Week 38: Statistical analysis, bias-variance tradeoff and resampling methods
Contents
Plans for week 38, lecture Monday September 15
Readings and Videos
Linking the regression analysis with a statistical interpretation
Assumptions made
Expectation value and variance
Expectation value and variance for \( \boldsymbol{\theta} \)
Deriving OLS from a probability distribution
Independent and Identically Distributed (iid)
Maximum Likelihood Estimation (MLE)
A new Cost Function
Why resampling methods
Resampling methods
Resampling approaches can be computationally expensive
Why resampling methods ?
Statistical analysis
Resampling methods
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
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
Material for the lab sessions
A way to Read the Bias-Variance Tradeoff
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