
Resampling methods: More Bootstrap background
Resampling methods: Bootstrap approach
Resampling methods: Bootstrap steps
Code example for the Bootstrap method
Plotting the Histogram
The bias-variance tradeoff
A way to Read the Bias-Variance Tradeoff
Example code for Bias-Variance tradeoff
Understanding what happens
Summing up
Another Example from Scikit-Learn's Repository
Various steps in cross-validation
How to set up the cross-validation for Ridge and/or Lasso
Cross-validation in brief
Code Example for Cross-validation and \( k \)-fold Cross-validation
More examples on bootstrap and cross-validation and errors
The same example but now with cross-validation
A way to Read the Bias-Variance Tradeoff
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