From e44e4093a3231bc90b767ba718c0432ee0bb9b33 Mon Sep 17 00:00:00 2001 From: Morten Hjorth-Jensen Date: Wed, 8 Sep 2021 16:18:49 +0200 Subject: [PATCH] update of week 36 --- doc/pub/week36/html/week36-bs.html | 63 ++++++++++--------- doc/pub/week36/html/week36-reveal.html | 14 +++++ doc/pub/week36/html/week36-solarized.html | 16 +++++ doc/pub/week36/html/week36.html | 16 +++++ doc/pub/week36/ipynb/ipynb-week36-src.tar.gz | Bin 192 -> 192 bytes doc/pub/week36/ipynb/week36.ipynb | 20 +++++- doc/src/week36/week36.do.txt | 9 +++ 7 files changed, 107 insertions(+), 31 deletions(-) diff --git a/doc/pub/week36/html/week36-bs.html b/doc/pub/week36/html/week36-bs.html index 67a426766..11aacc49a 100644 --- a/doc/pub/week36/html/week36-bs.html +++ b/doc/pub/week36/html/week36-bs.html @@ -106,6 +106,10 @@ Automatically generated HTML file from DocOnce source 2, None, 'deriving-ols-from-a-probability-distribution'), + ('Independent and Identically Distrubuted (iid)', + 2, + None, + 'independent-and-identically-distrubuted-iid'), ('Friday September 10', 2, None, 'friday-september-10'), ('Why resampling methods', 2, None, 'why-resampling-methods'), ('Resampling methods', 2, None, 'resampling-methods'), @@ -256,34 +260,35 @@ MathJax.Hub.Config({
  • Expectation value and variance
  • Expectation value and variance for \( \boldsymbol{\beta} \)
  • Deriving OLS from a probability distribution
    • -
  • Friday September 10
    • -
  • 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
    • -
  • Resampling methods: Bootstrap background
    • -
  • Resampling methods: More Bootstrap background
    • -
  • Resampling methods: Bootstrap approach
    • -
  • Resampling methods: Bootstrap steps
    • -
  • Code example for the Bootstrap method
    • -
  • 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
    • -
  • The bias-variance tradeoff
    • -
  • Example code for Bias-Variance tradeoff
    • -
  • Understanding what happens
    • -
  • Summing up
    • -
  • Another Example from Scikit-Learn's Repository
    • -
  • More examples on bootstrap and cross-validation and errors
    • -
  • The same example but now with cross-validation
    • -
  • Cross-validation with Ridge
    • +
  • Independent and Identically Distrubuted (iid)
    • +
  • Friday September 10
    • +
  • 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
    • +
  • Resampling methods: Bootstrap background
    • +
  • Resampling methods: More Bootstrap background
    • +
  • Resampling methods: Bootstrap approach
    • +
  • Resampling methods: Bootstrap steps
    • +
  • Code example for the Bootstrap method
    • +
  • 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
    • +
  • The bias-variance tradeoff
    • +
  • Example code for Bias-Variance tradeoff
    • +
  • Understanding what happens
    • +
  • Summing up
    • +
  • Another Example from Scikit-Learn's Repository
    • +
  • More examples on bootstrap and cross-validation and errors
    • +
  • The same example but now with cross-validation
    • +
  • Cross-validation with Ridge
    • @@ -342,7 +347,7 @@ MathJax.Hub.Config({
  • 9
  • 10
  • ...
    • -
  • 53
    • +
  • 54
  • »
    • diff --git a/doc/pub/week36/html/week36-reveal.html b/doc/pub/week36/html/week36-reveal.html index 4b0f3d4d0..d5e64189d 100644 --- a/doc/pub/week36/html/week36-reveal.html +++ b/doc/pub/week36/html/week36-reveal.html @@ -956,6 +956,20 @@ the design matrix are not stocastic variables, we can assume that the probability distribution of our targets is also a normal distribution but now with mean value \( \boldsymbol{X}\hat{\boldsymbol{\beta}} \). This means that a single output \( y_i \) is given by the Gaussian distribution + +

     
    +$$ +y_i\sim \mathcal{N}(\boldsymbol{X}{i,*}\boldsymbol{\beta}, \sigma^2)=\frac{1}{\sqrt{2\pi\sigma^2}}\exp{\left[-\frac{(y_i-\boldsymbol{X}{i,*}\boldsymbol{\beta})^2}{2\sigma^2}\right]}. +$$ +

     
    + + + +

    +

    Independent and Identically Distrubuted (iid)

    + +

    +We assume now that the various \( y_i \) values are stochastically distributed according to the above Gaussian distribution and

    diff --git a/doc/pub/week36/html/week36-solarized.html b/doc/pub/week36/html/week36-solarized.html index 063fa2ea7..1bccf3b26 100644 --- a/doc/pub/week36/html/week36-solarized.html +++ b/doc/pub/week36/html/week36-solarized.html @@ -126,6 +126,10 @@ div { text-align: justify; text-justify: inter-word; } 2, None, 'deriving-ols-from-a-probability-distribution'), + ('Independent and Identically Distrubuted (iid)', + 2, + None, + 'independent-and-identically-distrubuted-iid'), ('Friday September 10', 2, None, 'friday-september-10'), ('Why resampling methods', 2, None, 'why-resampling-methods'), ('Resampling methods', 2, None, 'resampling-methods'), @@ -948,6 +952,18 @@ probability distribution of our targets is also a normal distribution but now with mean value \( \boldsymbol{X}\hat{\boldsymbol{\beta}} \). This means that a single output \( y_i \) is given by the Gaussian distribution +$$ +y_i\sim \mathcal{N}(\boldsymbol{X}{i,*}\boldsymbol{\beta}, \sigma^2)=\frac{1}{\sqrt{2\pi\sigma^2}}\exp{\left[-\frac{(y_i-\boldsymbol{X}{i,*}\boldsymbol{\beta})^2}{2\sigma^2}\right]}. +$$ + +

    +









    + +

    Independent and Identically Distrubuted (iid)

    + +

    +We assume now that the various \( y_i \) values are stochastically distributed according to the above Gaussian distribution and +











    diff --git a/doc/pub/week36/html/week36.html b/doc/pub/week36/html/week36.html index 58b376813..fabda1bf3 100644 --- a/doc/pub/week36/html/week36.html +++ b/doc/pub/week36/html/week36.html @@ -131,6 +131,10 @@ div { text-align: justify; text-justify: inter-word; } 2, None, 'deriving-ols-from-a-probability-distribution'), + ('Independent and Identically Distrubuted (iid)', + 2, + None, + 'independent-and-identically-distrubuted-iid'), ('Friday September 10', 2, None, 'friday-september-10'), ('Why resampling methods', 2, None, 'why-resampling-methods'), ('Resampling methods', 2, None, 'resampling-methods'), @@ -953,6 +957,18 @@ probability distribution of our targets is also a normal distribution but now with mean value \( \boldsymbol{X}\hat{\boldsymbol{\beta}} \). This means that a single output \( y_i \) is given by the Gaussian distribution +$$ +y_i\sim \mathcal{N}(\boldsymbol{X}{i,*}\boldsymbol{\beta}, \sigma^2)=\frac{1}{\sqrt{2\pi\sigma^2}}\exp{\left[-\frac{(y_i-\boldsymbol{X}{i,*}\boldsymbol{\beta})^2}{2\sigma^2}\right]}. +$$ + +

    +









    + +

    Independent and Identically Distrubuted (iid)

    + +

    +We assume now that the various \( y_i \) values are stochastically distributed according to the above Gaussian distribution and +











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