diff --git a/doc/pub/week34/html/._week34-bs000.html b/doc/pub/week34/html/._week34-bs000.html
index 93dca0db3..83ac6fd24 100644
--- a/doc/pub/week34/html/._week34-bs000.html
+++ b/doc/pub/week34/html/._week34-bs000.html
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
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+
-Week 34: Introduction to the course, Logistics and Practicalities
+Week 35: Introduction to the course, Logistics and Practicalities
@@ -80,6 +80,20 @@ Automatically generated HTML file from DocOnce source
2,
None,
'types-of-machine-learning'),
+ ('Essential elements of ML', 2, None, 'essential-elements-of-ml'),
+ ('An optimization/minimization problem',
+ 2,
+ None,
+ 'an-optimization-minimization-problem'),
+ ('A Frequentist approach to data analysis',
+ 2,
+ None,
+ 'a-frequentist-approach-to-data-analysis'),
+ ('What is a good model?', 2, None, 'what-is-a-good-model'),
+ ('What is a good model? Can we define it?',
+ 2,
+ None,
+ 'what-is-a-good-model-can-we-define-it'),
('Software and needed installations',
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None,
@@ -108,7 +122,7 @@ Automatically generated HTML file from DocOnce source
('Numpy and arrays', 2, None, 'numpy-and-arrays'),
('Matrices in Python', 2, None, 'matrices-in-python'),
('Meet the Pandas', 2, None, 'meet-the-pandas'),
- ('Friday August 21', 2, None, 'friday-august-21'),
+ ('Friday August 27', 2, None, 'friday-august-27'),
('Reading Data and fitting', 2, None, 'reading-data-and-fitting'),
('Friday August 27', 2, None, 'friday-august-27'),
('Simple linear regression model using _scikit-learn_',
@@ -129,7 +143,15 @@ Automatically generated HTML file from DocOnce source
3,
None,
'and-what-about-using-neural-networks'),
- ('A first summary', 2, None, 'a-first-summary')]}
+ ('A first summary', 2, None, 'a-first-summary'),
+ ('Exercise 1: Setting up various Python environments',
+ 2,
+ None,
+ 'exercise-1-setting-up-various-python-environments'),
+ ('Exercise 2: making your own data and exploring scikit-learn',
+ 2,
+ None,
+ 'exercise-2-making-your-own-data-and-exploring-scikit-learn')]}
end of tocinfo -->
@@ -159,7 +181,7 @@ MathJax.Hub.Config({
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+ Week 35: Introduction to the course, Logistics and Practicalities
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index cf81a9d8d..da573ec08 100644
--- a/doc/pub/week34/html/._week34-bs001.html
+++ b/doc/pub/week34/html/._week34-bs001.html
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
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+
-Week 34: Introduction to the course, Logistics and Practicalities
+Week 35: Introduction to the course, Logistics and Practicalities
@@ -80,6 +80,20 @@ Automatically generated HTML file from DocOnce source
2,
None,
'types-of-machine-learning'),
+ ('Essential elements of ML', 2, None, 'essential-elements-of-ml'),
+ ('An optimization/minimization problem',
+ 2,
+ None,
+ 'an-optimization-minimization-problem'),
+ ('A Frequentist approach to data analysis',
+ 2,
+ None,
+ 'a-frequentist-approach-to-data-analysis'),
+ ('What is a good model?', 2, None, 'what-is-a-good-model'),
+ ('What is a good model? Can we define it?',
+ 2,
+ None,
+ 'what-is-a-good-model-can-we-define-it'),
('Software and needed installations',
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None,
@@ -108,7 +122,7 @@ Automatically generated HTML file from DocOnce source
('Numpy and arrays', 2, None, 'numpy-and-arrays'),
('Matrices in Python', 2, None, 'matrices-in-python'),
('Meet the Pandas', 2, None, 'meet-the-pandas'),
- ('Friday August 21', 2, None, 'friday-august-21'),
+ ('Friday August 27', 2, None, 'friday-august-27'),
('Reading Data and fitting', 2, None, 'reading-data-and-fitting'),
('Friday August 27', 2, None, 'friday-august-27'),
('Simple linear regression model using _scikit-learn_',
@@ -129,7 +143,15 @@ Automatically generated HTML file from DocOnce source
3,
None,
'and-what-about-using-neural-networks'),
- ('A first summary', 2, None, 'a-first-summary')]}
+ ('A first summary', 2, None, 'a-first-summary'),
+ ('Exercise 1: Setting up various Python environments',
+ 2,
+ None,
+ 'exercise-1-setting-up-various-python-environments'),
+ ('Exercise 2: making your own data and exploring scikit-learn',
+ 2,
+ None,
+ 'exercise-2-making-your-own-data-and-exploring-scikit-learn')]}
end of tocinfo -->
@@ -159,7 +181,7 @@ MathJax.Hub.Config({
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+ Week 35: Introduction to the course, Logistics and Practicalities
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index 4a55439a7..c541b596f 100644
--- a/doc/pub/week34/html/._week34-bs002.html
+++ b/doc/pub/week34/html/._week34-bs002.html
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
-
+
-Week 34: Introduction to the course, Logistics and Practicalities
+Week 35: Introduction to the course, Logistics and Practicalities
@@ -80,6 +80,20 @@ Automatically generated HTML file from DocOnce source
2,
None,
'types-of-machine-learning'),
+ ('Essential elements of ML', 2, None, 'essential-elements-of-ml'),
+ ('An optimization/minimization problem',
+ 2,
+ None,
+ 'an-optimization-minimization-problem'),
+ ('A Frequentist approach to data analysis',
+ 2,
+ None,
+ 'a-frequentist-approach-to-data-analysis'),
+ ('What is a good model?', 2, None, 'what-is-a-good-model'),
+ ('What is a good model? Can we define it?',
+ 2,
+ None,
+ 'what-is-a-good-model-can-we-define-it'),
('Software and needed installations',
2,
None,
@@ -108,7 +122,7 @@ Automatically generated HTML file from DocOnce source
('Numpy and arrays', 2, None, 'numpy-and-arrays'),
('Matrices in Python', 2, None, 'matrices-in-python'),
('Meet the Pandas', 2, None, 'meet-the-pandas'),
- ('Friday August 21', 2, None, 'friday-august-21'),
+ ('Friday August 27', 2, None, 'friday-august-27'),
('Reading Data and fitting', 2, None, 'reading-data-and-fitting'),
('Friday August 27', 2, None, 'friday-august-27'),
('Simple linear regression model using _scikit-learn_',
@@ -129,7 +143,15 @@ Automatically generated HTML file from DocOnce source
3,
None,
'and-what-about-using-neural-networks'),
- ('A first summary', 2, None, 'a-first-summary')]}
+ ('A first summary', 2, None, 'a-first-summary'),
+ ('Exercise 1: Setting up various Python environments',
+ 2,
+ None,
+ 'exercise-1-setting-up-various-python-environments'),
+ ('Exercise 2: making your own data and exploring scikit-learn',
+ 2,
+ None,
+ 'exercise-2-making-your-own-data-and-exploring-scikit-learn')]}
end of tocinfo -->
@@ -159,7 +181,7 @@ MathJax.Hub.Config({
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+ Week 35: Introduction to the course, Logistics and Practicalities
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index 8f26743c2..aa2ad653f 100644
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+++ b/doc/pub/week34/html/._week34-bs003.html
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
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+
-Week 34: Introduction to the course, Logistics and Practicalities
+Week 35: Introduction to the course, Logistics and Practicalities
@@ -80,6 +80,20 @@ Automatically generated HTML file from DocOnce source
2,
None,
'types-of-machine-learning'),
+ ('Essential elements of ML', 2, None, 'essential-elements-of-ml'),
+ ('An optimization/minimization problem',
+ 2,
+ None,
+ 'an-optimization-minimization-problem'),
+ ('A Frequentist approach to data analysis',
+ 2,
+ None,
+ 'a-frequentist-approach-to-data-analysis'),
+ ('What is a good model?', 2, None, 'what-is-a-good-model'),
+ ('What is a good model? Can we define it?',
+ 2,
+ None,
+ 'what-is-a-good-model-can-we-define-it'),
('Software and needed installations',
2,
None,
@@ -108,7 +122,7 @@ Automatically generated HTML file from DocOnce source
('Numpy and arrays', 2, None, 'numpy-and-arrays'),
('Matrices in Python', 2, None, 'matrices-in-python'),
('Meet the Pandas', 2, None, 'meet-the-pandas'),
- ('Friday August 21', 2, None, 'friday-august-21'),
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('Reading Data and fitting', 2, None, 'reading-data-and-fitting'),
('Friday August 27', 2, None, 'friday-august-27'),
('Simple linear regression model using _scikit-learn_',
@@ -129,7 +143,15 @@ Automatically generated HTML file from DocOnce source
3,
None,
'and-what-about-using-neural-networks'),
- ('A first summary', 2, None, 'a-first-summary')]}
+ ('A first summary', 2, None, 'a-first-summary'),
+ ('Exercise 1: Setting up various Python environments',
+ 2,
+ None,
+ 'exercise-1-setting-up-various-python-environments'),
+ ('Exercise 2: making your own data and exploring scikit-learn',
+ 2,
+ None,
+ 'exercise-2-making-your-own-data-and-exploring-scikit-learn')]}
end of tocinfo -->
@@ -159,7 +181,7 @@ MathJax.Hub.Config({
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+ Week 35: Introduction to the course, Logistics and Practicalities
diff --git a/doc/pub/week34/html/._week34-bs004.html b/doc/pub/week34/html/._week34-bs004.html
index 4ef00ac1d..9bd120809 100644
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+++ b/doc/pub/week34/html/._week34-bs004.html
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
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+
-Week 34: Introduction to the course, Logistics and Practicalities
+Week 35: Introduction to the course, Logistics and Practicalities
@@ -80,6 +80,20 @@ Automatically generated HTML file from DocOnce source
2,
None,
'types-of-machine-learning'),
+ ('Essential elements of ML', 2, None, 'essential-elements-of-ml'),
+ ('An optimization/minimization problem',
+ 2,
+ None,
+ 'an-optimization-minimization-problem'),
+ ('A Frequentist approach to data analysis',
+ 2,
+ None,
+ 'a-frequentist-approach-to-data-analysis'),
+ ('What is a good model?', 2, None, 'what-is-a-good-model'),
+ ('What is a good model? Can we define it?',
+ 2,
+ None,
+ 'what-is-a-good-model-can-we-define-it'),
('Software and needed installations',
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None,
@@ -108,7 +122,7 @@ Automatically generated HTML file from DocOnce source
('Numpy and arrays', 2, None, 'numpy-and-arrays'),
('Matrices in Python', 2, None, 'matrices-in-python'),
('Meet the Pandas', 2, None, 'meet-the-pandas'),
- ('Friday August 21', 2, None, 'friday-august-21'),
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('Reading Data and fitting', 2, None, 'reading-data-and-fitting'),
('Friday August 27', 2, None, 'friday-august-27'),
('Simple linear regression model using _scikit-learn_',
@@ -129,7 +143,15 @@ Automatically generated HTML file from DocOnce source
3,
None,
'and-what-about-using-neural-networks'),
- ('A first summary', 2, None, 'a-first-summary')]}
+ ('A first summary', 2, None, 'a-first-summary'),
+ ('Exercise 1: Setting up various Python environments',
+ 2,
+ None,
+ 'exercise-1-setting-up-various-python-environments'),
+ ('Exercise 2: making your own data and exploring scikit-learn',
+ 2,
+ None,
+ 'exercise-2-making-your-own-data-and-exploring-scikit-learn')]}
end of tocinfo -->
@@ -159,7 +181,7 @@ MathJax.Hub.Config({
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+ Week 35: Introduction to the course, Logistics and Practicalities
diff --git a/doc/pub/week34/html/._week34-bs005.html b/doc/pub/week34/html/._week34-bs005.html
index 43a148262..6b9e29264 100644
--- a/doc/pub/week34/html/._week34-bs005.html
+++ b/doc/pub/week34/html/._week34-bs005.html
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
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+
-Week 34: Introduction to the course, Logistics and Practicalities
+Week 35: Introduction to the course, Logistics and Practicalities
@@ -80,6 +80,20 @@ Automatically generated HTML file from DocOnce source
2,
None,
'types-of-machine-learning'),
+ ('Essential elements of ML', 2, None, 'essential-elements-of-ml'),
+ ('An optimization/minimization problem',
+ 2,
+ None,
+ 'an-optimization-minimization-problem'),
+ ('A Frequentist approach to data analysis',
+ 2,
+ None,
+ 'a-frequentist-approach-to-data-analysis'),
+ ('What is a good model?', 2, None, 'what-is-a-good-model'),
+ ('What is a good model? Can we define it?',
+ 2,
+ None,
+ 'what-is-a-good-model-can-we-define-it'),
('Software and needed installations',
2,
None,
@@ -108,7 +122,7 @@ Automatically generated HTML file from DocOnce source
('Numpy and arrays', 2, None, 'numpy-and-arrays'),
('Matrices in Python', 2, None, 'matrices-in-python'),
('Meet the Pandas', 2, None, 'meet-the-pandas'),
- ('Friday August 21', 2, None, 'friday-august-21'),
+ ('Friday August 27', 2, None, 'friday-august-27'),
('Reading Data and fitting', 2, None, 'reading-data-and-fitting'),
('Friday August 27', 2, None, 'friday-august-27'),
('Simple linear regression model using _scikit-learn_',
@@ -129,7 +143,15 @@ Automatically generated HTML file from DocOnce source
3,
None,
'and-what-about-using-neural-networks'),
- ('A first summary', 2, None, 'a-first-summary')]}
+ ('A first summary', 2, None, 'a-first-summary'),
+ ('Exercise 1: Setting up various Python environments',
+ 2,
+ None,
+ 'exercise-1-setting-up-various-python-environments'),
+ ('Exercise 2: making your own data and exploring scikit-learn',
+ 2,
+ None,
+ 'exercise-2-making-your-own-data-and-exploring-scikit-learn')]}
end of tocinfo -->
@@ -159,7 +181,7 @@ MathJax.Hub.Config({
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+ Week 35: Introduction to the course, Logistics and Practicalities
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index d56352d76..97268d195 100644
--- a/doc/pub/week34/html/._week34-bs006.html
+++ b/doc/pub/week34/html/._week34-bs006.html
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
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+
-Week 34: Introduction to the course, Logistics and Practicalities
+Week 35: Introduction to the course, Logistics and Practicalities
@@ -80,6 +80,20 @@ Automatically generated HTML file from DocOnce source
2,
None,
'types-of-machine-learning'),
+ ('Essential elements of ML', 2, None, 'essential-elements-of-ml'),
+ ('An optimization/minimization problem',
+ 2,
+ None,
+ 'an-optimization-minimization-problem'),
+ ('A Frequentist approach to data analysis',
+ 2,
+ None,
+ 'a-frequentist-approach-to-data-analysis'),
+ ('What is a good model?', 2, None, 'what-is-a-good-model'),
+ ('What is a good model? Can we define it?',
+ 2,
+ None,
+ 'what-is-a-good-model-can-we-define-it'),
('Software and needed installations',
2,
None,
@@ -108,7 +122,7 @@ Automatically generated HTML file from DocOnce source
('Numpy and arrays', 2, None, 'numpy-and-arrays'),
('Matrices in Python', 2, None, 'matrices-in-python'),
('Meet the Pandas', 2, None, 'meet-the-pandas'),
- ('Friday August 21', 2, None, 'friday-august-21'),
+ ('Friday August 27', 2, None, 'friday-august-27'),
('Reading Data and fitting', 2, None, 'reading-data-and-fitting'),
('Friday August 27', 2, None, 'friday-august-27'),
('Simple linear regression model using _scikit-learn_',
@@ -129,7 +143,15 @@ Automatically generated HTML file from DocOnce source
3,
None,
'and-what-about-using-neural-networks'),
- ('A first summary', 2, None, 'a-first-summary')]}
+ ('A first summary', 2, None, 'a-first-summary'),
+ ('Exercise 1: Setting up various Python environments',
+ 2,
+ None,
+ 'exercise-1-setting-up-various-python-environments'),
+ ('Exercise 2: making your own data and exploring scikit-learn',
+ 2,
+ None,
+ 'exercise-2-making-your-own-data-and-exploring-scikit-learn')]}
end of tocinfo -->
@@ -159,7 +181,7 @@ MathJax.Hub.Config({
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+ Week 35: Introduction to the course, Logistics and Practicalities
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index 01da5886d..810c57893 100644
--- a/doc/pub/week34/html/._week34-bs007.html
+++ b/doc/pub/week34/html/._week34-bs007.html
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
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+
-Week 34: Introduction to the course, Logistics and Practicalities
+Week 35: Introduction to the course, Logistics and Practicalities
@@ -80,6 +80,20 @@ Automatically generated HTML file from DocOnce source
2,
None,
'types-of-machine-learning'),
+ ('Essential elements of ML', 2, None, 'essential-elements-of-ml'),
+ ('An optimization/minimization problem',
+ 2,
+ None,
+ 'an-optimization-minimization-problem'),
+ ('A Frequentist approach to data analysis',
+ 2,
+ None,
+ 'a-frequentist-approach-to-data-analysis'),
+ ('What is a good model?', 2, None, 'what-is-a-good-model'),
+ ('What is a good model? Can we define it?',
+ 2,
+ None,
+ 'what-is-a-good-model-can-we-define-it'),
('Software and needed installations',
2,
None,
@@ -108,7 +122,7 @@ Automatically generated HTML file from DocOnce source
('Numpy and arrays', 2, None, 'numpy-and-arrays'),
('Matrices in Python', 2, None, 'matrices-in-python'),
('Meet the Pandas', 2, None, 'meet-the-pandas'),
- ('Friday August 21', 2, None, 'friday-august-21'),
+ ('Friday August 27', 2, None, 'friday-august-27'),
('Reading Data and fitting', 2, None, 'reading-data-and-fitting'),
('Friday August 27', 2, None, 'friday-august-27'),
('Simple linear regression model using _scikit-learn_',
@@ -129,7 +143,15 @@ Automatically generated HTML file from DocOnce source
3,
None,
'and-what-about-using-neural-networks'),
- ('A first summary', 2, None, 'a-first-summary')]}
+ ('A first summary', 2, None, 'a-first-summary'),
+ ('Exercise 1: Setting up various Python environments',
+ 2,
+ None,
+ 'exercise-1-setting-up-various-python-environments'),
+ ('Exercise 2: making your own data and exploring scikit-learn',
+ 2,
+ None,
+ 'exercise-2-making-your-own-data-and-exploring-scikit-learn')]}
end of tocinfo -->
@@ -159,7 +181,7 @@ MathJax.Hub.Config({
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+ Week 35: Introduction to the course, Logistics and Practicalities
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index da179f93f..ee3b95108 100644
--- a/doc/pub/week34/html/._week34-bs008.html
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@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
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+
-Week 34: Introduction to the course, Logistics and Practicalities
+Week 35: Introduction to the course, Logistics and Practicalities
@@ -80,6 +80,20 @@ Automatically generated HTML file from DocOnce source
2,
None,
'types-of-machine-learning'),
+ ('Essential elements of ML', 2, None, 'essential-elements-of-ml'),
+ ('An optimization/minimization problem',
+ 2,
+ None,
+ 'an-optimization-minimization-problem'),
+ ('A Frequentist approach to data analysis',
+ 2,
+ None,
+ 'a-frequentist-approach-to-data-analysis'),
+ ('What is a good model?', 2, None, 'what-is-a-good-model'),
+ ('What is a good model? Can we define it?',
+ 2,
+ None,
+ 'what-is-a-good-model-can-we-define-it'),
('Software and needed installations',
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None,
@@ -108,7 +122,7 @@ Automatically generated HTML file from DocOnce source
('Numpy and arrays', 2, None, 'numpy-and-arrays'),
('Matrices in Python', 2, None, 'matrices-in-python'),
('Meet the Pandas', 2, None, 'meet-the-pandas'),
- ('Friday August 21', 2, None, 'friday-august-21'),
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('Reading Data and fitting', 2, None, 'reading-data-and-fitting'),
('Friday August 27', 2, None, 'friday-august-27'),
('Simple linear regression model using _scikit-learn_',
@@ -129,7 +143,15 @@ Automatically generated HTML file from DocOnce source
3,
None,
'and-what-about-using-neural-networks'),
- ('A first summary', 2, None, 'a-first-summary')]}
+ ('A first summary', 2, None, 'a-first-summary'),
+ ('Exercise 1: Setting up various Python environments',
+ 2,
+ None,
+ 'exercise-1-setting-up-various-python-environments'),
+ ('Exercise 2: making your own data and exploring scikit-learn',
+ 2,
+ None,
+ 'exercise-2-making-your-own-data-and-exploring-scikit-learn')]}
end of tocinfo -->
@@ -159,7 +181,7 @@ MathJax.Hub.Config({
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+ Week 35: Introduction to the course, Logistics and Practicalities
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index 69b92d78a..c20b45c67 100644
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@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
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+
-Week 34: Introduction to the course, Logistics and Practicalities
+Week 35: Introduction to the course, Logistics and Practicalities
@@ -80,6 +80,20 @@ Automatically generated HTML file from DocOnce source
2,
None,
'types-of-machine-learning'),
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+ ('An optimization/minimization problem',
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+ None,
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+ ('A Frequentist approach to data analysis',
+ 2,
+ None,
+ 'a-frequentist-approach-to-data-analysis'),
+ ('What is a good model?', 2, None, 'what-is-a-good-model'),
+ ('What is a good model? Can we define it?',
+ 2,
+ None,
+ 'what-is-a-good-model-can-we-define-it'),
('Software and needed installations',
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@@ -108,7 +122,7 @@ Automatically generated HTML file from DocOnce source
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('Reading Data and fitting', 2, None, 'reading-data-and-fitting'),
('Friday August 27', 2, None, 'friday-august-27'),
('Simple linear regression model using _scikit-learn_',
@@ -129,7 +143,15 @@ Automatically generated HTML file from DocOnce source
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None,
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- ('A first summary', 2, None, 'a-first-summary')]}
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+ 2,
+ None,
+ 'exercise-2-making-your-own-data-and-exploring-scikit-learn')]}
end of tocinfo -->
@@ -159,7 +181,7 @@ MathJax.Hub.Config({
- Week 34: Introduction to the course, Logistics and Practicalities
+ Week 35: Introduction to the course, Logistics and Practicalities
diff --git a/doc/pub/week34/html/._week34-bs010.html b/doc/pub/week34/html/._week34-bs010.html
index 10d46efeb..995f6bf97 100644
--- a/doc/pub/week34/html/._week34-bs010.html
+++ b/doc/pub/week34/html/._week34-bs010.html
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
-
+
-Week 34: Introduction to the course, Logistics and Practicalities
+Week 35: Introduction to the course, Logistics and Practicalities
@@ -80,6 +80,20 @@ Automatically generated HTML file from DocOnce source
2,
None,
'types-of-machine-learning'),
+ ('Essential elements of ML', 2, None, 'essential-elements-of-ml'),
+ ('An optimization/minimization problem',
+ 2,
+ None,
+ 'an-optimization-minimization-problem'),
+ ('A Frequentist approach to data analysis',
+ 2,
+ None,
+ 'a-frequentist-approach-to-data-analysis'),
+ ('What is a good model?', 2, None, 'what-is-a-good-model'),
+ ('What is a good model? Can we define it?',
+ 2,
+ None,
+ 'what-is-a-good-model-can-we-define-it'),
('Software and needed installations',
2,
None,
@@ -108,7 +122,7 @@ Automatically generated HTML file from DocOnce source
('Numpy and arrays', 2, None, 'numpy-and-arrays'),
('Matrices in Python', 2, None, 'matrices-in-python'),
('Meet the Pandas', 2, None, 'meet-the-pandas'),
- ('Friday August 21', 2, None, 'friday-august-21'),
+ ('Friday August 27', 2, None, 'friday-august-27'),
('Reading Data and fitting', 2, None, 'reading-data-and-fitting'),
('Friday August 27', 2, None, 'friday-august-27'),
('Simple linear regression model using _scikit-learn_',
@@ -129,7 +143,15 @@ Automatically generated HTML file from DocOnce source
3,
None,
'and-what-about-using-neural-networks'),
- ('A first summary', 2, None, 'a-first-summary')]}
+ ('A first summary', 2, None, 'a-first-summary'),
+ ('Exercise 1: Setting up various Python environments',
+ 2,
+ None,
+ 'exercise-1-setting-up-various-python-environments'),
+ ('Exercise 2: making your own data and exploring scikit-learn',
+ 2,
+ None,
+ 'exercise-2-making-your-own-data-and-exploring-scikit-learn')]}
end of tocinfo -->
@@ -159,7 +181,7 @@ MathJax.Hub.Config({
- Week 34: Introduction to the course, Logistics and Practicalities
+ Week 35: Introduction to the course, Logistics and Practicalities
diff --git a/doc/pub/week34/html/._week34-bs011.html b/doc/pub/week34/html/._week34-bs011.html
index 5c91055b4..88f4d9c0c 100644
--- a/doc/pub/week34/html/._week34-bs011.html
+++ b/doc/pub/week34/html/._week34-bs011.html
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
-
+
-Week 34: Introduction to the course, Logistics and Practicalities
+Week 35: Introduction to the course, Logistics and Practicalities
@@ -80,6 +80,20 @@ Automatically generated HTML file from DocOnce source
2,
None,
'types-of-machine-learning'),
+ ('Essential elements of ML', 2, None, 'essential-elements-of-ml'),
+ ('An optimization/minimization problem',
+ 2,
+ None,
+ 'an-optimization-minimization-problem'),
+ ('A Frequentist approach to data analysis',
+ 2,
+ None,
+ 'a-frequentist-approach-to-data-analysis'),
+ ('What is a good model?', 2, None, 'what-is-a-good-model'),
+ ('What is a good model? Can we define it?',
+ 2,
+ None,
+ 'what-is-a-good-model-can-we-define-it'),
('Software and needed installations',
2,
None,
@@ -108,7 +122,7 @@ Automatically generated HTML file from DocOnce source
('Numpy and arrays', 2, None, 'numpy-and-arrays'),
('Matrices in Python', 2, None, 'matrices-in-python'),
('Meet the Pandas', 2, None, 'meet-the-pandas'),
- ('Friday August 21', 2, None, 'friday-august-21'),
+ ('Friday August 27', 2, None, 'friday-august-27'),
('Reading Data and fitting', 2, None, 'reading-data-and-fitting'),
('Friday August 27', 2, None, 'friday-august-27'),
('Simple linear regression model using _scikit-learn_',
@@ -129,7 +143,15 @@ Automatically generated HTML file from DocOnce source
3,
None,
'and-what-about-using-neural-networks'),
- ('A first summary', 2, None, 'a-first-summary')]}
+ ('A first summary', 2, None, 'a-first-summary'),
+ ('Exercise 1: Setting up various Python environments',
+ 2,
+ None,
+ 'exercise-1-setting-up-various-python-environments'),
+ ('Exercise 2: making your own data and exploring scikit-learn',
+ 2,
+ None,
+ 'exercise-2-making-your-own-data-and-exploring-scikit-learn')]}
end of tocinfo -->
@@ -159,7 +181,7 @@ MathJax.Hub.Config({
- Week 34: Introduction to the course, Logistics and Practicalities
+ Week 35: Introduction to the course, Logistics and Practicalities
diff --git a/doc/pub/week34/html/._week34-bs012.html b/doc/pub/week34/html/._week34-bs012.html
index 5434afd11..95b7cfecf 100644
--- a/doc/pub/week34/html/._week34-bs012.html
+++ b/doc/pub/week34/html/._week34-bs012.html
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
-
+
-Week 34: Introduction to the course, Logistics and Practicalities
+Week 35: Introduction to the course, Logistics and Practicalities
@@ -80,6 +80,20 @@ Automatically generated HTML file from DocOnce source
2,
None,
'types-of-machine-learning'),
+ ('Essential elements of ML', 2, None, 'essential-elements-of-ml'),
+ ('An optimization/minimization problem',
+ 2,
+ None,
+ 'an-optimization-minimization-problem'),
+ ('A Frequentist approach to data analysis',
+ 2,
+ None,
+ 'a-frequentist-approach-to-data-analysis'),
+ ('What is a good model?', 2, None, 'what-is-a-good-model'),
+ ('What is a good model? Can we define it?',
+ 2,
+ None,
+ 'what-is-a-good-model-can-we-define-it'),
('Software and needed installations',
2,
None,
@@ -108,7 +122,7 @@ Automatically generated HTML file from DocOnce source
('Numpy and arrays', 2, None, 'numpy-and-arrays'),
('Matrices in Python', 2, None, 'matrices-in-python'),
('Meet the Pandas', 2, None, 'meet-the-pandas'),
- ('Friday August 21', 2, None, 'friday-august-21'),
+ ('Friday August 27', 2, None, 'friday-august-27'),
('Reading Data and fitting', 2, None, 'reading-data-and-fitting'),
('Friday August 27', 2, None, 'friday-august-27'),
('Simple linear regression model using _scikit-learn_',
@@ -129,7 +143,15 @@ Automatically generated HTML file from DocOnce source
3,
None,
'and-what-about-using-neural-networks'),
- ('A first summary', 2, None, 'a-first-summary')]}
+ ('A first summary', 2, None, 'a-first-summary'),
+ ('Exercise 1: Setting up various Python environments',
+ 2,
+ None,
+ 'exercise-1-setting-up-various-python-environments'),
+ ('Exercise 2: making your own data and exploring scikit-learn',
+ 2,
+ None,
+ 'exercise-2-making-your-own-data-and-exploring-scikit-learn')]}
end of tocinfo -->
@@ -159,7 +181,7 @@ MathJax.Hub.Config({
- Week 34: Introduction to the course, Logistics and Practicalities
+ Week 35: Introduction to the course, Logistics and Practicalities
diff --git a/doc/pub/week34/html/._week34-bs013.html b/doc/pub/week34/html/._week34-bs013.html
index 36e1fb227..67ec9b786 100644
--- a/doc/pub/week34/html/._week34-bs013.html
+++ b/doc/pub/week34/html/._week34-bs013.html
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
-
+
-Week 34: Introduction to the course, Logistics and Practicalities
+Week 35: Introduction to the course, Logistics and Practicalities
@@ -80,6 +80,20 @@ Automatically generated HTML file from DocOnce source
2,
None,
'types-of-machine-learning'),
+ ('Essential elements of ML', 2, None, 'essential-elements-of-ml'),
+ ('An optimization/minimization problem',
+ 2,
+ None,
+ 'an-optimization-minimization-problem'),
+ ('A Frequentist approach to data analysis',
+ 2,
+ None,
+ 'a-frequentist-approach-to-data-analysis'),
+ ('What is a good model?', 2, None, 'what-is-a-good-model'),
+ ('What is a good model? Can we define it?',
+ 2,
+ None,
+ 'what-is-a-good-model-can-we-define-it'),
('Software and needed installations',
2,
None,
@@ -108,7 +122,7 @@ Automatically generated HTML file from DocOnce source
('Numpy and arrays', 2, None, 'numpy-and-arrays'),
('Matrices in Python', 2, None, 'matrices-in-python'),
('Meet the Pandas', 2, None, 'meet-the-pandas'),
- ('Friday August 21', 2, None, 'friday-august-21'),
+ ('Friday August 27', 2, None, 'friday-august-27'),
('Reading Data and fitting', 2, None, 'reading-data-and-fitting'),
('Friday August 27', 2, None, 'friday-august-27'),
('Simple linear regression model using _scikit-learn_',
@@ -129,7 +143,15 @@ Automatically generated HTML file from DocOnce source
3,
None,
'and-what-about-using-neural-networks'),
- ('A first summary', 2, None, 'a-first-summary')]}
+ ('A first summary', 2, None, 'a-first-summary'),
+ ('Exercise 1: Setting up various Python environments',
+ 2,
+ None,
+ 'exercise-1-setting-up-various-python-environments'),
+ ('Exercise 2: making your own data and exploring scikit-learn',
+ 2,
+ None,
+ 'exercise-2-making-your-own-data-and-exploring-scikit-learn')]}
end of tocinfo -->
@@ -159,7 +181,7 @@ MathJax.Hub.Config({
- Week 34: Introduction to the course, Logistics and Practicalities
+ Week 35: Introduction to the course, Logistics and Practicalities
diff --git a/doc/pub/week34/html/._week34-bs014.html b/doc/pub/week34/html/._week34-bs014.html
index 3e634cf55..dd82e18f2 100644
--- a/doc/pub/week34/html/._week34-bs014.html
+++ b/doc/pub/week34/html/._week34-bs014.html
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
-
+
-Week 34: Introduction to the course, Logistics and Practicalities
+Week 35: Introduction to the course, Logistics and Practicalities
@@ -80,6 +80,20 @@ Automatically generated HTML file from DocOnce source
2,
None,
'types-of-machine-learning'),
+ ('Essential elements of ML', 2, None, 'essential-elements-of-ml'),
+ ('An optimization/minimization problem',
+ 2,
+ None,
+ 'an-optimization-minimization-problem'),
+ ('A Frequentist approach to data analysis',
+ 2,
+ None,
+ 'a-frequentist-approach-to-data-analysis'),
+ ('What is a good model?', 2, None, 'what-is-a-good-model'),
+ ('What is a good model? Can we define it?',
+ 2,
+ None,
+ 'what-is-a-good-model-can-we-define-it'),
('Software and needed installations',
2,
None,
@@ -108,7 +122,7 @@ Automatically generated HTML file from DocOnce source
('Numpy and arrays', 2, None, 'numpy-and-arrays'),
('Matrices in Python', 2, None, 'matrices-in-python'),
('Meet the Pandas', 2, None, 'meet-the-pandas'),
- ('Friday August 21', 2, None, 'friday-august-21'),
+ ('Friday August 27', 2, None, 'friday-august-27'),
('Reading Data and fitting', 2, None, 'reading-data-and-fitting'),
('Friday August 27', 2, None, 'friday-august-27'),
('Simple linear regression model using _scikit-learn_',
@@ -129,7 +143,15 @@ Automatically generated HTML file from DocOnce source
3,
None,
'and-what-about-using-neural-networks'),
- ('A first summary', 2, None, 'a-first-summary')]}
+ ('A first summary', 2, None, 'a-first-summary'),
+ ('Exercise 1: Setting up various Python environments',
+ 2,
+ None,
+ 'exercise-1-setting-up-various-python-environments'),
+ ('Exercise 2: making your own data and exploring scikit-learn',
+ 2,
+ None,
+ 'exercise-2-making-your-own-data-and-exploring-scikit-learn')]}
end of tocinfo -->
@@ -159,7 +181,7 @@ MathJax.Hub.Config({
- Week 34: Introduction to the course, Logistics and Practicalities
+ Week 35: Introduction to the course, Logistics and Practicalities
diff --git a/doc/pub/week34/html/._week34-bs015.html b/doc/pub/week34/html/._week34-bs015.html
index bcb101c34..ee803f1cf 100644
--- a/doc/pub/week34/html/._week34-bs015.html
+++ b/doc/pub/week34/html/._week34-bs015.html
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
-
+
-Week 34: Introduction to the course, Logistics and Practicalities
+Week 35: Introduction to the course, Logistics and Practicalities
@@ -80,6 +80,20 @@ Automatically generated HTML file from DocOnce source
2,
None,
'types-of-machine-learning'),
+ ('Essential elements of ML', 2, None, 'essential-elements-of-ml'),
+ ('An optimization/minimization problem',
+ 2,
+ None,
+ 'an-optimization-minimization-problem'),
+ ('A Frequentist approach to data analysis',
+ 2,
+ None,
+ 'a-frequentist-approach-to-data-analysis'),
+ ('What is a good model?', 2, None, 'what-is-a-good-model'),
+ ('What is a good model? Can we define it?',
+ 2,
+ None,
+ 'what-is-a-good-model-can-we-define-it'),
('Software and needed installations',
2,
None,
@@ -108,7 +122,7 @@ Automatically generated HTML file from DocOnce source
('Numpy and arrays', 2, None, 'numpy-and-arrays'),
('Matrices in Python', 2, None, 'matrices-in-python'),
('Meet the Pandas', 2, None, 'meet-the-pandas'),
- ('Friday August 21', 2, None, 'friday-august-21'),
+ ('Friday August 27', 2, None, 'friday-august-27'),
('Reading Data and fitting', 2, None, 'reading-data-and-fitting'),
('Friday August 27', 2, None, 'friday-august-27'),
('Simple linear regression model using _scikit-learn_',
@@ -129,7 +143,15 @@ Automatically generated HTML file from DocOnce source
3,
None,
'and-what-about-using-neural-networks'),
- ('A first summary', 2, None, 'a-first-summary')]}
+ ('A first summary', 2, None, 'a-first-summary'),
+ ('Exercise 1: Setting up various Python environments',
+ 2,
+ None,
+ 'exercise-1-setting-up-various-python-environments'),
+ ('Exercise 2: making your own data and exploring scikit-learn',
+ 2,
+ None,
+ 'exercise-2-making-your-own-data-and-exploring-scikit-learn')]}
end of tocinfo -->
@@ -159,7 +181,7 @@ MathJax.Hub.Config({
- Week 34: Introduction to the course, Logistics and Practicalities
+ Week 35: Introduction to the course, Logistics and Practicalities
diff --git a/doc/pub/week34/html/._week34-bs016.html b/doc/pub/week34/html/._week34-bs016.html
index de62f21fb..f230f4484 100644
--- a/doc/pub/week34/html/._week34-bs016.html
+++ b/doc/pub/week34/html/._week34-bs016.html
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
-
+
-Week 34: Introduction to the course, Logistics and Practicalities
+Week 35: Introduction to the course, Logistics and Practicalities
@@ -80,6 +80,20 @@ Automatically generated HTML file from DocOnce source
2,
None,
'types-of-machine-learning'),
+ ('Essential elements of ML', 2, None, 'essential-elements-of-ml'),
+ ('An optimization/minimization problem',
+ 2,
+ None,
+ 'an-optimization-minimization-problem'),
+ ('A Frequentist approach to data analysis',
+ 2,
+ None,
+ 'a-frequentist-approach-to-data-analysis'),
+ ('What is a good model?', 2, None, 'what-is-a-good-model'),
+ ('What is a good model? Can we define it?',
+ 2,
+ None,
+ 'what-is-a-good-model-can-we-define-it'),
('Software and needed installations',
2,
None,
@@ -108,7 +122,7 @@ Automatically generated HTML file from DocOnce source
('Numpy and arrays', 2, None, 'numpy-and-arrays'),
('Matrices in Python', 2, None, 'matrices-in-python'),
('Meet the Pandas', 2, None, 'meet-the-pandas'),
- ('Friday August 21', 2, None, 'friday-august-21'),
+ ('Friday August 27', 2, None, 'friday-august-27'),
('Reading Data and fitting', 2, None, 'reading-data-and-fitting'),
('Friday August 27', 2, None, 'friday-august-27'),
('Simple linear regression model using _scikit-learn_',
@@ -129,7 +143,15 @@ Automatically generated HTML file from DocOnce source
3,
None,
'and-what-about-using-neural-networks'),
- ('A first summary', 2, None, 'a-first-summary')]}
+ ('A first summary', 2, None, 'a-first-summary'),
+ ('Exercise 1: Setting up various Python environments',
+ 2,
+ None,
+ 'exercise-1-setting-up-various-python-environments'),
+ ('Exercise 2: making your own data and exploring scikit-learn',
+ 2,
+ None,
+ 'exercise-2-making-your-own-data-and-exploring-scikit-learn')]}
end of tocinfo -->
@@ -159,7 +181,7 @@ MathJax.Hub.Config({
- Week 34: Introduction to the course, Logistics and Practicalities
+ Week 35: Introduction to the course, Logistics and Practicalities
diff --git a/doc/pub/week34/html/._week34-bs017.html b/doc/pub/week34/html/._week34-bs017.html
index 61ca0a442..f3d582f02 100644
--- a/doc/pub/week34/html/._week34-bs017.html
+++ b/doc/pub/week34/html/._week34-bs017.html
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
-
+
-Week 34: Introduction to the course, Logistics and Practicalities
+Week 35: Introduction to the course, Logistics and Practicalities
@@ -80,6 +80,20 @@ Automatically generated HTML file from DocOnce source
2,
None,
'types-of-machine-learning'),
+ ('Essential elements of ML', 2, None, 'essential-elements-of-ml'),
+ ('An optimization/minimization problem',
+ 2,
+ None,
+ 'an-optimization-minimization-problem'),
+ ('A Frequentist approach to data analysis',
+ 2,
+ None,
+ 'a-frequentist-approach-to-data-analysis'),
+ ('What is a good model?', 2, None, 'what-is-a-good-model'),
+ ('What is a good model? Can we define it?',
+ 2,
+ None,
+ 'what-is-a-good-model-can-we-define-it'),
('Software and needed installations',
2,
None,
@@ -108,7 +122,7 @@ Automatically generated HTML file from DocOnce source
('Numpy and arrays', 2, None, 'numpy-and-arrays'),
('Matrices in Python', 2, None, 'matrices-in-python'),
('Meet the Pandas', 2, None, 'meet-the-pandas'),
- ('Friday August 21', 2, None, 'friday-august-21'),
+ ('Friday August 27', 2, None, 'friday-august-27'),
('Reading Data and fitting', 2, None, 'reading-data-and-fitting'),
('Friday August 27', 2, None, 'friday-august-27'),
('Simple linear regression model using _scikit-learn_',
@@ -129,7 +143,15 @@ Automatically generated HTML file from DocOnce source
3,
None,
'and-what-about-using-neural-networks'),
- ('A first summary', 2, None, 'a-first-summary')]}
+ ('A first summary', 2, None, 'a-first-summary'),
+ ('Exercise 1: Setting up various Python environments',
+ 2,
+ None,
+ 'exercise-1-setting-up-various-python-environments'),
+ ('Exercise 2: making your own data and exploring scikit-learn',
+ 2,
+ None,
+ 'exercise-2-making-your-own-data-and-exploring-scikit-learn')]}
end of tocinfo -->
@@ -159,7 +181,7 @@ MathJax.Hub.Config({
- Week 34: Introduction to the course, Logistics and Practicalities
+ Week 35: Introduction to the course, Logistics and Practicalities
@@ -243,19 +272,6 @@ desired output of a system. Some of the most common tasks are:
Clustering: Data are divided into groups with certain common traits, without knowing the different groups beforehand. It is thus a form of unsupervised learning.
-The methods we cover have three main topics in common, irrespective of
-whether we deal with supervised or unsupervised learning. The first
-ingredient is normally our data set (which can be subdivided into
-training and test data), the second item is a model which is normally a
-function of some parameters. The model reflects our knowledge of the system (or lack thereof). As an example, if we know that our data show a behavior similar to what would be predicted by a polynomial, fitting our data to a polynomial of some degree would then determin our model.
-
-
-The last ingredient is a so-called cost
-function which allows us to present an estimate on how good our model
-is in reproducing the data it is supposed to train.
-At the heart of basically all ML algorithms there are so-called minimization algorithms, often we end up with various variants of gradient methods.
-
-
@@ -281,7 +297,7 @@ At the heart of basically all ML algorithms there are so-called minimization alg
diff --git a/doc/pub/week34/html/._week34-bs018.html b/doc/pub/week34/html/._week34-bs018.html
index 6ea40f8c9..338b631e9 100644
--- a/doc/pub/week34/html/._week34-bs018.html
+++ b/doc/pub/week34/html/._week34-bs018.html
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
-
+
-Week 34: Introduction to the course, Logistics and Practicalities
+Week 35: Introduction to the course, Logistics and Practicalities
@@ -80,6 +80,20 @@ Automatically generated HTML file from DocOnce source
2,
None,
'types-of-machine-learning'),
+ ('Essential elements of ML', 2, None, 'essential-elements-of-ml'),
+ ('An optimization/minimization problem',
+ 2,
+ None,
+ 'an-optimization-minimization-problem'),
+ ('A Frequentist approach to data analysis',
+ 2,
+ None,
+ 'a-frequentist-approach-to-data-analysis'),
+ ('What is a good model?', 2, None, 'what-is-a-good-model'),
+ ('What is a good model? Can we define it?',
+ 2,
+ None,
+ 'what-is-a-good-model-can-we-define-it'),
('Software and needed installations',
2,
None,
@@ -108,7 +122,7 @@ Automatically generated HTML file from DocOnce source
('Numpy and arrays', 2, None, 'numpy-and-arrays'),
('Matrices in Python', 2, None, 'matrices-in-python'),
('Meet the Pandas', 2, None, 'meet-the-pandas'),
- ('Friday August 21', 2, None, 'friday-august-21'),
+ ('Friday August 27', 2, None, 'friday-august-27'),
('Reading Data and fitting', 2, None, 'reading-data-and-fitting'),
('Friday August 27', 2, None, 'friday-august-27'),
('Simple linear regression model using _scikit-learn_',
@@ -129,7 +143,15 @@ Automatically generated HTML file from DocOnce source
3,
None,
'and-what-about-using-neural-networks'),
- ('A first summary', 2, None, 'a-first-summary')]}
+ ('A first summary', 2, None, 'a-first-summary'),
+ ('Exercise 1: Setting up various Python environments',
+ 2,
+ None,
+ 'exercise-1-setting-up-various-python-environments'),
+ ('Exercise 2: making your own data and exploring scikit-learn',
+ 2,
+ None,
+ 'exercise-2-making-your-own-data-and-exploring-scikit-learn')]}
end of tocinfo -->
@@ -159,7 +181,7 @@ MathJax.Hub.Config({
- Week 34: Introduction to the course, Logistics and Practicalities
+ Week 35: Introduction to the course, Logistics and Practicalities
-We will make extensive use of Python as programming language and its
-myriad of available libraries. You will find
-Jupyter notebooks invaluable in your work. You can run R
-codes in the Jupyter/IPython notebooks, with the immediate benefit of
-visualizing your data. You can also use compiled languages like C++,
-Rust, Julia, Fortran etc if you prefer. The focus in these lectures will be
-on Python.
+The methods we cover have three main topics in common, irrespective of
+whether we deal with supervised or unsupervised learning.
+
-
-If you have Python installed (we strongly recommend Python3) and you feel
-pretty familiar with installing different packages, we recommend that
-you install the following Python packages via pip as
+
+
The first ingredient is normally our data set (which can be subdivided into training, validation and test data). Many find the most difficult part of using Machine Learning to be the set up of your data in a meaningful way.
+
The second item is a model which is normally a function of some parameters. The model reflects our knowledge of the system (or lack thereof). As an example, if we know that our data show a behavior similar to what would be predicted by a polynomial, fitting our data to a polynomial of some degree would then determin our model.
+
The last ingredient is a so-called cost/loss function (or error or risk function) which allows us to present an estimate on how good our model is in reproducing the data it is supposed to train.
-For OSX users we recommend, after having installed Xcode, to
-install brew. Brew allows for a seamless installation of additional
-software via for example
-
-
-
brew install python3
-
-
-For Linux users, with its variety of distributions like for example the widely popular Ubuntu distribution,
-you can use pip as well and simply install Python as
-
-
-
sudo apt-get install python3 (or python for pyhton2.7)
diff --git a/doc/pub/week34/html/._week34-bs019.html b/doc/pub/week34/html/._week34-bs019.html
index ceb1b8d13..4ac64f02e 100644
--- a/doc/pub/week34/html/._week34-bs019.html
+++ b/doc/pub/week34/html/._week34-bs019.html
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
-
+
-Week 34: Introduction to the course, Logistics and Practicalities
+Week 35: Introduction to the course, Logistics and Practicalities
@@ -80,6 +80,20 @@ Automatically generated HTML file from DocOnce source
2,
None,
'types-of-machine-learning'),
+ ('Essential elements of ML', 2, None, 'essential-elements-of-ml'),
+ ('An optimization/minimization problem',
+ 2,
+ None,
+ 'an-optimization-minimization-problem'),
+ ('A Frequentist approach to data analysis',
+ 2,
+ None,
+ 'a-frequentist-approach-to-data-analysis'),
+ ('What is a good model?', 2, None, 'what-is-a-good-model'),
+ ('What is a good model? Can we define it?',
+ 2,
+ None,
+ 'what-is-a-good-model-can-we-define-it'),
('Software and needed installations',
2,
None,
@@ -108,7 +122,7 @@ Automatically generated HTML file from DocOnce source
('Numpy and arrays', 2, None, 'numpy-and-arrays'),
('Matrices in Python', 2, None, 'matrices-in-python'),
('Meet the Pandas', 2, None, 'meet-the-pandas'),
- ('Friday August 21', 2, None, 'friday-august-21'),
+ ('Friday August 27', 2, None, 'friday-august-27'),
('Reading Data and fitting', 2, None, 'reading-data-and-fitting'),
('Friday August 27', 2, None, 'friday-august-27'),
('Simple linear regression model using _scikit-learn_',
@@ -129,7 +143,15 @@ Automatically generated HTML file from DocOnce source
3,
None,
'and-what-about-using-neural-networks'),
- ('A first summary', 2, None, 'a-first-summary')]}
+ ('A first summary', 2, None, 'a-first-summary'),
+ ('Exercise 1: Setting up various Python environments',
+ 2,
+ None,
+ 'exercise-1-setting-up-various-python-environments'),
+ ('Exercise 2: making your own data and exploring scikit-learn',
+ 2,
+ None,
+ 'exercise-2-making-your-own-data-and-exploring-scikit-learn')]}
end of tocinfo -->
@@ -159,7 +181,7 @@ MathJax.Hub.Config({
- Week 34: Introduction to the course, Logistics and Practicalities
+ Week 35: Introduction to the course, Logistics and Practicalities
-If you don't want to perform these operations separately and venture
-into the hassle of exploring how to set up dependencies and paths, we
-recommend two widely used distrubutions which set up all relevant
-dependencies for Python, namely
-
-
-
-which is an open source
-distribution of the Python and R programming languages for large-scale
-data processing, predictive analytics, and scientific computing, that
-aims to simplify package management and deployment. Package versions
-are managed by the package management system conda.
-
-
-
-is a Python
-distribution for scientific and analytic computing distribution and
-analysis environment, available for free and under a commercial
-license.
-
-
-Furthermore, Google's Colab is a free Jupyter notebook environment that requires
-no setup and runs entirely in the cloud. Try it out!
+At the heart of basically all Machine Learning algorithms we will encounter so-called minimization or optimization algorithms. A large family of such methods are so-called gradient methods.
@@ -277,7 +280,7 @@ no setup and runs entirely in the cloud. Try it out!
diff --git a/doc/pub/week34/html/._week34-bs020.html b/doc/pub/week34/html/._week34-bs020.html
index 81b239aab..59f0926ed 100644
--- a/doc/pub/week34/html/._week34-bs020.html
+++ b/doc/pub/week34/html/._week34-bs020.html
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
-
+
-Week 34: Introduction to the course, Logistics and Practicalities
+Week 35: Introduction to the course, Logistics and Practicalities
@@ -80,6 +80,20 @@ Automatically generated HTML file from DocOnce source
2,
None,
'types-of-machine-learning'),
+ ('Essential elements of ML', 2, None, 'essential-elements-of-ml'),
+ ('An optimization/minimization problem',
+ 2,
+ None,
+ 'an-optimization-minimization-problem'),
+ ('A Frequentist approach to data analysis',
+ 2,
+ None,
+ 'a-frequentist-approach-to-data-analysis'),
+ ('What is a good model?', 2, None, 'what-is-a-good-model'),
+ ('What is a good model? Can we define it?',
+ 2,
+ None,
+ 'what-is-a-good-model-can-we-define-it'),
('Software and needed installations',
2,
None,
@@ -108,7 +122,7 @@ Automatically generated HTML file from DocOnce source
('Numpy and arrays', 2, None, 'numpy-and-arrays'),
('Matrices in Python', 2, None, 'matrices-in-python'),
('Meet the Pandas', 2, None, 'meet-the-pandas'),
- ('Friday August 21', 2, None, 'friday-august-21'),
+ ('Friday August 27', 2, None, 'friday-august-27'),
('Reading Data and fitting', 2, None, 'reading-data-and-fitting'),
('Friday August 27', 2, None, 'friday-august-27'),
('Simple linear regression model using _scikit-learn_',
@@ -129,7 +143,15 @@ Automatically generated HTML file from DocOnce source
3,
None,
'and-what-about-using-neural-networks'),
- ('A first summary', 2, None, 'a-first-summary')]}
+ ('A first summary', 2, None, 'a-first-summary'),
+ ('Exercise 1: Setting up various Python environments',
+ 2,
+ None,
+ 'exercise-1-setting-up-various-python-environments'),
+ ('Exercise 2: making your own data and exploring scikit-learn',
+ 2,
+ None,
+ 'exercise-2-making-your-own-data-and-exploring-scikit-learn')]}
end of tocinfo -->
@@ -159,7 +181,7 @@ MathJax.Hub.Config({
- Week 34: Introduction to the course, Logistics and Practicalities
+ Week 35: Introduction to the course, Logistics and Practicalities
-Here we list several useful Python libraries we strongly recommend (if you use anaconda many of these are already there)
+
A Frequentist approach to data analysis
-
-
NumPy is a highly popular library for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays
-
The pandas library provides high-performance, easy-to-use data structures and data analysis tools
-
Xarray is a Python package that makes working with labelled multi-dimensional arrays simple, efficient, and fun!
-
Scipy (pronounced “Sigh Pie”) is a Python-based ecosystem of open-source software for mathematics, science, and engineering.
-
Matplotlib is a Python 2D plotting library which produces publication quality figures in a variety of hardcopy formats and interactive environments across platforms.
-
Autograd can automatically differentiate native Python and Numpy code. It can handle a large subset of Python's features, including loops, ifs, recursion and closures, and it can even take derivatives of derivatives of derivatives
-
SymPy is a Python library for symbolic mathematics.
-
scikit-learn has simple and efficient tools for machine learning, data mining and data analysis
-
TensorFlow is a Python library for fast numerical computing created and released by Google
-
Keras is a high-level neural networks API, written in Python and capable of running on top of TensorFlow, CNTK, or Theano
+When you hear phrases like predictions and estimations and
+correlations and causations, what do you think of? May be you think
+of the difference between classifying new data points and generating
+new data points.
+Or perhaps you consider that correlations represent some kind of symmetric statements like
+if \( A \) is correlated with \( B \), then \( B \) is correlated with
+\( A \). Causation on the other hand is directional, that is if \( A \) causes \( B \), \( B \) does not
+necessarily cause \( A \).
+
+These concepts are in some sense the difference between machine
+learning and statistics. In machine learning and prediction based
+tasks, we are often interested in developing algorithms that are
+capable of learning patterns from given data in an automated fashion,
+and then using these learned patterns to make predictions or
+assessments of newly given data. In many cases, our primary concern
+is the quality of the predictions or assessments, and we are less
+concerned about the underlying patterns that were learned in order
+to make these predictions.
+
+
+In machine learning we normally use a so-called frequentist approach,
+where the aim is to make predictions and find correlations. We focus
+less on for example extracting a probability distribution function (PDF). The PDF can be
+used in turn to make estimations and find causations such as given \( A \)
+what is the likelihood of finding \( B \).
+
+
@@ -262,7 +305,7 @@ Here we list several useful Python libraries we strongly recommend (if you use a
diff --git a/doc/pub/week34/html/._week34-bs021.html b/doc/pub/week34/html/._week34-bs021.html
index 98b7c985d..430c21a9c 100644
--- a/doc/pub/week34/html/._week34-bs021.html
+++ b/doc/pub/week34/html/._week34-bs021.html
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
-
+
-Week 34: Introduction to the course, Logistics and Practicalities
+Week 35: Introduction to the course, Logistics and Practicalities
@@ -80,6 +80,20 @@ Automatically generated HTML file from DocOnce source
2,
None,
'types-of-machine-learning'),
+ ('Essential elements of ML', 2, None, 'essential-elements-of-ml'),
+ ('An optimization/minimization problem',
+ 2,
+ None,
+ 'an-optimization-minimization-problem'),
+ ('A Frequentist approach to data analysis',
+ 2,
+ None,
+ 'a-frequentist-approach-to-data-analysis'),
+ ('What is a good model?', 2, None, 'what-is-a-good-model'),
+ ('What is a good model? Can we define it?',
+ 2,
+ None,
+ 'what-is-a-good-model-can-we-define-it'),
('Software and needed installations',
2,
None,
@@ -108,7 +122,7 @@ Automatically generated HTML file from DocOnce source
('Numpy and arrays', 2, None, 'numpy-and-arrays'),
('Matrices in Python', 2, None, 'matrices-in-python'),
('Meet the Pandas', 2, None, 'meet-the-pandas'),
- ('Friday August 21', 2, None, 'friday-august-21'),
+ ('Friday August 27', 2, None, 'friday-august-27'),
('Reading Data and fitting', 2, None, 'reading-data-and-fitting'),
('Friday August 27', 2, None, 'friday-august-27'),
('Simple linear regression model using _scikit-learn_',
@@ -129,7 +143,15 @@ Automatically generated HTML file from DocOnce source
3,
None,
'and-what-about-using-neural-networks'),
- ('A first summary', 2, None, 'a-first-summary')]}
+ ('A first summary', 2, None, 'a-first-summary'),
+ ('Exercise 1: Setting up various Python environments',
+ 2,
+ None,
+ 'exercise-1-setting-up-various-python-environments'),
+ ('Exercise 2: making your own data and exploring scikit-learn',
+ 2,
+ None,
+ 'exercise-2-making-your-own-data-and-exploring-scikit-learn')]}
end of tocinfo -->
@@ -159,7 +181,7 @@ MathJax.Hub.Config({
- Week 34: Introduction to the course, Logistics and Practicalities
+ Week 35: Introduction to the course, Logistics and Practicalities
-You will also find it convenient to utilize R. We will mainly
-use Python during our lectures and in various projects and exercises.
-Those of you
-already familiar with R should feel free to continue using R, keeping
-however an eye on the parallel Python set ups. Similarly, if you are a
-Python afecionado, feel free to explore R as well. Jupyter/Ipython
-notebook allows you to run R codes interactively in your
-browser. The software library R is really tailored for statistical data analysis
-and allows for an easy usage of the tools and algorithms we will discuss in these
-lectures.
+In science and engineering we often end up in situations where we want to infer (or learn) a
+quantitative model \( M \) for a given set of sample points \( \boldsymbol{X} \in [x_1, x_2,\dots x_N] \).
-To install R with Jupyter notebook
-follow the link here
+As we will see repeatedely in these lectures, we could try to fit these data points to a model given by a
+straight line, or if we wish to be more sophisticated to a more complex
+function.
+
+
+The reason for inferring such a model is that it
+serves many useful purposes. On the one hand, the model can reveal information
+encoded in the data or underlying mechanisms from which the data were generated. For instance, we could discover important
+corelations that relate interesting physics interpretations.
+
+
+In addition, it can simplify the representation of the given data set and help
+us in making predictions about future data samples.
+
+
+A first important consideration to keep in mind is that inferring the correct model
+for a given data set is an elusive, if not impossible, task. The fundamental difficulty
+is that if we are not specific about what we mean by a correct model, there
+could easily be many different models that fit the given data set equally well.
@@ -264,7 +302,7 @@ To install R with Jupyter notebook
diff --git a/doc/pub/week34/html/._week34-bs022.html b/doc/pub/week34/html/._week34-bs022.html
index e49719cab..4654e95a8 100644
--- a/doc/pub/week34/html/._week34-bs022.html
+++ b/doc/pub/week34/html/._week34-bs022.html
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
-
+
-Week 34: Introduction to the course, Logistics and Practicalities
+Week 35: Introduction to the course, Logistics and Practicalities
@@ -80,6 +80,20 @@ Automatically generated HTML file from DocOnce source
2,
None,
'types-of-machine-learning'),
+ ('Essential elements of ML', 2, None, 'essential-elements-of-ml'),
+ ('An optimization/minimization problem',
+ 2,
+ None,
+ 'an-optimization-minimization-problem'),
+ ('A Frequentist approach to data analysis',
+ 2,
+ None,
+ 'a-frequentist-approach-to-data-analysis'),
+ ('What is a good model?', 2, None, 'what-is-a-good-model'),
+ ('What is a good model? Can we define it?',
+ 2,
+ None,
+ 'what-is-a-good-model-can-we-define-it'),
('Software and needed installations',
2,
None,
@@ -108,7 +122,7 @@ Automatically generated HTML file from DocOnce source
('Numpy and arrays', 2, None, 'numpy-and-arrays'),
('Matrices in Python', 2, None, 'matrices-in-python'),
('Meet the Pandas', 2, None, 'meet-the-pandas'),
- ('Friday August 21', 2, None, 'friday-august-21'),
+ ('Friday August 27', 2, None, 'friday-august-27'),
('Reading Data and fitting', 2, None, 'reading-data-and-fitting'),
('Friday August 27', 2, None, 'friday-august-27'),
('Simple linear regression model using _scikit-learn_',
@@ -129,7 +143,15 @@ Automatically generated HTML file from DocOnce source
3,
None,
'and-what-about-using-neural-networks'),
- ('A first summary', 2, None, 'a-first-summary')]}
+ ('A first summary', 2, None, 'a-first-summary'),
+ ('Exercise 1: Setting up various Python environments',
+ 2,
+ None,
+ 'exercise-1-setting-up-various-python-environments'),
+ ('Exercise 2: making your own data and exploring scikit-learn',
+ 2,
+ None,
+ 'exercise-2-making-your-own-data-and-exploring-scikit-learn')]}
end of tocinfo -->
@@ -159,7 +181,7 @@ MathJax.Hub.Config({
- Week 34: Introduction to the course, Logistics and Practicalities
+ Week 35: Introduction to the course, Logistics and Practicalities
-For the C++ aficionados, Jupyter/IPython notebook allows you also to
-install C++ and run codes written in this language interactively in
-the browser. Since we will emphasize writing many of the algorithms
-yourself, you can thus opt for either Python or C++ (or Fortran or other compiled languages) as programming
-languages.
+The central question is this: what leads us to say that a model is correct or
+optimal for a given data set? To make the model inference problem well posed, i.e.,
+to guarantee that there is a unique optimal model for the given data, we need to
+impose additional assumptions or restrictions on the class of models considered. To
+this end, we should not be looking for just any model that can describe the data.
+Instead, we should look for a model \( M \) that is the best among a restricted class
+of models. In addition, to make the model inference problem computationally
+tractable, we need to specify how restricted the class of models needs to be. A
+common strategy is to start
+with the simplest possible class of models that is just necessary to describe the data
+or solve the problem at hand. More precisely, the model class should be rich enough
+to contain at least one model that can fit the data to a desired accuracy and yet be
+restricted enough that it is relatively simple to find the best model for the given data.
-To add more entropy, cython can also be used when running your
-notebooks. It means that Python with the jupyter notebook
-setup allows you to integrate widely popular softwares and tools for
-scientific computing. Similarly, the
-Numba Python package delivers increased performance
-capabilities with minimal rewrites of your codes. With its
-versatility, including symbolic operations, Python offers a unique
-computational environment. Your jupyter notebook can easily be
-converted into a nicely rendered PDF file or a Latex file for
-further processing. For example, convert to latex as
+Thus, the most popular strategy is to start from the
+simplest class of models and increase the complexity of the models only when the
+simpler models become inadequate. For instance, if we work with a regression problem to fit a set of sample points, one
+may first try the simplest class of models, namely linear models, followed obviously by more complex models.
-And to add more versatility, the Python package SymPy is a Python library for symbolic mathematics. It aims to become a full-featured computer algebra system (CAS) and is entirely written in Python.
-
-
-Finally, if you wish to use the light mark-up language
-doconce you can convert a standard ascii text file into various HTML
-formats, ipython notebooks, latex files, pdf files etc with minimal edits. These lectures were generated using doconce.
+How to evaluate which model fits best the data is something we will come back to over and over again in these sets of lectures.
@@ -280,7 +301,7 @@ formats, ipython notebooks, latex files, pdf files etc with minimal edits. These
diff --git a/doc/pub/week34/html/._week34-bs023.html b/doc/pub/week34/html/._week34-bs023.html
index ef6250daa..44529fd50 100644
--- a/doc/pub/week34/html/._week34-bs023.html
+++ b/doc/pub/week34/html/._week34-bs023.html
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
-
+
-Week 34: Introduction to the course, Logistics and Practicalities
+Week 35: Introduction to the course, Logistics and Practicalities
@@ -80,6 +80,20 @@ Automatically generated HTML file from DocOnce source
2,
None,
'types-of-machine-learning'),
+ ('Essential elements of ML', 2, None, 'essential-elements-of-ml'),
+ ('An optimization/minimization problem',
+ 2,
+ None,
+ 'an-optimization-minimization-problem'),
+ ('A Frequentist approach to data analysis',
+ 2,
+ None,
+ 'a-frequentist-approach-to-data-analysis'),
+ ('What is a good model?', 2, None, 'what-is-a-good-model'),
+ ('What is a good model? Can we define it?',
+ 2,
+ None,
+ 'what-is-a-good-model-can-we-define-it'),
('Software and needed installations',
2,
None,
@@ -108,7 +122,7 @@ Automatically generated HTML file from DocOnce source
('Numpy and arrays', 2, None, 'numpy-and-arrays'),
('Matrices in Python', 2, None, 'matrices-in-python'),
('Meet the Pandas', 2, None, 'meet-the-pandas'),
- ('Friday August 21', 2, None, 'friday-august-21'),
+ ('Friday August 27', 2, None, 'friday-august-27'),
('Reading Data and fitting', 2, None, 'reading-data-and-fitting'),
('Friday August 27', 2, None, 'friday-august-27'),
('Simple linear regression model using _scikit-learn_',
@@ -129,7 +143,15 @@ Automatically generated HTML file from DocOnce source
3,
None,
'and-what-about-using-neural-networks'),
- ('A first summary', 2, None, 'a-first-summary')]}
+ ('A first summary', 2, None, 'a-first-summary'),
+ ('Exercise 1: Setting up various Python environments',
+ 2,
+ None,
+ 'exercise-1-setting-up-various-python-environments'),
+ ('Exercise 2: making your own data and exploring scikit-learn',
+ 2,
+ None,
+ 'exercise-2-making-your-own-data-and-exploring-scikit-learn')]}
end of tocinfo -->
@@ -159,7 +181,7 @@ MathJax.Hub.Config({
- Week 34: Introduction to the course, Logistics and Practicalities
+ Week 35: Introduction to the course, Logistics and Practicalities
Numpy examples and Important Matrix and vector handling packages
+
Software and needed installations
-There are several central software libraries for linear algebra and eigenvalue problems. Several of the more
-popular ones have been wrapped into ofter software packages like those from the widely used text Numerical Recipes. The original source codes in many of the available packages are often taken from the widely used
-software package LAPACK, which follows two other popular packages
-developed in the 1970s, namely EISPACK and LINPACK. We describe them shortly here.
+We will make extensive use of Python as programming language and its
+myriad of available libraries. You will find
+Jupyter notebooks invaluable in your work. You can run R
+codes in the Jupyter/IPython notebooks, with the immediate benefit of
+visualizing your data. You can also use compiled languages like C++,
+Rust, Julia, Fortran etc if you prefer. The focus in these lectures will be
+on Python.
-
-
LINPACK: package for linear equations and least square problems.
-
LAPACK:package for solving symmetric, unsymmetric and generalized eigenvalue problems. From LAPACK's website http://www.netlib.org it is possible to download for free all source codes from this library. Both C/C++ and Fortran versions are available.
-
BLAS (I, II and III): (Basic Linear Algebra Subprograms) are routines that provide standard building blocks for performing basic vector and matrix operations. Blas I is vector operations, II vector-matrix operations and III matrix-matrix operations. Highly parallelized and efficient codes, all available for download from http://www.netlib.org.
-
+
+If you have Python installed (we strongly recommend Python3) and you feel
+pretty familiar with installing different packages, we recommend that
+you install the following Python packages via pip as
+
+For OSX users we recommend, after having installed Xcode, to
+install brew. Brew allows for a seamless installation of additional
+software via for example
+
+
+
brew install python3
+
+
+For Linux users, with its variety of distributions like for example the widely popular Ubuntu distribution,
+you can use pip as well and simply install Python as
+
+
+
sudo apt-get install python3 (or python for pyhton2.7)
+
+
+etc etc.
+
+
@@ -259,7 +315,7 @@ developed in the 1970s, namely EISPACK and LINPACK. We describe them shortly he
diff --git a/doc/pub/week34/html/._week34-bs024.html b/doc/pub/week34/html/._week34-bs024.html
index 98ece82b4..03f7f94a8 100644
--- a/doc/pub/week34/html/._week34-bs024.html
+++ b/doc/pub/week34/html/._week34-bs024.html
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
-
+
-Week 34: Introduction to the course, Logistics and Practicalities
+Week 35: Introduction to the course, Logistics and Practicalities
@@ -80,6 +80,20 @@ Automatically generated HTML file from DocOnce source
2,
None,
'types-of-machine-learning'),
+ ('Essential elements of ML', 2, None, 'essential-elements-of-ml'),
+ ('An optimization/minimization problem',
+ 2,
+ None,
+ 'an-optimization-minimization-problem'),
+ ('A Frequentist approach to data analysis',
+ 2,
+ None,
+ 'a-frequentist-approach-to-data-analysis'),
+ ('What is a good model?', 2, None, 'what-is-a-good-model'),
+ ('What is a good model? Can we define it?',
+ 2,
+ None,
+ 'what-is-a-good-model-can-we-define-it'),
('Software and needed installations',
2,
None,
@@ -108,7 +122,7 @@ Automatically generated HTML file from DocOnce source
('Numpy and arrays', 2, None, 'numpy-and-arrays'),
('Matrices in Python', 2, None, 'matrices-in-python'),
('Meet the Pandas', 2, None, 'meet-the-pandas'),
- ('Friday August 21', 2, None, 'friday-august-21'),
+ ('Friday August 27', 2, None, 'friday-august-27'),
('Reading Data and fitting', 2, None, 'reading-data-and-fitting'),
('Friday August 27', 2, None, 'friday-august-27'),
('Simple linear regression model using _scikit-learn_',
@@ -129,7 +143,15 @@ Automatically generated HTML file from DocOnce source
3,
None,
'and-what-about-using-neural-networks'),
- ('A first summary', 2, None, 'a-first-summary')]}
+ ('A first summary', 2, None, 'a-first-summary'),
+ ('Exercise 1: Setting up various Python environments',
+ 2,
+ None,
+ 'exercise-1-setting-up-various-python-environments'),
+ ('Exercise 2: making your own data and exploring scikit-learn',
+ 2,
+ None,
+ 'exercise-2-making-your-own-data-and-exploring-scikit-learn')]}
end of tocinfo -->
@@ -159,7 +181,7 @@ MathJax.Hub.Config({
- Week 34: Introduction to the course, Logistics and Practicalities
+ Week 35: Introduction to the course, Logistics and Practicalities
+
+which is an open source
+distribution of the Python and R programming languages for large-scale
+data processing, predictive analytics, and scientific computing, that
+aims to simplify package management and deployment. Package versions
+are managed by the package management system conda.
+
+
+
+is a Python
+distribution for scientific and analytic computing distribution and
+analysis environment, available for free and under a commercial
+license.
-The inverse of a matrix is defined by
-
-$$
-\mathbf{A}^{-1} \cdot \mathbf{A} = I
-$$
-
-
diff --git a/doc/pub/week34/html/._week34-bs025.html b/doc/pub/week34/html/._week34-bs025.html
index e7140f12c..afe39c9f2 100644
--- a/doc/pub/week34/html/._week34-bs025.html
+++ b/doc/pub/week34/html/._week34-bs025.html
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
-
+
-Week 34: Introduction to the course, Logistics and Practicalities
+Week 35: Introduction to the course, Logistics and Practicalities
@@ -80,6 +80,20 @@ Automatically generated HTML file from DocOnce source
2,
None,
'types-of-machine-learning'),
+ ('Essential elements of ML', 2, None, 'essential-elements-of-ml'),
+ ('An optimization/minimization problem',
+ 2,
+ None,
+ 'an-optimization-minimization-problem'),
+ ('A Frequentist approach to data analysis',
+ 2,
+ None,
+ 'a-frequentist-approach-to-data-analysis'),
+ ('What is a good model?', 2, None, 'what-is-a-good-model'),
+ ('What is a good model? Can we define it?',
+ 2,
+ None,
+ 'what-is-a-good-model-can-we-define-it'),
('Software and needed installations',
2,
None,
@@ -108,7 +122,7 @@ Automatically generated HTML file from DocOnce source
('Numpy and arrays', 2, None, 'numpy-and-arrays'),
('Matrices in Python', 2, None, 'matrices-in-python'),
('Meet the Pandas', 2, None, 'meet-the-pandas'),
- ('Friday August 21', 2, None, 'friday-august-21'),
+ ('Friday August 27', 2, None, 'friday-august-27'),
('Reading Data and fitting', 2, None, 'reading-data-and-fitting'),
('Friday August 27', 2, None, 'friday-august-27'),
('Simple linear regression model using _scikit-learn_',
@@ -129,7 +143,15 @@ Automatically generated HTML file from DocOnce source
3,
None,
'and-what-about-using-neural-networks'),
- ('A first summary', 2, None, 'a-first-summary')]}
+ ('A first summary', 2, None, 'a-first-summary'),
+ ('Exercise 1: Setting up various Python environments',
+ 2,
+ None,
+ 'exercise-1-setting-up-various-python-environments'),
+ ('Exercise 2: making your own data and exploring scikit-learn',
+ 2,
+ None,
+ 'exercise-2-making-your-own-data-and-exploring-scikit-learn')]}
end of tocinfo -->
@@ -159,7 +181,7 @@ MathJax.Hub.Config({
- Week 34: Introduction to the course, Logistics and Practicalities
+ Week 35: Introduction to the course, Logistics and Practicalities
NumPy is a highly popular library for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays
+
The pandas library provides high-performance, easy-to-use data structures and data analysis tools
+
Xarray is a Python package that makes working with labelled multi-dimensional arrays simple, efficient, and fun!
+
Scipy (pronounced “Sigh Pie”) is a Python-based ecosystem of open-source software for mathematics, science, and engineering.
+
Matplotlib is a Python 2D plotting library which produces publication quality figures in a variety of hardcopy formats and interactive environments across platforms.
+
Autograd can automatically differentiate native Python and Numpy code. It can handle a large subset of Python's features, including loops, ifs, recursion and closures, and it can even take derivatives of derivatives of derivatives
+
SymPy is a Python library for symbolic mathematics.
+
scikit-learn has simple and efficient tools for machine learning, data mining and data analysis
+
TensorFlow is a Python library for fast numerical computing created and released by Google
+
Keras is a high-level neural networks API, written in Python and capable of running on top of TensorFlow, CNTK, or Theano
diff --git a/doc/pub/week34/html/._week34-bs026.html b/doc/pub/week34/html/._week34-bs026.html
index 06e109ce3..6607ccb25 100644
--- a/doc/pub/week34/html/._week34-bs026.html
+++ b/doc/pub/week34/html/._week34-bs026.html
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
-
+
-Week 34: Introduction to the course, Logistics and Practicalities
+Week 35: Introduction to the course, Logistics and Practicalities
@@ -80,6 +80,20 @@ Automatically generated HTML file from DocOnce source
2,
None,
'types-of-machine-learning'),
+ ('Essential elements of ML', 2, None, 'essential-elements-of-ml'),
+ ('An optimization/minimization problem',
+ 2,
+ None,
+ 'an-optimization-minimization-problem'),
+ ('A Frequentist approach to data analysis',
+ 2,
+ None,
+ 'a-frequentist-approach-to-data-analysis'),
+ ('What is a good model?', 2, None, 'what-is-a-good-model'),
+ ('What is a good model? Can we define it?',
+ 2,
+ None,
+ 'what-is-a-good-model-can-we-define-it'),
('Software and needed installations',
2,
None,
@@ -108,7 +122,7 @@ Automatically generated HTML file from DocOnce source
('Numpy and arrays', 2, None, 'numpy-and-arrays'),
('Matrices in Python', 2, None, 'matrices-in-python'),
('Meet the Pandas', 2, None, 'meet-the-pandas'),
- ('Friday August 21', 2, None, 'friday-august-21'),
+ ('Friday August 27', 2, None, 'friday-august-27'),
('Reading Data and fitting', 2, None, 'reading-data-and-fitting'),
('Friday August 27', 2, None, 'friday-august-27'),
('Simple linear regression model using _scikit-learn_',
@@ -129,7 +143,15 @@ Automatically generated HTML file from DocOnce source
3,
None,
'and-what-about-using-neural-networks'),
- ('A first summary', 2, None, 'a-first-summary')]}
+ ('A first summary', 2, None, 'a-first-summary'),
+ ('Exercise 1: Setting up various Python environments',
+ 2,
+ None,
+ 'exercise-1-setting-up-various-python-environments'),
+ ('Exercise 2: making your own data and exploring scikit-learn',
+ 2,
+ None,
+ 'exercise-2-making-your-own-data-and-exploring-scikit-learn')]}
end of tocinfo -->
@@ -159,7 +181,7 @@ MathJax.Hub.Config({
- Week 34: Introduction to the course, Logistics and Practicalities
+ Week 35: Introduction to the course, Logistics and Practicalities
-For an \( N\times N \) matrix \( \mathbf{A} \) the following properties are all equivalent
-
-
-
If the inverse of \( \mathbf{A} \) exists, \( \mathbf{A} \) is nonsingular.
-
The equation \( \mathbf{Ax}=0 \) implies \( \mathbf{x}=0 \).
-
The rows of \( \mathbf{A} \) form a basis of \( R^N \).
-
The columns of \( \mathbf{A} \) form a basis of \( R^N \).
-
\( \mathbf{A} \) is a product of elementary matrices.
-
\( 0 \) is not eigenvalue of \( \mathbf{A} \).
-
-
-
+You will also find it convenient to utilize R. We will mainly
+use Python during our lectures and in various projects and exercises.
+Those of you
+already familiar with R should feel free to continue using R, keeping
+however an eye on the parallel Python set ups. Similarly, if you are a
+Python afecionado, feel free to explore R as well. Jupyter/Ipython
+notebook allows you to run R codes interactively in your
+browser. The software library R is really tailored for statistical data analysis
+and allows for an easy usage of the tools and algorithms we will discuss in these
+lectures.
+
diff --git a/doc/pub/week34/html/._week34-bs027.html b/doc/pub/week34/html/._week34-bs027.html
index 85e979ca7..de4d779b5 100644
--- a/doc/pub/week34/html/._week34-bs027.html
+++ b/doc/pub/week34/html/._week34-bs027.html
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
-
+
-Week 34: Introduction to the course, Logistics and Practicalities
+Week 35: Introduction to the course, Logistics and Practicalities
@@ -80,6 +80,20 @@ Automatically generated HTML file from DocOnce source
2,
None,
'types-of-machine-learning'),
+ ('Essential elements of ML', 2, None, 'essential-elements-of-ml'),
+ ('An optimization/minimization problem',
+ 2,
+ None,
+ 'an-optimization-minimization-problem'),
+ ('A Frequentist approach to data analysis',
+ 2,
+ None,
+ 'a-frequentist-approach-to-data-analysis'),
+ ('What is a good model?', 2, None, 'what-is-a-good-model'),
+ ('What is a good model? Can we define it?',
+ 2,
+ None,
+ 'what-is-a-good-model-can-we-define-it'),
('Software and needed installations',
2,
None,
@@ -108,7 +122,7 @@ Automatically generated HTML file from DocOnce source
('Numpy and arrays', 2, None, 'numpy-and-arrays'),
('Matrices in Python', 2, None, 'matrices-in-python'),
('Meet the Pandas', 2, None, 'meet-the-pandas'),
- ('Friday August 21', 2, None, 'friday-august-21'),
+ ('Friday August 27', 2, None, 'friday-august-27'),
('Reading Data and fitting', 2, None, 'reading-data-and-fitting'),
('Friday August 27', 2, None, 'friday-august-27'),
('Simple linear regression model using _scikit-learn_',
@@ -129,7 +143,15 @@ Automatically generated HTML file from DocOnce source
3,
None,
'and-what-about-using-neural-networks'),
- ('A first summary', 2, None, 'a-first-summary')]}
+ ('A first summary', 2, None, 'a-first-summary'),
+ ('Exercise 1: Setting up various Python environments',
+ 2,
+ None,
+ 'exercise-1-setting-up-various-python-environments'),
+ ('Exercise 2: making your own data and exploring scikit-learn',
+ 2,
+ None,
+ 'exercise-2-making-your-own-data-and-exploring-scikit-learn')]}
end of tocinfo -->
@@ -159,7 +181,7 @@ MathJax.Hub.Config({
- Week 34: Introduction to the course, Logistics and Practicalities
+ Week 35: Introduction to the course, Logistics and Practicalities
-Numpy provides an easy way to handle arrays in Python. The standard way to import this library is as
+
Installing R, C++, cython, Numba etc
+
+
+For the C++ aficionados, Jupyter/IPython notebook allows you also to
+install C++ and run codes written in this language interactively in
+the browser. Since we will emphasize writing many of the algorithms
+yourself, you can thus opt for either Python or C++ (or Fortran or other compiled languages) as programming
+languages.
+
+
+To add more entropy, cython can also be used when running your
+notebooks. It means that Python with the jupyter notebook
+setup allows you to integrate widely popular softwares and tools for
+scientific computing. Similarly, the
+Numba Python package delivers increased performance
+capabilities with minimal rewrites of your codes. With its
+versatility, including symbolic operations, Python offers a unique
+computational environment. Your jupyter notebook can easily be
+converted into a nicely rendered PDF file or a Latex file for
+further processing. For example, convert to latex as
-
-
importnumpyasnp
+
+
pycod jupyter nbconvert filename.ipynb --to latex
-Here follows a simple example where we set up an array of ten elements, all determined by random numbers drawn according to the normal distribution,
-
-
-
-
n =10
-x = np.random.normal(size=n)
-print(x)
-
-
-We defined a vector \( x \) with \( n=10 \) elements with its values given by the Normal distribution \( N(0,1) \).
-Another alternative is to declare a vector as follows
-
-Here we have defined a vector with three elements, with \( x_0=1 \), \( x_1=2 \) and \( x_2=3 \). Note that both Python and C++
-start numbering array elements from \( 0 \) and on. This means that a vector with \( n \) elements has a sequence of entities \( x_0, x_1, x_2, \dots, x_{n-1} \). We could also let (recommended) Numpy to compute the logarithms of a specific array as
-
-In the last example we used Numpy's unary function \( np.log \). This function is
-highly tuned to compute array elements since the code is vectorized
-and does not require looping. We normaly recommend that you use the
-Numpy intrinsic functions instead of the corresponding log function
-from Python's math module. The looping is done explicitely by the
-np.log function. The alternative, and slower way to compute the
-logarithms of a vector would be to write
+And to add more versatility, the Python package SymPy is a Python library for symbolic mathematics. It aims to become a full-featured computer algebra system (CAS) and is entirely written in Python.
+Finally, if you wish to use the light mark-up language
+doconce you can convert a standard ascii text file into various HTML
+formats, ipython notebooks, latex files, pdf files etc with minimal edits. These lectures were generated using doconce.
-
-
-We note that our code is much longer already and we need to import the log function from the math module.
-The attentive reader will also notice that the output is \( [1, 1, 2] \). Python interprets automagically our numbers as integers (like the automatic keyword in C++). To change this we could define our array elements to be double precision numbers as
-
-To check the number of bytes (remember that one byte contains eight bits for double precision variables), you can use simple use the itemsize functionality (the array \( x \) is actually an object which inherits the functionalities defined in Numpy) as
-
diff --git a/doc/pub/week34/html/._week34-bs028.html b/doc/pub/week34/html/._week34-bs028.html
index fc73de012..b48e0586d 100644
--- a/doc/pub/week34/html/._week34-bs028.html
+++ b/doc/pub/week34/html/._week34-bs028.html
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
-
+
-Week 34: Introduction to the course, Logistics and Practicalities
+Week 35: Introduction to the course, Logistics and Practicalities
@@ -80,6 +80,20 @@ Automatically generated HTML file from DocOnce source
2,
None,
'types-of-machine-learning'),
+ ('Essential elements of ML', 2, None, 'essential-elements-of-ml'),
+ ('An optimization/minimization problem',
+ 2,
+ None,
+ 'an-optimization-minimization-problem'),
+ ('A Frequentist approach to data analysis',
+ 2,
+ None,
+ 'a-frequentist-approach-to-data-analysis'),
+ ('What is a good model?', 2, None, 'what-is-a-good-model'),
+ ('What is a good model? Can we define it?',
+ 2,
+ None,
+ 'what-is-a-good-model-can-we-define-it'),
('Software and needed installations',
2,
None,
@@ -108,7 +122,7 @@ Automatically generated HTML file from DocOnce source
('Numpy and arrays', 2, None, 'numpy-and-arrays'),
('Matrices in Python', 2, None, 'matrices-in-python'),
('Meet the Pandas', 2, None, 'meet-the-pandas'),
- ('Friday August 21', 2, None, 'friday-august-21'),
+ ('Friday August 27', 2, None, 'friday-august-27'),
('Reading Data and fitting', 2, None, 'reading-data-and-fitting'),
('Friday August 27', 2, None, 'friday-august-27'),
('Simple linear regression model using _scikit-learn_',
@@ -129,7 +143,15 @@ Automatically generated HTML file from DocOnce source
3,
None,
'and-what-about-using-neural-networks'),
- ('A first summary', 2, None, 'a-first-summary')]}
+ ('A first summary', 2, None, 'a-first-summary'),
+ ('Exercise 1: Setting up various Python environments',
+ 2,
+ None,
+ 'exercise-1-setting-up-various-python-environments'),
+ ('Exercise 2: making your own data and exploring scikit-learn',
+ 2,
+ None,
+ 'exercise-2-making-your-own-data-and-exploring-scikit-learn')]}
end of tocinfo -->
@@ -159,7 +181,7 @@ MathJax.Hub.Config({
- Week 34: Introduction to the course, Logistics and Practicalities
+ Week 35: Introduction to the course, Logistics and Practicalities
Numpy examples and Important Matrix and vector handling packages
-Having defined vectors, we are now ready to try out matrices. We can
-define a \( 3 \times 3 \) real matrix \( \hat{A} \) as (recall that we user
-lowercase letters for vectors and uppercase letters for matrices)
+There are several central software libraries for linear algebra and eigenvalue problems. Several of the more
+popular ones have been wrapped into ofter software packages like those from the widely used text Numerical Recipes. The original source codes in many of the available packages are often taken from the widely used
+software package LAPACK, which follows two other popular packages
+developed in the 1970s, namely EISPACK and LINPACK. We describe them shortly here.
-
+
+
LINPACK: package for linear equations and least square problems.
+
LAPACK:package for solving symmetric, unsymmetric and generalized eigenvalue problems. From LAPACK's website http://www.netlib.org it is possible to download for free all source codes from this library. Both C/C++ and Fortran versions are available.
+
BLAS (I, II and III): (Basic Linear Algebra Subprograms) are routines that provide standard building blocks for performing basic vector and matrix operations. Blas I is vector operations, II vector-matrix operations and III matrix-matrix operations. Highly parallelized and efficient codes, all available for download from http://www.netlib.org.
-If we use the shape function we would get \( (3, 3) \) as output, that is verifying that our matrix is a \( 3\times 3 \) matrix. We can slice the matrix and print for example the first column (Python organized matrix elements in a row-major order, see below) as
-
-
-
-
importnumpyasnp
-A = np.log(np.array([ [4.0, 7.0, 8.0], [3.0, 10.0, 11.0], [4.0, 5.0, 7.0] ]))
-# print the first column, row-major order and elements start with 0
-print(A[:,0])
-
-
-We can continue this was by printing out other columns or rows. The example here prints out the second column
-
-
-
-
importnumpyasnp
-A = np.log(np.array([ [4.0, 7.0, 8.0], [3.0, 10.0, 11.0], [4.0, 5.0, 7.0] ]))
-# print the first column, row-major order and elements start with 0
-print(A[1,:])
-
-
-Numpy contains many other functionalities that allow us to slice, subdivide etc etc arrays. We strongly recommend that you look up the Numpy website for more details. Useful functions when defining a matrix are the np.zeros function which declares a matrix of a given dimension and sets all elements to zero
-
-
-
-
importnumpyasnp
-n =10
-# define a matrix of dimension 10 x 10 and set all elements to zero
-A = np.zeros( (n, n) )
-print(A)
-
-
-or initializing all elements to
-
-
-
-
importnumpyasnp
-n =10
-# define a matrix of dimension 10 x 10 and set all elements to one
-A = np.ones( (n, n) )
-print(A)
-
-
-or as unitarily distributed random numbers (see the material on random number generators in the statistics part)
-
-
-
-
importnumpyasnp
-n =10
-# define a matrix of dimension 10 x 10 and set all elements to random numbers with x \in [0, 1]
-A = np.random.rand(n, n)
-print(A)
-
-
-As we will see throughout these lectures, there are several extremely useful functionalities in Numpy.
-As an example, consider the discussion of the covariance matrix. Suppose we have defined three vectors
-\( \hat{x}, \hat{y}, \hat{z} \) with \( n \) elements each. The covariance matrix is defined as
-$$
-\hat{\Sigma} = \begin{bmatrix} \sigma_{xx} & \sigma_{xy} & \sigma_{xz} \\
- \sigma_{yx} & \sigma_{yy} & \sigma_{yz} \\
- \sigma_{zx} & \sigma_{zy} & \sigma_{zz}
- \end{bmatrix},
-$$
-
-where for example
-$$
-\sigma_{xy} =\frac{1}{n} \sum_{i=0}^{n-1}(x_i- \overline{x})(y_i- \overline{y}).
-$$
-
-The Numpy function np.cov calculates the covariance elements using the factor \( 1/(n-1) \) instead of \( 1/n \) since it assumes we do not have the exact mean values.
-The following simple function uses the np.vstack function which takes each vector of dimension \( 1\times n \) and produces a \( 3\times n \) matrix \( \hat{W} \)
-$$
-\hat{W} = \begin{bmatrix} x_0 & y_0 & z_0 \\
- x_1 & y_1 & z_1 \\
- x_2 & y_2 & z_2 \\
- \dots & \dots & \dots \\
- x_{n-2} & y_{n-2} & z_{n-2} \\
- x_{n-1} & y_{n-1} & z_{n-1}
- \end{bmatrix},
-$$
-
-
-which in turn is converted into into the \( 3\times 3 \) covariance matrix
-\( \hat{\Sigma} \) via the Numpy function np.cov(). We note that we can also calculate
-the mean value of each set of samples \( \hat{x} \) etc using the Numpy
-function np.mean(x). We can also extract the eigenvalues of the
-covariance matrix through the np.linalg.eig() function.
-
-
diff --git a/doc/pub/week34/html/._week34-bs029.html b/doc/pub/week34/html/._week34-bs029.html
index 1bb9c5e34..55b27b4f1 100644
--- a/doc/pub/week34/html/._week34-bs029.html
+++ b/doc/pub/week34/html/._week34-bs029.html
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
-
+
-Week 34: Introduction to the course, Logistics and Practicalities
+Week 35: Introduction to the course, Logistics and Practicalities
@@ -80,6 +80,20 @@ Automatically generated HTML file from DocOnce source
2,
None,
'types-of-machine-learning'),
+ ('Essential elements of ML', 2, None, 'essential-elements-of-ml'),
+ ('An optimization/minimization problem',
+ 2,
+ None,
+ 'an-optimization-minimization-problem'),
+ ('A Frequentist approach to data analysis',
+ 2,
+ None,
+ 'a-frequentist-approach-to-data-analysis'),
+ ('What is a good model?', 2, None, 'what-is-a-good-model'),
+ ('What is a good model? Can we define it?',
+ 2,
+ None,
+ 'what-is-a-good-model-can-we-define-it'),
('Software and needed installations',
2,
None,
@@ -108,7 +122,7 @@ Automatically generated HTML file from DocOnce source
('Numpy and arrays', 2, None, 'numpy-and-arrays'),
('Matrices in Python', 2, None, 'matrices-in-python'),
('Meet the Pandas', 2, None, 'meet-the-pandas'),
- ('Friday August 21', 2, None, 'friday-august-21'),
+ ('Friday August 27', 2, None, 'friday-august-27'),
('Reading Data and fitting', 2, None, 'reading-data-and-fitting'),
('Friday August 27', 2, None, 'friday-august-27'),
('Simple linear regression model using _scikit-learn_',
@@ -129,7 +143,15 @@ Automatically generated HTML file from DocOnce source
3,
None,
'and-what-about-using-neural-networks'),
- ('A first summary', 2, None, 'a-first-summary')]}
+ ('A first summary', 2, None, 'a-first-summary'),
+ ('Exercise 1: Setting up various Python environments',
+ 2,
+ None,
+ 'exercise-1-setting-up-various-python-environments'),
+ ('Exercise 2: making your own data and exploring scikit-learn',
+ 2,
+ None,
+ 'exercise-2-making-your-own-data-and-exploring-scikit-learn')]}
end of tocinfo -->
@@ -159,7 +181,7 @@ MathJax.Hub.Config({
- Week 34: Introduction to the course, Logistics and Practicalities
+ Week 35: Introduction to the course, Logistics and Practicalities
-Another useful Python package is
-pandas, which is an open source library
-providing high-performance, easy-to-use data structures and data
-analysis tools for Python. pandas stands for panel data, a term borrowed from econometrics and is an efficient library for data analysis with an emphasis on tabular data.
-pandas has two major classes, the DataFrame class with two-dimensional data objects and tabular data organized in columns and the class Series with a focus on one-dimensional data objects. Both classes allow you to index data easily as we will see in the examples below.
-pandas allows you also to perform mathematical operations on the data, spanning from simple reshapings of vectors and matrices to statistical operations.
+The inverse of a matrix is defined by
-
-The following simple example shows how we can, in an easy way make tables of our data. Here we define a data set which includes names, place of birth and date of birth, and displays the data in an easy to read way. We will see repeated use of pandas, in particular in connection with classification of data.
+$$
+\mathbf{A}^{-1} \cdot \mathbf{A} = I
+$$
-In the above we have imported pandas with the shorthand pd, the latter has become the standard way we import pandas. We make then a list of various variables
-and reorganize the aboves lists into a DataFrame and then print out a neat table with specific column labels as Name, place of birth and date of birth.
-Displaying these results, we see that the indices are given by the default numbers from zero to three.
-pandas is extremely flexible and we can easily change the above indices by defining a new type of indexing as
+
-Here are other examples where we use the DataFrame functionality to handle arrays, now with more interesting features for us, namely numbers. We set up a matrix
-of dimensionality \( 10\times 5 \) and compute the mean value and standard deviation of each column. Similarly, we can perform mathematial operations like squaring the matrix elements and many other operations.
-
-
-
-
importnumpyasnp
-importpandasaspd
-fromIPython.displayimport display
-np.random.seed(100)
-# setting up a 10 x 5 matrix
-rows =10
-cols =5
-a = np.random.randn(rows,cols)
-df = pd.DataFrame(a)
-display(df)
-print(df.mean())
-print(df.std())
-display(df**2)
-
-
-Thereafter we can select specific columns only and plot final results
-
b = np.arange(16).reshape((4,4))
-print(b)
-df1 = pd.DataFrame(b)
-print(df1)
-
-
-and many other operations.
-
-
-The Series class is another important class included in
-pandas. You can view it as a specialization of DataFrame but where
-we have just a single column of data. It shares many of the same features as _DataFrame. As with DataFrame,
-most operations are vectorized, achieving thereby a high performance when dealing with computations of arrays, in particular labeled arrays.
-As we will see below it leads also to a very concice code close to the mathematical operations we may be interested in.
-For multidimensional arrays, we recommend strongly xarray. xarray has much of the same flexibility as pandas, but allows for the extension to higher dimensions than two. We will see examples later of the usage of both pandas and xarray.
@@ -365,6 +320,13 @@ For multidimensional arrays, we recommend strongly 32
diff --git a/doc/pub/week34/html/._week34-bs030.html b/doc/pub/week34/html/._week34-bs030.html
index b2caaec3a..b5734a5ed 100644
--- a/doc/pub/week34/html/._week34-bs030.html
+++ b/doc/pub/week34/html/._week34-bs030.html
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
-
+
-Week 34: Introduction to the course, Logistics and Practicalities
+Week 35: Introduction to the course, Logistics and Practicalities
@@ -80,6 +80,20 @@ Automatically generated HTML file from DocOnce source
2,
None,
'types-of-machine-learning'),
+ ('Essential elements of ML', 2, None, 'essential-elements-of-ml'),
+ ('An optimization/minimization problem',
+ 2,
+ None,
+ 'an-optimization-minimization-problem'),
+ ('A Frequentist approach to data analysis',
+ 2,
+ None,
+ 'a-frequentist-approach-to-data-analysis'),
+ ('What is a good model?', 2, None, 'what-is-a-good-model'),
+ ('What is a good model? Can we define it?',
+ 2,
+ None,
+ 'what-is-a-good-model-can-we-define-it'),
('Software and needed installations',
2,
None,
@@ -108,7 +122,7 @@ Automatically generated HTML file from DocOnce source
('Numpy and arrays', 2, None, 'numpy-and-arrays'),
('Matrices in Python', 2, None, 'matrices-in-python'),
('Meet the Pandas', 2, None, 'meet-the-pandas'),
- ('Friday August 21', 2, None, 'friday-august-21'),
+ ('Friday August 27', 2, None, 'friday-august-27'),
('Reading Data and fitting', 2, None, 'reading-data-and-fitting'),
('Friday August 27', 2, None, 'friday-august-27'),
('Simple linear regression model using _scikit-learn_',
@@ -129,7 +143,15 @@ Automatically generated HTML file from DocOnce source
3,
None,
'and-what-about-using-neural-networks'),
- ('A first summary', 2, None, 'a-first-summary')]}
+ ('A first summary', 2, None, 'a-first-summary'),
+ ('Exercise 1: Setting up various Python environments',
+ 2,
+ None,
+ 'exercise-1-setting-up-various-python-environments'),
+ ('Exercise 2: making your own data and exploring scikit-learn',
+ 2,
+ None,
+ 'exercise-2-making-your-own-data-and-exploring-scikit-learn')]}
end of tocinfo -->
@@ -159,7 +181,7 @@ MathJax.Hub.Config({
- Week 34: Introduction to the course, Logistics and Practicalities
+ Week 35: Introduction to the course, Logistics and Practicalities
diff --git a/doc/pub/week34/html/._week34-bs031.html b/doc/pub/week34/html/._week34-bs031.html
index c62a62ec2..5f4b008cc 100644
--- a/doc/pub/week34/html/._week34-bs031.html
+++ b/doc/pub/week34/html/._week34-bs031.html
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
-
+
-Week 34: Introduction to the course, Logistics and Practicalities
+Week 35: Introduction to the course, Logistics and Practicalities
@@ -80,6 +80,20 @@ Automatically generated HTML file from DocOnce source
2,
None,
'types-of-machine-learning'),
+ ('Essential elements of ML', 2, None, 'essential-elements-of-ml'),
+ ('An optimization/minimization problem',
+ 2,
+ None,
+ 'an-optimization-minimization-problem'),
+ ('A Frequentist approach to data analysis',
+ 2,
+ None,
+ 'a-frequentist-approach-to-data-analysis'),
+ ('What is a good model?', 2, None, 'what-is-a-good-model'),
+ ('What is a good model? Can we define it?',
+ 2,
+ None,
+ 'what-is-a-good-model-can-we-define-it'),
('Software and needed installations',
2,
None,
@@ -108,7 +122,7 @@ Automatically generated HTML file from DocOnce source
('Numpy and arrays', 2, None, 'numpy-and-arrays'),
('Matrices in Python', 2, None, 'matrices-in-python'),
('Meet the Pandas', 2, None, 'meet-the-pandas'),
- ('Friday August 21', 2, None, 'friday-august-21'),
+ ('Friday August 27', 2, None, 'friday-august-27'),
('Reading Data and fitting', 2, None, 'reading-data-and-fitting'),
('Friday August 27', 2, None, 'friday-august-27'),
('Simple linear regression model using _scikit-learn_',
@@ -129,7 +143,15 @@ Automatically generated HTML file from DocOnce source
3,
None,
'and-what-about-using-neural-networks'),
- ('A first summary', 2, None, 'a-first-summary')]}
+ ('A first summary', 2, None, 'a-first-summary'),
+ ('Exercise 1: Setting up various Python environments',
+ 2,
+ None,
+ 'exercise-1-setting-up-various-python-environments'),
+ ('Exercise 2: making your own data and exploring scikit-learn',
+ 2,
+ None,
+ 'exercise-2-making-your-own-data-and-exploring-scikit-learn')]}
end of tocinfo -->
@@ -159,7 +181,7 @@ MathJax.Hub.Config({
- Week 34: Introduction to the course, Logistics and Practicalities
+ Week 35: Introduction to the course, Logistics and Practicalities
-In order to study various Machine Learning algorithms, we need to
-access data. Acccessing data is an essential step in all machine
-learning algorithms. In particular, setting up the so-called design
-matrix (to be defined below) is often the first element we need in
-order to perform our calculations. To set up the design matrix means
-reading (and later, when the calculations are done, writing) data
-in various formats, The formats span from reading files from disk,
-loading data from databases and interacting with online sources
-like web application programming interfaces (APIs).
+
+
+
+For an \( N\times N \) matrix \( \mathbf{A} \) the following properties are all equivalent
-
-In handling various input formats, as discussed above, we will mainly stay with pandas,
-a Python package which allows us, in a seamless and painless way, to
-deal with a multitude of formats, from standard csv (comma separated
-values) files, via excel, html to hdf5 formats. With pandas
-and the DataFrame and Series functionalities we are able to convert text data
-into the calculational formats we need for a specific algorithm. And our code is going to be
-pretty close the basic mathematical expressions.
+
+
If the inverse of \( \mathbf{A} \) exists, \( \mathbf{A} \) is nonsingular.
+
The equation \( \mathbf{Ax}=0 \) implies \( \mathbf{x}=0 \).
+
The rows of \( \mathbf{A} \) form a basis of \( R^N \).
+
The columns of \( \mathbf{A} \) form a basis of \( R^N \).
+
\( \mathbf{A} \) is a product of elementary matrices.
+
\( 0 \) is not eigenvalue of \( \mathbf{A} \).
+
+
+
-
-Our first data set is going to be a classic from nuclear physics, namely all
-available data on binding energies. Don't be intimidated if you are not familiar with nuclear physics. It serves merely as an example here of a data set.
-
-
-We will show some of the
-strengths of packages like Scikit-Learn in fitting nuclear binding energies to
-specific functions using linear regression first. Then, as a teaser, we will show you how
-you can easily implement other algorithms like decision trees and random forests and neural networks.
-
-
-But before we really start with nuclear physics data, let's just look at some simpler polynomial fitting cases, such as,
-(don't be offended) fitting straight lines!
@@ -274,6 +287,12 @@ But before we really start with nuclear physics data, let's just look at some si
diff --git a/doc/pub/week34/html/._week34-bs032.html b/doc/pub/week34/html/._week34-bs032.html
index 1ce97a062..dccd1f57a 100644
--- a/doc/pub/week34/html/._week34-bs032.html
+++ b/doc/pub/week34/html/._week34-bs032.html
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
-
+
-Week 34: Introduction to the course, Logistics and Practicalities
+Week 35: Introduction to the course, Logistics and Practicalities
@@ -80,6 +80,20 @@ Automatically generated HTML file from DocOnce source
2,
None,
'types-of-machine-learning'),
+ ('Essential elements of ML', 2, None, 'essential-elements-of-ml'),
+ ('An optimization/minimization problem',
+ 2,
+ None,
+ 'an-optimization-minimization-problem'),
+ ('A Frequentist approach to data analysis',
+ 2,
+ None,
+ 'a-frequentist-approach-to-data-analysis'),
+ ('What is a good model?', 2, None, 'what-is-a-good-model'),
+ ('What is a good model? Can we define it?',
+ 2,
+ None,
+ 'what-is-a-good-model-can-we-define-it'),
('Software and needed installations',
2,
None,
@@ -108,7 +122,7 @@ Automatically generated HTML file from DocOnce source
('Numpy and arrays', 2, None, 'numpy-and-arrays'),
('Matrices in Python', 2, None, 'matrices-in-python'),
('Meet the Pandas', 2, None, 'meet-the-pandas'),
- ('Friday August 21', 2, None, 'friday-august-21'),
+ ('Friday August 27', 2, None, 'friday-august-27'),
('Reading Data and fitting', 2, None, 'reading-data-and-fitting'),
('Friday August 27', 2, None, 'friday-august-27'),
('Simple linear regression model using _scikit-learn_',
@@ -129,7 +143,15 @@ Automatically generated HTML file from DocOnce source
3,
None,
'and-what-about-using-neural-networks'),
- ('A first summary', 2, None, 'a-first-summary')]}
+ ('A first summary', 2, None, 'a-first-summary'),
+ ('Exercise 1: Setting up various Python environments',
+ 2,
+ None,
+ 'exercise-1-setting-up-various-python-environments'),
+ ('Exercise 2: making your own data and exploring scikit-learn',
+ 2,
+ None,
+ 'exercise-2-making-your-own-data-and-exploring-scikit-learn')]}
end of tocinfo -->
@@ -159,7 +181,7 @@ MathJax.Hub.Config({
- Week 34: Introduction to the course, Logistics and Practicalities
+ Week 35: Introduction to the course, Logistics and Practicalities
+Numpy provides an easy way to handle arrays in Python. The standard way to import this library is as
+
+
+
+
importnumpyasnp
+
+
+Here follows a simple example where we set up an array of ten elements, all determined by random numbers drawn according to the normal distribution,
+
+
+
+
n =10
+x = np.random.normal(size=n)
+print(x)
+
+
+We defined a vector \( x \) with \( n=10 \) elements with its values given by the Normal distribution \( N(0,1) \).
+Another alternative is to declare a vector as follows
+
+Here we have defined a vector with three elements, with \( x_0=1 \), \( x_1=2 \) and \( x_2=3 \). Note that both Python and C++
+start numbering array elements from \( 0 \) and on. This means that a vector with \( n \) elements has a sequence of entities \( x_0, x_1, x_2, \dots, x_{n-1} \). We could also let (recommended) Numpy to compute the logarithms of a specific array as
+
+In the last example we used Numpy's unary function \( np.log \). This function is
+highly tuned to compute array elements since the code is vectorized
+and does not require looping. We normaly recommend that you use the
+Numpy intrinsic functions instead of the corresponding log function
+from Python's math module. The looping is done explicitely by the
+np.log function. The alternative, and slower way to compute the
+logarithms of a vector would be to write
+
+
+We note that our code is much longer already and we need to import the log function from the math module.
+The attentive reader will also notice that the output is \( [1, 1, 2] \). Python interprets automagically our numbers as integers (like the automatic keyword in C++). To change this we could define our array elements to be double precision numbers as
+
+To check the number of bytes (remember that one byte contains eight bits for double precision variables), you can use simple use the itemsize functionality (the array \( x \) is actually an object which inherits the functionalities defined in Numpy) as
+
diff --git a/doc/pub/week34/html/._week34-bs033.html b/doc/pub/week34/html/._week34-bs033.html
index 56c5baac6..24f0d88b8 100644
--- a/doc/pub/week34/html/._week34-bs033.html
+++ b/doc/pub/week34/html/._week34-bs033.html
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
-
+
-Week 34: Introduction to the course, Logistics and Practicalities
+Week 35: Introduction to the course, Logistics and Practicalities
@@ -80,6 +80,20 @@ Automatically generated HTML file from DocOnce source
2,
None,
'types-of-machine-learning'),
+ ('Essential elements of ML', 2, None, 'essential-elements-of-ml'),
+ ('An optimization/minimization problem',
+ 2,
+ None,
+ 'an-optimization-minimization-problem'),
+ ('A Frequentist approach to data analysis',
+ 2,
+ None,
+ 'a-frequentist-approach-to-data-analysis'),
+ ('What is a good model?', 2, None, 'what-is-a-good-model'),
+ ('What is a good model? Can we define it?',
+ 2,
+ None,
+ 'what-is-a-good-model-can-we-define-it'),
('Software and needed installations',
2,
None,
@@ -108,7 +122,7 @@ Automatically generated HTML file from DocOnce source
('Numpy and arrays', 2, None, 'numpy-and-arrays'),
('Matrices in Python', 2, None, 'matrices-in-python'),
('Meet the Pandas', 2, None, 'meet-the-pandas'),
- ('Friday August 21', 2, None, 'friday-august-21'),
+ ('Friday August 27', 2, None, 'friday-august-27'),
('Reading Data and fitting', 2, None, 'reading-data-and-fitting'),
('Friday August 27', 2, None, 'friday-august-27'),
('Simple linear regression model using _scikit-learn_',
@@ -129,7 +143,15 @@ Automatically generated HTML file from DocOnce source
3,
None,
'and-what-about-using-neural-networks'),
- ('A first summary', 2, None, 'a-first-summary')]}
+ ('A first summary', 2, None, 'a-first-summary'),
+ ('Exercise 1: Setting up various Python environments',
+ 2,
+ None,
+ 'exercise-1-setting-up-various-python-environments'),
+ ('Exercise 2: making your own data and exploring scikit-learn',
+ 2,
+ None,
+ 'exercise-2-making-your-own-data-and-exploring-scikit-learn')]}
end of tocinfo -->
@@ -159,7 +181,7 @@ MathJax.Hub.Config({
- Week 34: Introduction to the course, Logistics and Practicalities
+ Week 35: Introduction to the course, Logistics and Practicalities
-We start with perhaps our simplest possible example, using Scikit-Learn to perform linear regression analysis on a data set produced by us.
+Having defined vectors, we are now ready to try out matrices. We can
+define a \( 3 \times 3 \) real matrix \( \hat{A} \) as (recall that we user
+lowercase letters for vectors and uppercase letters for matrices)
-What follows is a simple Python code where we have defined a function
-\( y \) in terms of the variable \( x \). Both are defined as vectors with \( 100 \) entries.
-The numbers in the vector \( \hat{x} \) are given
-by random numbers generated with a uniform distribution with entries
-\( x_i \in [0,1] \) (more about probability distribution functions
-later). These values are then used to define a function \( y(x) \)
-(tabulated again as a vector) with a linear dependence on \( x \) plus a
-random noise added via the normal distribution.
+
+
+If we use the shape function we would get \( (3, 3) \) as output, that is verifying that our matrix is a \( 3\times 3 \) matrix. We can slice the matrix and print for example the first column (Python organized matrix elements in a row-major order, see below) as
-The Numpy functions are imported used the import numpy as np
-statement and the random number generator for the uniform distribution
-is called using the function np.random.rand(), where we specificy
-that we want \( 100 \) random variables. Using Numpy we define
-automatically an array with the specified number of elements, \( 100 \) in
-our case. With the Numpy function randn() we can compute random
-numbers with the normal distribution (mean value \( \mu \) equal to zero and
-variance \( \sigma^2 \) set to one) and produce the values of \( y \) assuming a linear
-dependence as function of \( x \)
+
+
importnumpyasnp
+A = np.log(np.array([ [4.0, 7.0, 8.0], [3.0, 10.0, 11.0], [4.0, 5.0, 7.0] ]))
+# print the first column, row-major order and elements start with 0
+print(A[:,0])
+
+
+We can continue this was by printing out other columns or rows. The example here prints out the second column
+
+
+
+
importnumpyasnp
+A = np.log(np.array([ [4.0, 7.0, 8.0], [3.0, 10.0, 11.0], [4.0, 5.0, 7.0] ]))
+# print the first column, row-major order and elements start with 0
+print(A[1,:])
+
+
+Numpy contains many other functionalities that allow us to slice, subdivide etc etc arrays. We strongly recommend that you look up the Numpy website for more details. Useful functions when defining a matrix are the np.zeros function which declares a matrix of a given dimension and sets all elements to zero
+
+
+
+
importnumpyasnp
+n =10
+# define a matrix of dimension 10 x 10 and set all elements to zero
+A = np.zeros( (n, n) )
+print(A)
+
+
+or initializing all elements to
+
+
+
+
importnumpyasnp
+n =10
+# define a matrix of dimension 10 x 10 and set all elements to one
+A = np.ones( (n, n) )
+print(A)
+
+
+or as unitarily distributed random numbers (see the material on random number generators in the statistics part)
+
+
+
+
importnumpyasnp
+n =10
+# define a matrix of dimension 10 x 10 and set all elements to random numbers with x \in [0, 1]
+A = np.random.rand(n, n)
+print(A)
+
+
+As we will see throughout these lectures, there are several extremely useful functionalities in Numpy.
+As an example, consider the discussion of the covariance matrix. Suppose we have defined three vectors
+\( \hat{x}, \hat{y}, \hat{z} \) with \( n \) elements each. The covariance matrix is defined as
$$
-y = 2x+N(0,1),
+\hat{\Sigma} = \begin{bmatrix} \sigma_{xx} & \sigma_{xy} & \sigma_{xz} \\
+ \sigma_{yx} & \sigma_{yy} & \sigma_{yz} \\
+ \sigma_{zx} & \sigma_{zy} & \sigma_{zz}
+ \end{bmatrix},
+$$
+
+where for example
+$$
+\sigma_{xy} =\frac{1}{n} \sum_{i=0}^{n-1}(x_i- \overline{x})(y_i- \overline{y}).
+$$
+
+The Numpy function np.cov calculates the covariance elements using the factor \( 1/(n-1) \) instead of \( 1/n \) since it assumes we do not have the exact mean values.
+The following simple function uses the np.vstack function which takes each vector of dimension \( 1\times n \) and produces a \( 3\times n \) matrix \( \hat{W} \)
+$$
+\hat{W} = \begin{bmatrix} x_0 & y_0 & z_0 \\
+ x_1 & y_1 & z_1 \\
+ x_2 & y_2 & z_2 \\
+ \dots & \dots & \dots \\
+ x_{n-2} & y_{n-2} & z_{n-2} \\
+ x_{n-1} & y_{n-1} & z_{n-1}
+ \end{bmatrix},
$$
-where \( N(0,1) \) represents random numbers generated by the normal
-distribution. From Scikit-Learn we import then the
-LinearRegression functionality and make a prediction \( \tilde{y} =
-\alpha + \beta x \) using the function fit(x,y). We call the set of
-data \( (\hat{x},\hat{y}) \) for our training data. The Python package
-scikit-learn has also a functionality which extracts the above
-fitting parameters \( \alpha \) and \( \beta \) (see below). Later we will
-distinguish between training data and test data.
+which in turn is converted into into the \( 3\times 3 \) covariance matrix
+\( \hat{\Sigma} \) via the Numpy function np.cov(). We note that we can also calculate
+the mean value of each set of samples \( \hat{x} \) etc using the Numpy
+function np.mean(x). We can also extract the eigenvalues of the
+covariance matrix through the np.linalg.eig() function.
-
-For plotting we use the Python package
-matplotlib which produces publication
-quality figures. Feel free to explore the extensive
-gallery of examples. In
-this example we plot our original values of \( x \) and \( y \) as well as the
-prediction ypredict (\( \tilde{y} \)), which attempts at fitting our
-data with a straight line.
-
-
-This example serves several aims. It allows us to demonstrate several
-aspects of data analysis and later machine learning algorithms. The
-immediate visualization shows that our linear fit is not
-impressive. It goes through the data points, but there are many
-outliers which are not reproduced by our linear regression. We could
-now play around with this small program and change for example the
-factor in front of \( x \) and the normal distribution. Try to change the
-function \( y \) to
-
-$$
-y = 10x+0.01 \times N(0,1),
-$$
-
-
-where \( x \) is defined as before. Does the fit look better? Indeed, by
-reducing the role of the noise given by the normal distribution we see immediately that
-our linear prediction seemingly reproduces better the training
-set. However, this testing 'by the eye' is obviouly not satisfactory in the
-long run. Here we have only defined the training data and our model, and
-have not discussed a more rigorous approach to the cost function.
-
-
-We need more rigorous criteria in defining whether we have succeeded or
-not in modeling our training data. You will be surprised to see that
-many scientists seldomly venture beyond this 'by the eye' approach. A
-standard approach for the cost function is the so-called \( \chi^2 \)
-function (a variant of the mean-squared error (MSE))
-
-$$ \chi^2 = \frac{1}{n}
-\sum_{i=0}^{n-1}\frac{(y_i-\tilde{y}_i)^2}{\sigma_i^2},
-$$
-
-
-where \( \sigma_i^2 \) is the variance (to be defined later) of the entry
-\( y_i \). We may not know the explicit value of \( \sigma_i^2 \), it serves
-however the aim of scaling the equations and make the cost function
-dimensionless.
-
-
-Minimizing the cost function is a central aspect of
-our discussions to come. Finding its minima as function of the model
-parameters (\( \alpha \) and \( \beta \) in our case) will be a recurring
-theme in these series of lectures. Essentially all machine learning
-algorithms we will discuss center around the minimization of the
-chosen cost function. This depends in turn on our specific
-model for describing the data, a typical situation in supervised
-learning. Automatizing the search for the minima of the cost function is a
-central ingredient in all algorithms. Typical methods which are
-employed are various variants of gradient methods. These will be
-discussed in more detail later. Again, you'll be surprised to hear that
-many practitioners minimize the above function ''by the eye', popularly dubbed as
-'chi by the eye'. That is, change a parameter and see (visually and numerically) that
-the \( \chi^2 \) function becomes smaller.
-
-
-There are many ways to define the cost function. A simpler approach is to look at the relative difference between the training data and the predicted data, that is we define
-the relative error (why would we prefer the MSE instead of the relative error?) as
-
-$$
-\epsilon_{\mathrm{relative}}= \frac{\vert \hat{y} -\hat{\tilde{y}}\vert}{\vert \hat{y}\vert}.
-$$
-
-
-The squared cost function results in an arithmetic mean-unbiased
-estimator, and the absolute-value cost function results in a
-median-unbiased estimator (in the one-dimensional case, and a
-geometric median-unbiased estimator for the multi-dimensional
-case). The squared cost function has the disadvantage that it has the tendency
-to be dominated by outliers.
-
-
-We can modify easily the above Python code and plot the relative error instead
-
-Depending on the parameter in front of the normal distribution, we may
-have a small or larger relative error. Try to play around with
-different training data sets and study (graphically) the value of the
-relative error.
-
-
-As mentioned above, Scikit-Learn has an impressive functionality.
-We can for example extract the values of \( \alpha \) and \( \beta \) and
-their error estimates, or the variance and standard deviation and many
-other properties from the statistical data analysis.
-
-
-Here we show an
-example of the functionality of Scikit-Learn.
-
-The function coef gives us the parameter \( \beta \) of our fit while intercept yields
-\( \alpha \). Depending on the constant in front of the normal distribution, we get values near or far from \( \alpha =2 \) and \( \beta =5 \). Try to play around with different parameters in front of the normal distribution. The function meansquarederror gives us the mean square error, a risk metric corresponding to the expected value of the squared (quadratic) error or loss defined as
-$$ MSE(\hat{y},\hat{\tilde{y}}) = \frac{1}{n}
-\sum_{i=0}^{n-1}(y_i-\tilde{y}_i)^2,
-$$
-
-
-The smaller the value, the better the fit. Ideally we would like to
-have an MSE equal zero. The attentive reader has probably recognized
-this function as being similar to the \( \chi^2 \) function defined above.
-
-
-The r2score function computes \( R^2 \), the coefficient of
-determination. It provides a measure of how well future samples are
-likely to be predicted by the model. Best possible score is 1.0 and it
-can be negative (because the model can be arbitrarily worse). A
-constant model that always predicts the expected value of \( \hat{y} \),
-disregarding the input features, would get a \( R^2 \) score of \( 0.0 \).
-
-
-If \( \tilde{\hat{y}}_i \) is the predicted value of the \( i-th \) sample and \( y_i \) is the corresponding true value, then the score \( R^2 \) is defined as
-$$
-R^2(\hat{y}, \tilde{\hat{y}}) = 1 - \frac{\sum_{i=0}^{n - 1} (y_i - \tilde{y}_i)^2}{\sum_{i=0}^{n - 1} (y_i - \bar{y})^2},
-$$
-
-where we have defined the mean value of \( \hat{y} \) as
-$$
-\bar{y} = \frac{1}{n} \sum_{i=0}^{n - 1} y_i.
-$$
-
-Another quantity taht we will meet again in our discussions of regression analysis is
- the mean absolute error (MAE), a risk metric corresponding to the expected value of the absolute error loss or what we call the \( l1 \)-norm loss. In our discussion above we presented the relative error.
-The MAE is defined as follows
-$$
-\text{MAE}(\hat{y}, \hat{\tilde{y}}) = \frac{1}{n} \sum_{i=0}^{n-1} \left| y_i - \tilde{y}_i \right|.
-$$
-
-We present the
-squared logarithmic (quadratic) error
-$$
-\text{MSLE}(\hat{y}, \hat{\tilde{y}}) = \frac{1}{n} \sum_{i=0}^{n - 1} (\log_e (1 + y_i) - \log_e (1 + \tilde{y}_i) )^2,
-$$
-
-
-where \( \log_e (x) \) stands for the natural logarithm of \( x \). This error
-estimate is best to use when targets having exponential growth, such
-as population counts, average sales of a commodity over a span of
-years etc.
-
-
-Finally, another cost function is the Huber cost function used in robust regression.
-
-
-The rationale behind this possible cost function is its reduced
-sensitivity to outliers in the data set. In our discussions on
-dimensionality reduction and normalization of data we will meet other
-ways of dealing with outliers.
-
-
-The Huber cost function is defined as
-$$
-H_{\delta}(a)=\left\{\begin{array}\frac{1}{2}a^{2}&{\text{for }}|a|\leq \delta ,\\ \delta (|a|-\frac {1}{2}\delta ),&{\text{otherwise.}\end{array}\right.
-$$
-
-Here \( a=\boldsymbol{y} - \boldsymbol{\tilde{y}} \).
-We will discuss in more
-detail these and other functions in the various lectures. We conclude this part with another example. Instead of
-a linear \( x \)-dependence we study now a cubic polynomial and use the polynomial regression analysis tools of scikit-learn.
-
-
To our real data: nuclear binding energies. Brief reminder on masses and binding energies
-
-
-Let us now dive into nuclear physics and remind ourselves briefly about some basic features about binding
-energies. A basic quantity which can be measured for the ground
-states of nuclei is the atomic mass \( M(N, Z) \) of the neutral atom with
-atomic mass number \( A \) and charge \( Z \). The number of neutrons is \( N \). There are indeed several sophisticated experiments worldwide which allow us to measure this quantity to high precision (parts per million even).
-
-
-Atomic masses are usually tabulated in terms of the mass excess defined by
-$$
-\Delta M(N, Z) = M(N, Z) - uA,
-$$
-
-where \( u \) is the Atomic Mass Unit
-$$
-u = M(^{12}\mathrm{C})/12 = 931.4940954(57) \hspace{0.1cm} \mathrm{MeV}/c^2.
-$$
-
-The nucleon masses are
-$$
-m_p = 1.00727646693(9)u,
-$$
-
-and
-$$
-m_n = 939.56536(8)\hspace{0.1cm} \mathrm{MeV}/c^2 = 1.0086649156(6)u.
-$$
-
-
-The nuclear binding energy is defined as the energy required to break
-up a given nucleus into its constituent parts of \( N \) neutrons and \( Z \)
-protons. In terms of the atomic masses \( M(N, Z) \) the binding energy is
-defined by
-
-$$
-BE(N, Z) = ZM_H c^2 + Nm_n c^2 - M(N, Z)c^2 ,
-$$
-
-where \( M_H \) is the mass of the hydrogen atom and \( m_n \) is the mass of the neutron.
-In terms of the mass excess the binding energy is given by
-$$
-BE(N, Z) = Z\Delta_H c^2 + N\Delta_n c^2 -\Delta(N, Z)c^2 ,
-$$
-
-where \( \Delta_H c^2 = 7.2890 \) MeV and \( \Delta_n c^2 = 8.0713 \) MeV.
-
-
-A popular and physically intuitive model which can be used to parametrize
-the experimental binding energies as function of \( A \), is the so-called
-liquid drop model. The ansatz is based on the following expression
-
-$$
-BE(N,Z) = a_1A-a_2A^{2/3}-a_3\frac{Z^2}{A^{1/3}}-a_4\frac{(N-Z)^2}{A},
-$$
-
-
-where \( A \) stands for the number of nucleons and the $a_i$s are parameters which are determined by a fit
-to the experimental data.
-
-
-To arrive at the above expression we have assumed that we can make the following assumptions:
-
-
-
There is a volume term \( a_1A \) proportional with the number of nucleons (the energy is also an extensive quantity). When an assembly of nucleons of the same size is packed together into the smallest volume, each interior nucleon has a certain number of other nucleons in contact with it. This contribution is proportional to the volume.
-
There is a surface energy term \( a_2A^{2/3} \). The assumption here is that a nucleon at the surface of a nucleus interacts with fewer other nucleons than one in the interior of the nucleus and hence its binding energy is less. This surface energy term takes that into account and is therefore negative and is proportional to the surface area.
-
There is a Coulomb energy term \( a_3\frac{Z^2}{A^{1/3}} \). The electric repulsion between each pair of protons in a nucleus yields less binding.
-
There is an asymmetry term \( a_4\frac{(N-Z)^2}{A} \). This term is associated with the Pauli exclusion principle and reflects the fact that the proton-neutron interaction is more attractive on the average than the neutron-neutron and proton-proton interactions.
-
-
-We could also add a so-called pairing term, which is a correction term that
-arises from the tendency of proton pairs and neutron pairs to
-occur. An even number of particles is more stable than an odd number.
-
-
Organizing our data
-
-
-Let us start with reading and organizing our data.
-We start with the compilation of masses and binding energies from 2016.
-After having downloaded this file to our own computer, we are now ready to read the file and start structuring our data.
-
-
-We start with preparing folders for storing our calculations and the data file over masses and binding energies. We import also various modules that we will find useful in order to present various Machine Learning methods. Here we focus mainly on the functionality of scikit-learn.
-
-
-
-
# Common imports
-importnumpyasnp
-importpandasaspd
-importmatplotlib.pyplotasplt
-importsklearn.linear_modelasskl
-fromsklearn.model_selectionimport train_test_split
-fromsklearn.metricsimport mean_squared_error, r2_score, mean_absolute_error
-importos
-
-# Where to save the figures and data files
-PROJECT_ROOT_DIR ="Results"
-FIGURE_ID ="Results/FigureFiles"
-DATA_ID ="DataFiles/"
-
-ifnot os.path.exists(PROJECT_ROOT_DIR):
- os.mkdir(PROJECT_ROOT_DIR)
-
-ifnot os.path.exists(FIGURE_ID):
- os.makedirs(FIGURE_ID)
-
-ifnot os.path.exists(DATA_ID):
- os.makedirs(DATA_ID)
-
-defimage_path(fig_id):
- return os.path.join(FIGURE_ID, fig_id)
-
-defdata_path(dat_id):
- return os.path.join(DATA_ID, dat_id)
-
-defsave_fig(fig_id):
- plt.savefig(image_path(fig_id) +".png", format='png')
-
-infile =open(data_path("MassEval2016.dat"),'r')
-
-
-Before we proceed, we define also a function for making our plots. You can obviously avoid this and simply set up various matplotlib commands every time you need them. You may however find it convenient to collect all such commands in one function and simply call this function.
-
-Our next step is to read the data on experimental binding energies and
-reorganize them as functions of the mass number \( A \), the number of
-protons \( Z \) and neutrons \( N \) using pandas. Before we do this it is
-always useful (unless you have a binary file or other types of compressed
-data) to actually open the file and simply take a look at it!
-
-
-In particular, the program that outputs the final nuclear masses is written in Fortran with a specific format. It means that we need to figure out the format and which columns contain the data we are interested in. Pandas comes with a function that reads formatted output. After having admired the file, we are now ready to start massaging it with pandas. The file begins with some basic format information.
-
-
-
-
"""
-This is taken from the data file of the mass 2016 evaluation.
-All files are 3436 lines long with 124 character per line.
- Headers are 39 lines long.
- col 1 : Fortran character control: 1 = page feed 0 = line feed
- format : a1,i3,i5,i5,i5,1x,a3,a4,1x,f13.5,f11.5,f11.3,f9.3,1x,a2,f11.3,f9.3,1x,i3,1x,f12.5,f11.5
- These formats are reflected in the pandas widths variable below, see the statement
- widths=(1,3,5,5,5,1,3,4,1,13,11,11,9,1,2,11,9,1,3,1,12,11,1),
- Pandas has also a variable header, with length 39 in this case.
-"""
-
-
-The data we are interested in are in columns 2, 3, 4 and 11, giving us
-the number of neutrons, protons, mass numbers and binding energies,
-respectively. We add also for the sake of completeness the element name. The data are in fixed-width formatted lines and we will
-covert them into the pandas DataFrame structure.
-
-
-
-
-
# Read the experimental data with Pandas
-Masses = pd.read_fwf(infile, usecols=(2,3,4,6,11),
- names=('N', 'Z', 'A', 'Element', 'Ebinding'),
- widths=(1,3,5,5,5,1,3,4,1,13,11,11,9,1,2,11,9,1,3,1,12,11,1),
- header=39,
- index_col=False)
-
-# Extrapolated values are indicated by '#' in place of the decimal place, so
-# the Ebinding column won't be numeric. Coerce to float and drop these entries.
-Masses['Ebinding'] = pd.to_numeric(Masses['Ebinding'], errors='coerce')
-Masses = Masses.dropna()
-# Convert from keV to MeV.
-Masses['Ebinding'] /=1000
-
-# Group the DataFrame by nucleon number, A.
-Masses = Masses.groupby('A')
-# Find the rows of the grouped DataFrame with the maximum binding energy.
-Masses = Masses.apply(lambda t: t[t.Ebinding==t.Ebinding.max()])
-
-
-We have now read in the data, grouped them according to the variables we are interested in.
-We see how easy it is to reorganize the data using pandas. If we
-were to do these operations in C/C++ or Fortran, we would have had to
-write various functions/subroutines which perform the above
-reorganizations for us. Having reorganized the data, we can now start
-to make some simple fits using both the functionalities in numpy and
-Scikit-Learn afterwards.
-
-
-Now we define five variables which contain
-the number of nucleons \( A \), the number of protons \( Z \) and the number of neutrons \( N \), the element name and finally the energies themselves.
-
-The next step, and we will define this mathematically later, is to set up the so-called design matrix. We will throughout call this matrix \( \boldsymbol{X} \).
-It has dimensionality \( p\times n \), where \( n \) is the number of data points and \( p \) are the so-called predictors. In our case here they are given by the number of polynomials in \( A \) we wish to include in the fit.
-
-
-
-
# Now we set up the design matrix X
-X = np.zeros((len(A),5))
-X[:,0] =1
-X[:,1] = A
-X[:,2] = A**(2.0/3.0)
-X[:,3] = A**(-1.0/3.0)
-X[:,4] = A**(-1.0)
-
-
-With scikitlearn we are now ready to use linear regression and fit our data.
-
-
-The seaborn package allows us to visualize data in an efficient way. Note that we use scikit-learn's multi-layer perceptron (or feed forward neural network)
-functionality.
-
-
-
-
fromsklearn.neural_networkimport MLPRegressor
-fromsklearn.metricsimport accuracy_score
-importseabornassns
-
-X_train = X
-Y_train = Energies
-n_hidden_neurons =100
-epochs =100
-# store models for later use
-eta_vals = np.logspace(-5, 1, 7)
-lmbd_vals = np.logspace(-5, 1, 7)
-# store the models for later use
-DNN_scikit = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)
-train_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))
-sns.set()
-for i, eta inenumerate(eta_vals):
- for j, lmbd inenumerate(lmbd_vals):
- dnn = MLPRegressor(hidden_layer_sizes=(n_hidden_neurons), activation='logistic',
- alpha=lmbd, learning_rate_init=eta, max_iter=epochs)
- dnn.fit(X_train, Y_train)
- DNN_scikit[i][j] = dnn
- train_accuracy[i][j] = dnn.score(X_train, Y_train)
-
-fig, ax = plt.subplots(figsize = (10, 10))
-sns.heatmap(train_accuracy, annot=True, ax=ax, cmap="viridis")
-ax.set_title("Training Accuracy")
-ax.set_ylabel("$\eta$")
-ax.set_xlabel("$\lambda$")
-plt.show()
-
-
-
A first summary
-
-
-The aim behind these introductory words was to present to you various
-Python libraries and their functionalities, in particular libraries like
-numpy, pandas, xarray and matplotlib and other that make our life much easier
-in handling various data sets and visualizing data.
-
-
-Furthermore,
-Scikit-Learn allows us with few lines of code to implement popular
-Machine Learning algorithms for supervised learning. Later we will meet Tensorflow, a powerful library for deep learning.
-Now it is time to dive more into the details of various methods. We will start with linear regression and try to take a deeper look at what it entails.
-
-
-
@@ -910,6 +401,13 @@ Now it is time to dive more into the details of various methods. We will start w
diff --git a/doc/pub/week34/html/week34-bs.html b/doc/pub/week34/html/week34-bs.html
index 93dca0db3..83ac6fd24 100644
--- a/doc/pub/week34/html/week34-bs.html
+++ b/doc/pub/week34/html/week34-bs.html
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
-
+
-Week 34: Introduction to the course, Logistics and Practicalities
+Week 35: Introduction to the course, Logistics and Practicalities
@@ -80,6 +80,20 @@ Automatically generated HTML file from DocOnce source
2,
None,
'types-of-machine-learning'),
+ ('Essential elements of ML', 2, None, 'essential-elements-of-ml'),
+ ('An optimization/minimization problem',
+ 2,
+ None,
+ 'an-optimization-minimization-problem'),
+ ('A Frequentist approach to data analysis',
+ 2,
+ None,
+ 'a-frequentist-approach-to-data-analysis'),
+ ('What is a good model?', 2, None, 'what-is-a-good-model'),
+ ('What is a good model? Can we define it?',
+ 2,
+ None,
+ 'what-is-a-good-model-can-we-define-it'),
('Software and needed installations',
2,
None,
@@ -108,7 +122,7 @@ Automatically generated HTML file from DocOnce source
('Numpy and arrays', 2, None, 'numpy-and-arrays'),
('Matrices in Python', 2, None, 'matrices-in-python'),
('Meet the Pandas', 2, None, 'meet-the-pandas'),
- ('Friday August 21', 2, None, 'friday-august-21'),
+ ('Friday August 27', 2, None, 'friday-august-27'),
('Reading Data and fitting', 2, None, 'reading-data-and-fitting'),
('Friday August 27', 2, None, 'friday-august-27'),
('Simple linear regression model using _scikit-learn_',
@@ -129,7 +143,15 @@ Automatically generated HTML file from DocOnce source
3,
None,
'and-what-about-using-neural-networks'),
- ('A first summary', 2, None, 'a-first-summary')]}
+ ('A first summary', 2, None, 'a-first-summary'),
+ ('Exercise 1: Setting up various Python environments',
+ 2,
+ None,
+ 'exercise-1-setting-up-various-python-environments'),
+ ('Exercise 2: making your own data and exploring scikit-learn',
+ 2,
+ None,
+ 'exercise-2-making-your-own-data-and-exploring-scikit-learn')]}
end of tocinfo -->
@@ -159,7 +181,7 @@ MathJax.Hub.Config({
- Week 34: Introduction to the course, Logistics and Practicalities
+ Week 35: Introduction to the course, Logistics and Practicalities
diff --git a/doc/pub/week34/html/week34-reveal.html b/doc/pub/week34/html/week34-reveal.html
index e56c0e709..262e19aea 100644
--- a/doc/pub/week34/html/week34-reveal.html
+++ b/doc/pub/week34/html/week34-reveal.html
@@ -3,9 +3,9 @@
-
+
-Week 34: Introduction to the course, Logistics and Practicalities
+Week 35: Introduction to the course, Logistics and Practicalities
@@ -132,7 +132,7 @@ MathJax.Hub.Config({
-
Week 34: Introduction to the course, Logistics and Practicalities
+
Week 35: Introduction to the course, Logistics and Practicalities
@@ -148,7 +148,7 @@ MathJax.Hub.Config({
[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University
-
Aug 24, 2021
+
Aug 26, 2021
@@ -422,7 +422,7 @@ These topics will be scattered thorughout the course and may not necessarily be
Statistical analysis and optimization of data
-The following topics will be covered
+We plan to cover the following topics:
Basic concepts, expectation values, variance, covariance, correlation functions and errors;
@@ -643,19 +643,122 @@ desired output of a system. Some of the most common tasks are:
Clustering: Data are divided into groups with certain common traits, without knowing the different groups beforehand. It is thus a form of unsupervised learning.
-
+
+
+
+
Essential elements of ML
+
+
The methods we cover have three main topics in common, irrespective of
-whether we deal with supervised or unsupervised learning. The first
-ingredient is normally our data set (which can be subdivided into
-training and test data), the second item is a model which is normally a
-function of some parameters. The model reflects our knowledge of the system (or lack thereof). As an example, if we know that our data show a behavior similar to what would be predicted by a polynomial, fitting our data to a polynomial of some degree would then determin our model.
+whether we deal with supervised or unsupervised learning.
+
+
+
+
The first ingredient is normally our data set (which can be subdivided into training, validation and test data). Many find the most difficult part of using Machine Learning to be the set up of your data in a meaningful way.
+
The second item is a model which is normally a function of some parameters. The model reflects our knowledge of the system (or lack thereof). As an example, if we know that our data show a behavior similar to what would be predicted by a polynomial, fitting our data to a polynomial of some degree would then determin our model.
+
The last ingredient is a so-called cost/loss function (or error or risk function) which allows us to present an estimate on how good our model is in reproducing the data it is supposed to train.
+
+
+
+
+
+
An optimization/minimization problem
-The last ingredient is a so-called cost
-function which allows us to present an estimate on how good our model
-is in reproducing the data it is supposed to train.
-At the heart of basically all ML algorithms there are so-called minimization algorithms, often we end up with various variants of gradient methods.
+At the heart of basically all Machine Learning algorithms we will encounter so-called minimization or optimization algorithms. A large family of such methods are so-called gradient methods.
+
+
+
+
+
A Frequentist approach to data analysis
+
+
+When you hear phrases like predictions and estimations and
+correlations and causations, what do you think of? May be you think
+of the difference between classifying new data points and generating
+new data points.
+Or perhaps you consider that correlations represent some kind of symmetric statements like
+if \( A \) is correlated with \( B \), then \( B \) is correlated with
+\( A \). Causation on the other hand is directional, that is if \( A \) causes \( B \), \( B \) does not
+necessarily cause \( A \).
+
+
+These concepts are in some sense the difference between machine
+learning and statistics. In machine learning and prediction based
+tasks, we are often interested in developing algorithms that are
+capable of learning patterns from given data in an automated fashion,
+and then using these learned patterns to make predictions or
+assessments of newly given data. In many cases, our primary concern
+is the quality of the predictions or assessments, and we are less
+concerned about the underlying patterns that were learned in order
+to make these predictions.
+
+
+In machine learning we normally use a so-called frequentist approach,
+where the aim is to make predictions and find correlations. We focus
+less on for example extracting a probability distribution function (PDF). The PDF can be
+used in turn to make estimations and find causations such as given \( A \)
+what is the likelihood of finding \( B \).
+
+
+
+
+
What is a good model?
+
+
+In science and engineering we often end up in situations where we want to infer (or learn) a
+quantitative model \( M \) for a given set of sample points \( \boldsymbol{X} \in [x_1, x_2,\dots x_N] \).
+
+
+As we will see repeatedely in these lectures, we could try to fit these data points to a model given by a
+straight line, or if we wish to be more sophisticated to a more complex
+function.
+
+
+The reason for inferring such a model is that it
+serves many useful purposes. On the one hand, the model can reveal information
+encoded in the data or underlying mechanisms from which the data were generated. For instance, we could discover important
+corelations that relate interesting physics interpretations.
+
+
+In addition, it can simplify the representation of the given data set and help
+us in making predictions about future data samples.
+
+
+A first important consideration to keep in mind is that inferring the correct model
+for a given data set is an elusive, if not impossible, task. The fundamental difficulty
+is that if we are not specific about what we mean by a correct model, there
+could easily be many different models that fit the given data set equally well.
+
+
+
+
+
What is a good model? Can we define it?
+
+
+The central question is this: what leads us to say that a model is correct or
+optimal for a given data set? To make the model inference problem well posed, i.e.,
+to guarantee that there is a unique optimal model for the given data, we need to
+impose additional assumptions or restrictions on the class of models considered. To
+this end, we should not be looking for just any model that can describe the data.
+Instead, we should look for a model \( M \) that is the best among a restricted class
+of models. In addition, to make the model inference problem computationally
+tractable, we need to specify how restricted the class of models needs to be. A
+common strategy is to start
+with the simplest possible class of models that is just necessary to describe the data
+or solve the problem at hand. More precisely, the model class should be rich enough
+to contain at least one model that can fit the data to a desired accuracy and yet be
+restricted enough that it is relatively simple to find the best model for the given data.
+
+
+Thus, the most popular strategy is to start from the
+simplest class of models and increase the complexity of the models only when the
+simpler models become inadequate. For instance, if we work with a regression problem to fit a set of sample points, one
+may first try the simplest class of models, namely linear models, followed obviously by more complex models.
+
+
+How to evaluate which model fits best the data is something we will come back to over and over again in these sets of lectures.
@@ -1307,10 +1410,10 @@ For multidimensional arrays, we recommend strongly Friday August 21
+
Exercise 1: Setting up various Python environments
+
+
+The first exercise here is of a mere technical art. We want you to have
+
+
+
git as a version control software and to establish a user account on a provider like GitHub. Other providers like GitLab etc are equally fine. You can also use the University of Oslo GitHub facilities.
+
Install various Python packages
+
+
+
+We will make extensive use of Python as programming language and its
+myriad of available libraries. You will find
+IPython/Jupyter notebooks invaluable in your work. You can run R
+codes in the Jupyter/IPython notebooks, with the immediate benefit of
+visualizing your data. You can also use compiled languages like C++,
+Rust, Fortran etc if you prefer. The focus in these lectures will be
+on Python.
+
+
+If you have Python installed (we recommend Python3) and you feel
+pretty familiar with installing different packages, we recommend that
+you install the following Python packages via pip as
+
+
+For OSX users we recommend, after having installed Xcode, to
+install brew. Brew allows for a seamless installation of additional
+software via for example
+
+
+
brew install python3
+
+
+
+For Linux users, with its variety of distributions like for example the widely popular Ubuntu distribution,
+you can use pip as well and simply install Python as
+
+
+
sudo apt-get install python3 (or python for Python2.7)
+
+
+
+If you don't want to perform these operations separately and venture
+into the hassle of exploring how to set up dependencies and paths, we
+recommend two widely used distrubutions which set up all relevant
+dependencies for Python, namely
+
+
+
+which is an open source
+distribution of the Python and R programming languages for large-scale
+data processing, predictive analytics, and scientific computing, that
+aims to simplify package management and deployment. Package versions
+are managed by the package management system conda.
+
+
+
+is a Python
+distribution for scientific and analytic computing distribution and
+analysis environment, available for free and under a commercial
+license.
+
+
+We recommend using Anaconda.
+
+
+
+
+
+
+
+
Exercise 2: making your own data and exploring scikit-learn
+
+
+We will generate our own dataset for a function \( y(x) \) where \( x \in [0,1] \) and defined by random numbers computed with the uniform distribution. The function \( y \) is a quadratic polynomial in \( x \) with added stochastic noise according to the normal distribution \( \cal {N}(0,1) \).
+The following simple Python instructions define our \( x \) and \( y \) values (with 100 data points).
+
+
+
+
x = np.random.rand(100,1)
+y = 2.0+5*x*x+0.1*np.random.randn(100,1)
+
+
+
Write your own code (following the examples under the regression slides) for computing the parametrization of the data set fitting a second-order polynomial.
+
Use thereafter scikit-learn (see again the examples in the regression slides) and compare with your own code.
+
+
Using scikit-learn, compute also the mean square error, a risk metric corresponding to the expected value of the squared (quadratic) error defined as
+
+and the \( R^2 \) score function.
+If \( \tilde{\hat{y}}_i \) is the predicted value of the \( i-th \) sample and \( y_i \) is the corresponding true value, then the score \( R^2 \) is defined as
+
+
+You can use the functionality included in scikit-learn. If you feel for it, you can use your own program and define functions which compute the above two functions.
+Discuss the meaning of these results. Try also to vary the coefficient in front of the added stochastic noise term and discuss the quality of the fits.
+
+
+
+Solution.
+The code here is an example of where we define our own design matrix and fit parameters \( \beta \).
+
+
+
+
importos
+importnumpyasnp
+importpandasaspd
+importmatplotlib.pyplotasplt
+fromsklearn.model_selectionimport train_test_split
+
+defsave_fig(fig_id):
+ plt.savefig(image_path(fig_id) + ".png", format='png')
+
+defR2(y_data, y_model):
+ return1 - np.sum((y_data - y_model) ** 2) / np.sum((y_data - np.mean(y_data)) ** 2)
+defMSE(y_data,y_model):
+ n = np.size(y_model)
+ return np.sum((y_data-y_model)**2)/n
+
+x = np.random.rand(100)
+y = 2.0+5*x*x+0.1*np.random.randn(100)
+
+
+# The design matrix now as function of a given polynomial
+X = np.zeros((len(x),3))
+X[:,0] = 1.0
+X[:,1] = x
+X[:,2] = x**2
+# We split the data in test and training data
+X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)
+# matrix inversion to find beta
+beta = np.linalg.inv(X_train.T @ X_train) @ X_train.T @ y_train
+print(beta)
+# and then make the prediction
+ytilde = X_train @ beta
+print("Training R2")
+print(R2(y_train,ytilde))
+print("Training MSE")
+print(MSE(y_train,ytilde))
+ypredict = X_test @ beta
+print("Test R2")
+print(R2(y_test,ypredict))
+print("Test MSE")
+print(MSE(y_test,ypredict))
+
+
+
+
+
+
+
+
+
diff --git a/doc/pub/week34/html/week34-solarized.html b/doc/pub/week34/html/week34-solarized.html
index fc756c9e7..550f27dd5 100644
--- a/doc/pub/week34/html/week34-solarized.html
+++ b/doc/pub/week34/html/week34-solarized.html
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
-
+
-Week 34: Introduction to the course, Logistics and Practicalities
+Week 35: Introduction to the course, Logistics and Practicalities
@@ -100,6 +100,20 @@ div { text-align: justify; text-justify: inter-word; }
2,
None,
'types-of-machine-learning'),
+ ('Essential elements of ML', 2, None, 'essential-elements-of-ml'),
+ ('An optimization/minimization problem',
+ 2,
+ None,
+ 'an-optimization-minimization-problem'),
+ ('A Frequentist approach to data analysis',
+ 2,
+ None,
+ 'a-frequentist-approach-to-data-analysis'),
+ ('What is a good model?', 2, None, 'what-is-a-good-model'),
+ ('What is a good model? Can we define it?',
+ 2,
+ None,
+ 'what-is-a-good-model-can-we-define-it'),
('Software and needed installations',
2,
None,
@@ -128,7 +142,7 @@ div { text-align: justify; text-justify: inter-word; }
('Numpy and arrays', 2, None, 'numpy-and-arrays'),
('Matrices in Python', 2, None, 'matrices-in-python'),
('Meet the Pandas', 2, None, 'meet-the-pandas'),
- ('Friday August 21', 2, None, 'friday-august-21'),
+ ('Friday August 27', 2, None, 'friday-august-27'),
('Reading Data and fitting', 2, None, 'reading-data-and-fitting'),
('Friday August 27', 2, None, 'friday-august-27'),
('Simple linear regression model using _scikit-learn_',
@@ -149,7 +163,15 @@ div { text-align: justify; text-justify: inter-word; }
3,
None,
'and-what-about-using-neural-networks'),
- ('A first summary', 2, None, 'a-first-summary')]}
+ ('A first summary', 2, None, 'a-first-summary'),
+ ('Exercise 1: Setting up various Python environments',
+ 2,
+ None,
+ 'exercise-1-setting-up-various-python-environments'),
+ ('Exercise 2: making your own data and exploring scikit-learn',
+ 2,
+ None,
+ 'exercise-2-making-your-own-data-and-exploring-scikit-learn')]}
end of tocinfo -->
@@ -175,7 +197,7 @@ MathJax.Hub.Config({
-
Week 34: Introduction to the course, Logistics and Practicalities
+
Week 35: Introduction to the course, Logistics and Practicalities
@@ -191,7 +213,7 @@ MathJax.Hub.Config({
[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University
-
Aug 24, 2021
+
Aug 26, 2021
@@ -456,7 +478,7 @@ These topics will be scattered thorughout the course and may not necessarily be
-The following topics will be covered
+We plan to cover the following topics:
Basic concepts, expectation values, variance, covariance, correlation functions and errors;
@@ -676,17 +698,122 @@ desired output of a system. Some of the most common tasks are:
Clustering: Data are divided into groups with certain common traits, without knowing the different groups beforehand. It is thus a form of unsupervised learning.
-The methods we cover have three main topics in common, irrespective of
-whether we deal with supervised or unsupervised learning. The first
-ingredient is normally our data set (which can be subdivided into
-training and test data), the second item is a model which is normally a
-function of some parameters. The model reflects our knowledge of the system (or lack thereof). As an example, if we know that our data show a behavior similar to what would be predicted by a polynomial, fitting our data to a polynomial of some degree would then determin our model.
+
+
+
Essential elements of ML
-The last ingredient is a so-called cost
-function which allows us to present an estimate on how good our model
-is in reproducing the data it is supposed to train.
-At the heart of basically all ML algorithms there are so-called minimization algorithms, often we end up with various variants of gradient methods.
+The methods we cover have three main topics in common, irrespective of
+whether we deal with supervised or unsupervised learning.
+
+
+
+
The first ingredient is normally our data set (which can be subdivided into training, validation and test data). Many find the most difficult part of using Machine Learning to be the set up of your data in a meaningful way.
+
The second item is a model which is normally a function of some parameters. The model reflects our knowledge of the system (or lack thereof). As an example, if we know that our data show a behavior similar to what would be predicted by a polynomial, fitting our data to a polynomial of some degree would then determin our model.
+
The last ingredient is a so-called cost/loss function (or error or risk function) which allows us to present an estimate on how good our model is in reproducing the data it is supposed to train.
+
+
+
+
+
+
+
+
An optimization/minimization problem
+
+
+At the heart of basically all Machine Learning algorithms we will encounter so-called minimization or optimization algorithms. A large family of such methods are so-called gradient methods.
+
+
+
+
+
A Frequentist approach to data analysis
+
+
+When you hear phrases like predictions and estimations and
+correlations and causations, what do you think of? May be you think
+of the difference between classifying new data points and generating
+new data points.
+Or perhaps you consider that correlations represent some kind of symmetric statements like
+if \( A \) is correlated with \( B \), then \( B \) is correlated with
+\( A \). Causation on the other hand is directional, that is if \( A \) causes \( B \), \( B \) does not
+necessarily cause \( A \).
+
+
+These concepts are in some sense the difference between machine
+learning and statistics. In machine learning and prediction based
+tasks, we are often interested in developing algorithms that are
+capable of learning patterns from given data in an automated fashion,
+and then using these learned patterns to make predictions or
+assessments of newly given data. In many cases, our primary concern
+is the quality of the predictions or assessments, and we are less
+concerned about the underlying patterns that were learned in order
+to make these predictions.
+
+
+In machine learning we normally use a so-called frequentist approach,
+where the aim is to make predictions and find correlations. We focus
+less on for example extracting a probability distribution function (PDF). The PDF can be
+used in turn to make estimations and find causations such as given \( A \)
+what is the likelihood of finding \( B \).
+
+
+
+
+
What is a good model?
+
+
+In science and engineering we often end up in situations where we want to infer (or learn) a
+quantitative model \( M \) for a given set of sample points \( \boldsymbol{X} \in [x_1, x_2,\dots x_N] \).
+
+
+As we will see repeatedely in these lectures, we could try to fit these data points to a model given by a
+straight line, or if we wish to be more sophisticated to a more complex
+function.
+
+
+The reason for inferring such a model is that it
+serves many useful purposes. On the one hand, the model can reveal information
+encoded in the data or underlying mechanisms from which the data were generated. For instance, we could discover important
+corelations that relate interesting physics interpretations.
+
+
+In addition, it can simplify the representation of the given data set and help
+us in making predictions about future data samples.
+
+
+A first important consideration to keep in mind is that inferring the correct model
+for a given data set is an elusive, if not impossible, task. The fundamental difficulty
+is that if we are not specific about what we mean by a correct model, there
+could easily be many different models that fit the given data set equally well.
+
+
+
+
+
What is a good model? Can we define it?
+
+
+The central question is this: what leads us to say that a model is correct or
+optimal for a given data set? To make the model inference problem well posed, i.e.,
+to guarantee that there is a unique optimal model for the given data, we need to
+impose additional assumptions or restrictions on the class of models considered. To
+this end, we should not be looking for just any model that can describe the data.
+Instead, we should look for a model \( M \) that is the best among a restricted class
+of models. In addition, to make the model inference problem computationally
+tractable, we need to specify how restricted the class of models needs to be. A
+common strategy is to start
+with the simplest possible class of models that is just necessary to describe the data
+or solve the problem at hand. More precisely, the model class should be rich enough
+to contain at least one model that can fit the data to a desired accuracy and yet be
+restricted enough that it is relatively simple to find the best model for the given data.
+
+
+Thus, the most popular strategy is to start from the
+simplest class of models and increase the complexity of the models only when the
+simpler models become inadequate. For instance, if we work with a regression problem to fit a set of sample points, one
+may first try the simplest class of models, namely linear models, followed obviously by more complex models.
+
+
+How to evaluate which model fits best the data is something we will come back to over and over again in these sets of lectures.
@@ -1301,10 +1428,10 @@ For multidimensional arrays, we recommend strongly Friday August 21
+
@@ -2027,6 +2154,184 @@ Machine Learning algorithms for supervised learning. Later we will meet Tenso
Now it is time to dive more into the details of various methods. We will start with linear regression and try to take a deeper look at what it entails.
+
+
+
+
+
+
Exercise 1: Setting up various Python environments
+
+
+The first exercise here is of a mere technical art. We want you to have
+
+
+
git as a version control software and to establish a user account on a provider like GitHub. Other providers like GitLab etc are equally fine. You can also use the University of Oslo GitHub facilities.
+
Install various Python packages
+
+
+We will make extensive use of Python as programming language and its
+myriad of available libraries. You will find
+IPython/Jupyter notebooks invaluable in your work. You can run R
+codes in the Jupyter/IPython notebooks, with the immediate benefit of
+visualizing your data. You can also use compiled languages like C++,
+Rust, Fortran etc if you prefer. The focus in these lectures will be
+on Python.
+
+
+If you have Python installed (we recommend Python3) and you feel
+pretty familiar with installing different packages, we recommend that
+you install the following Python packages via pip as
+
+
+For OSX users we recommend, after having installed Xcode, to
+install brew. Brew allows for a seamless installation of additional
+software via for example
+
+
+
brew install python3
+
+
+For Linux users, with its variety of distributions like for example the widely popular Ubuntu distribution,
+you can use pip as well and simply install Python as
+
+
+
sudo apt-get install python3 (or python for Python2.7)
+
+
+If you don't want to perform these operations separately and venture
+into the hassle of exploring how to set up dependencies and paths, we
+recommend two widely used distrubutions which set up all relevant
+dependencies for Python, namely
+
+
+
+which is an open source
+distribution of the Python and R programming languages for large-scale
+data processing, predictive analytics, and scientific computing, that
+aims to simplify package management and deployment. Package versions
+are managed by the package management system conda.
+
+
+
+is a Python
+distribution for scientific and analytic computing distribution and
+analysis environment, available for free and under a commercial
+license.
+
+
+We recommend using Anaconda.
+
+
+
+
+
+
+
+
Exercise 2: making your own data and exploring scikit-learn
+
+
+We will generate our own dataset for a function \( y(x) \) where \( x \in [0,1] \) and defined by random numbers computed with the uniform distribution. The function \( y \) is a quadratic polynomial in \( x \) with added stochastic noise according to the normal distribution \( \cal {N}(0,1) \).
+The following simple Python instructions define our \( x \) and \( y \) values (with 100 data points).
+
+
+
+
x = np.random.rand(100,1)
+y = 2.0+5*x*x+0.1*np.random.randn(100,1)
+
+
+
Write your own code (following the examples under the regression slides) for computing the parametrization of the data set fitting a second-order polynomial.
+
Use thereafter scikit-learn (see again the examples in the regression slides) and compare with your own code.
+
Using scikit-learn, compute also the mean square error, a risk metric corresponding to the expected value of the squared (quadratic) error defined as
+
+
+$$ MSE(\hat{y},\hat{\tilde{y}}) = \frac{1}{n}
+\sum_{i=0}^{n-1}(y_i-\tilde{y}_i)^2,
+$$
+
+and the \( R^2 \) score function.
+If \( \tilde{\hat{y}}_i \) is the predicted value of the \( i-th \) sample and \( y_i \) is the corresponding true value, then the score \( R^2 \) is defined as
+$$
+R^2(\hat{y}, \tilde{\hat{y}}) = 1 - \frac{\sum_{i=0}^{n - 1} (y_i - \tilde{y}_i)^2}{\sum_{i=0}^{n - 1} (y_i - \bar{y})^2},
+$$
+
+where we have defined the mean value of \( \hat{y} \) as
+$$
+\bar{y} = \frac{1}{n} \sum_{i=0}^{n - 1} y_i.
+$$
+
+You can use the functionality included in scikit-learn. If you feel for it, you can use your own program and define functions which compute the above two functions.
+Discuss the meaning of these results. Try also to vary the coefficient in front of the added stochastic noise term and discuss the quality of the fits.
+
+
+
+Solution.
+The code here is an example of where we define our own design matrix and fit parameters \( \beta \).
+
+
+
+
importos
+importnumpyasnp
+importpandasaspd
+importmatplotlib.pyplotasplt
+fromsklearn.model_selectionimport train_test_split
+
+defsave_fig(fig_id):
+ plt.savefig(image_path(fig_id) + ".png", format='png')
+
+defR2(y_data, y_model):
+ return1 - np.sum((y_data - y_model) ** 2) / np.sum((y_data - np.mean(y_data)) ** 2)
+defMSE(y_data,y_model):
+ n = np.size(y_model)
+ return np.sum((y_data-y_model)**2)/n
+
+x = np.random.rand(100)
+y = 2.0+5*x*x+0.1*np.random.randn(100)
+
+
+# The design matrix now as function of a given polynomial
+X = np.zeros((len(x),3))
+X[:,0] = 1.0
+X[:,1] = x
+X[:,2] = x**2
+# We split the data in test and training data
+X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)
+# matrix inversion to find beta
+beta = np.linalg.inv(X_train.T @ X_train) @ X_train.T @ y_train
+print(beta)
+# and then make the prediction
+ytilde = X_train @ beta
+print("Training R2")
+print(R2(y_train,ytilde))
+print("Training MSE")
+print(MSE(y_train,ytilde))
+ypredict = X_test @ beta
+print("Test R2")
+print(R2(y_test,ypredict))
+print("Test MSE")
+print(MSE(y_test,ypredict))
+
+
+
+
+
+
diff --git a/doc/pub/week34/html/week34.html b/doc/pub/week34/html/week34.html
index c9373a43b..8d431a547 100644
--- a/doc/pub/week34/html/week34.html
+++ b/doc/pub/week34/html/week34.html
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
-
+
-
Week 34: Introduction to the course, Logistics and Practicalities
+Week 35: Introduction to the course, Logistics and Practicalities
\n",
- "
"
- ],
- "text/plain": [
- " 0 1 2 3 4\n",
- "0 3.061679 0.117430 1.329492 0.063724 0.962990\n",
- "1 0.264421 0.048920 1.144993 0.035909 0.065026\n",
- "2 0.209789 0.189367 0.340583 0.667239 0.452553\n",
- "3 0.010902 0.282259 1.060349 0.191963 1.250636\n",
- "4 2.621102 2.376547 0.063443 0.709698 0.034047\n",
- "5 0.878123 0.534362 1.853835 0.106431 0.003100\n",
- "6 0.049462 2.082875 0.572069 0.666597 0.563167\n",
- "7 0.207888 1.415201 2.858185 1.839818 1.518895\n",
- "8 0.296414 0.446453 0.000054 0.375694 1.689345\n",
- "9 3.003620 0.966899 0.127812 2.603636 2.162999"
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
+ "execution_count": null,
+ "metadata": {
+ "collapsed": false,
+ "editable": true
+ },
+ "outputs": [],
"source": [
"import numpy as np\n",
"import pandas as pd\n",
@@ -1751,7 +1372,10 @@
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": false,
+ "editable": true
+ },
"outputs": [],
"source": [
"df.columns = ['First', 'Second', 'Third', 'Fourth', 'Fifth']\n",
@@ -1784,7 +1408,10 @@
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": false,
+ "editable": true
+ },
"outputs": [],
"source": [
"b = np.arange(16).reshape((4,4))\n",
@@ -1807,9 +1434,9 @@
"For multidimensional arrays, we recommend strongly [xarray](http://xarray.pydata.org/en/stable/). **xarray** has much of the same flexibility as **pandas**, but allows for the extension to higher dimensions than two. We will see examples later of the usage of both **pandas** and **xarray**. \n",
"\n",
"\n",
- "## Friday August 21\n",
+ "## Friday August 27\n",
"\n",
- "[Video of Lecture](https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h20/forelesningsvideoer/LectureAug21.mp4?vrtx=view-as-webpage) and [Handwritten notes](https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/NotesAugust21.pdf)\n",
+ "[Video of Lecture from fall 2020](https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h20/forelesningsvideoer/LectureAug21.mp4?vrtx=view-as-webpage) and [Handwritten notes](https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/NotesAugust21.pdf)\n",
"\n",
"\n",
"\n",
@@ -1908,7 +1535,10 @@
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": false,
+ "editable": true
+ },
"outputs": [],
"source": [
"# Importing various packages\n",
@@ -2037,7 +1667,10 @@
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": false,
+ "editable": true
+ },
"outputs": [],
"source": [
"import numpy as np\n",
@@ -2079,7 +1712,10 @@
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": false,
+ "editable": true
+ },
"outputs": [],
"source": [
"import numpy as np \n",
@@ -2249,7 +1885,10 @@
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": false,
+ "editable": true
+ },
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
@@ -2453,7 +2092,10 @@
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": false,
+ "editable": true
+ },
"outputs": [],
"source": [
"# Common imports\n",
@@ -2501,7 +2143,10 @@
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": false,
+ "editable": true
+ },
"outputs": [],
"source": [
"from pylab import plt, mpl\n",
@@ -2534,7 +2179,10 @@
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": false,
+ "editable": true
+ },
"outputs": [],
"source": [
"\"\"\" \n",
@@ -2562,7 +2210,10 @@
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": false,
+ "editable": true
+ },
"outputs": [],
"source": [
"# Read the experimental data with Pandas\n",
@@ -2604,7 +2255,10 @@
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": false,
+ "editable": true
+ },
"outputs": [],
"source": [
"A = Masses['A']\n",
@@ -2626,7 +2280,10 @@
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": false,
+ "editable": true
+ },
"outputs": [],
"source": [
"# Now we set up the design matrix X\n",
@@ -2648,7 +2305,10 @@
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": false,
+ "editable": true
+ },
"outputs": [],
"source": [
"clf = skl.LinearRegression().fit(X, Energies)\n",
@@ -2666,7 +2326,10 @@
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": false,
+ "editable": true
+ },
"outputs": [],
"source": [
"# The mean squared error \n",
@@ -2703,7 +2366,10 @@
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": false,
+ "editable": true
+ },
"outputs": [],
"source": [
"\n",
@@ -2751,7 +2417,10 @@
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": false,
+ "editable": true
+ },
"outputs": [],
"source": [
"from sklearn.neural_network import MLPRegressor\n",
@@ -2799,29 +2468,229 @@
"Furthermore,\n",
"**Scikit-Learn** allows us with few lines of code to implement popular\n",
"Machine Learning algorithms for supervised learning. Later we will meet **Tensorflow**, a powerful library for deep learning. \n",
- "Now it is time to dive more into the details of various methods. We will start with linear regression and try to take a deeper look at what it entails."
+ "Now it is time to dive more into the details of various methods. We will start with linear regression and try to take a deeper look at what it entails.\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "## Exercise 1: Setting up various Python environments\n",
+ "\n",
+ "The first exercise here is of a mere technical art. We want you to have \n",
+ "* git as a version control software and to establish a user account on a provider like GitHub. Other providers like GitLab etc are equally fine. You can also use the University of Oslo [GitHub facilities](https://www.uio.no/tjenester/it/maskin/filer/versjonskontroll/github.html). \n",
+ "\n",
+ "* Install various Python packages\n",
+ "\n",
+ "We will make extensive use of Python as programming language and its\n",
+ "myriad of available libraries. You will find\n",
+ "IPython/Jupyter notebooks invaluable in your work. You can run **R**\n",
+ "codes in the Jupyter/IPython notebooks, with the immediate benefit of\n",
+ "visualizing your data. You can also use compiled languages like C++,\n",
+ "Rust, Fortran etc if you prefer. The focus in these lectures will be\n",
+ "on Python.\n",
+ "\n",
+ "If you have Python installed (we recommend Python3) and you feel\n",
+ "pretty familiar with installing different packages, we recommend that\n",
+ "you install the following Python packages via **pip** as \n",
+ "\n",
+ "1. pip install numpy scipy matplotlib ipython scikit-learn sympy pandas pillow \n",
+ "\n",
+ "For **Tensorflow**, we recommend following the instructions in the text of \n",
+ "[Aurelien Geron, Hands‑On Machine Learning with Scikit‑Learn and TensorFlow, O'Reilly](http://shop.oreilly.com/product/0636920052289.do)\n",
+ "\n",
+ "We will come back to **tensorflow** later. \n",
+ "\n",
+ "For Python3, replace **pip** with **pip3**.\n",
+ "\n",
+ "For OSX users we recommend, after having installed Xcode, to\n",
+ "install **brew**. Brew allows for a seamless installation of additional\n",
+ "software via for example \n",
+ "\n",
+ "1. brew install python3\n",
+ "\n",
+ "For Linux users, with its variety of distributions like for example the widely popular Ubuntu distribution,\n",
+ "you can use **pip** as well and simply install Python as \n",
+ "\n",
+ "1. sudo apt-get install python3 (or python for Python2.7)\n",
+ "\n",
+ "If you don't want to perform these operations separately and venture\n",
+ "into the hassle of exploring how to set up dependencies and paths, we\n",
+ "recommend two widely used distrubutions which set up all relevant\n",
+ "dependencies for Python, namely \n",
+ "\n",
+ "* [Anaconda](https://docs.anaconda.com/), \n",
+ "\n",
+ "which is an open source\n",
+ "distribution of the Python and R programming languages for large-scale\n",
+ "data processing, predictive analytics, and scientific computing, that\n",
+ "aims to simplify package management and deployment. Package versions\n",
+ "are managed by the package management system **conda**. \n",
+ "\n",
+ "* [Enthought canopy](https://www.enthought.com/product/canopy/) \n",
+ "\n",
+ "is a Python\n",
+ "distribution for scientific and analytic computing distribution and\n",
+ "analysis environment, available for free and under a commercial\n",
+ "license.\n",
+ "\n",
+ "We recommend using **Anaconda**.\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "## Exercise 2: making your own data and exploring scikit-learn\n",
+ "\n",
+ "We will generate our own dataset for a function $y(x)$ where $x \\in [0,1]$ and defined by random numbers computed with the uniform distribution. The function $y$ is a quadratic polynomial in $x$ with added stochastic noise according to the normal distribution $\\cal {N}(0,1)$.\n",
+ "The following simple Python instructions define our $x$ and $y$ values (with 100 data points)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": false,
+ "editable": true
+ },
+ "outputs": [],
+ "source": [
+ "x = np.random.rand(100,1)\n",
+ "y = 2.0+5*x*x+0.1*np.random.randn(100,1)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "1. Write your own code (following the examples under the [regression slides](https://compphysics.github.io/MachineLearningECT/doc/pub/Day1/html/Day1-bs.html)) for computing the parametrization of the data set fitting a second-order polynomial. \n",
+ "\n",
+ "2. Use thereafter **scikit-learn** (see again the examples in the regression slides) and compare with your own code. \n",
+ "\n",
+ "3. Using scikit-learn, compute also the mean square error, a risk metric corresponding to the expected value of the squared (quadratic) error defined as"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "$$\n",
+ "MSE(\\hat{y},\\hat{\\tilde{y}}) = \\frac{1}{n}\n",
+ "\\sum_{i=0}^{n-1}(y_i-\\tilde{y}_i)^2,\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "and the $R^2$ score function.\n",
+ "If $\\tilde{\\hat{y}}_i$ is the predicted value of the $i-th$ sample and $y_i$ is the corresponding true value, then the score $R^2$ is defined as"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "$$\n",
+ "R^2(\\hat{y}, \\tilde{\\hat{y}}) = 1 - \\frac{\\sum_{i=0}^{n - 1} (y_i - \\tilde{y}_i)^2}{\\sum_{i=0}^{n - 1} (y_i - \\bar{y})^2},\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "where we have defined the mean value of $\\hat{y}$ as"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "$$\n",
+ "\\bar{y} = \\frac{1}{n} \\sum_{i=0}^{n - 1} y_i.\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "You can use the functionality included in scikit-learn. If you feel for it, you can use your own program and define functions which compute the above two functions. \n",
+ "Discuss the meaning of these results. Try also to vary the coefficient in front of the added stochastic noise term and discuss the quality of the fits.\n",
+ "\n",
+ "\n",
+ "\n",
+ "**Solution.**\n",
+ "The code here is an example of where we define our own design matrix and fit parameters $\\beta$."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": false,
+ "editable": true
+ },
+ "outputs": [],
+ "source": [
+ "import os\n",
+ "import numpy as np\n",
+ "import pandas as pd\n",
+ "import matplotlib.pyplot as plt\n",
+ "from sklearn.model_selection import train_test_split\n",
+ "\n",
+ "def save_fig(fig_id):\n",
+ " plt.savefig(image_path(fig_id) + \".png\", format='png')\n",
+ "\n",
+ "def R2(y_data, y_model):\n",
+ " return 1 - np.sum((y_data - y_model) ** 2) / np.sum((y_data - np.mean(y_data)) ** 2)\n",
+ "def MSE(y_data,y_model):\n",
+ " n = np.size(y_model)\n",
+ " return np.sum((y_data-y_model)**2)/n\n",
+ "\n",
+ "x = np.random.rand(100)\n",
+ "y = 2.0+5*x*x+0.1*np.random.randn(100)\n",
+ "\n",
+ "\n",
+ "# The design matrix now as function of a given polynomial\n",
+ "X = np.zeros((len(x),3))\n",
+ "X[:,0] = 1.0\n",
+ "X[:,1] = x\n",
+ "X[:,2] = x**2\n",
+ "# We split the data in test and training data\n",
+ "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)\n",
+ "# matrix inversion to find beta\n",
+ "beta = np.linalg.inv(X_train.T @ X_train) @ X_train.T @ y_train\n",
+ "print(beta)\n",
+ "# and then make the prediction\n",
+ "ytilde = X_train @ beta\n",
+ "print(\"Training R2\")\n",
+ "print(R2(y_train,ytilde))\n",
+ "print(\"Training MSE\")\n",
+ "print(MSE(y_train,ytilde))\n",
+ "ypredict = X_test @ beta\n",
+ "print(\"Test R2\")\n",
+ "print(R2(y_test,ypredict))\n",
+ "print(\"Test MSE\")\n",
+ "print(MSE(y_test,ypredict))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "\n",
+ "\n",
+ ""
]
}
],
- "metadata": {
- "kernelspec": {
- "display_name": "Python 3",
- "language": "python",
- "name": "python3"
- },
- "language_info": {
- "codemirror_mode": {
- "name": "ipython",
- "version": 3
- },
- "file_extension": ".py",
- "mimetype": "text/x-python",
- "name": "python",
- "nbconvert_exporter": "python",
- "pygments_lexer": "ipython3",
- "version": "3.8.5"
- }
- },
+ "metadata": {},
"nbformat": 4,
"nbformat_minor": 4
}
diff --git a/doc/src/week34/week34.do.txt b/doc/src/week34/week34.do.txt
index 1b4067a92..2e4233ac1 100644
--- a/doc/src/week34/week34.do.txt
+++ b/doc/src/week34/week34.do.txt
@@ -1,4 +1,4 @@
-TITLE: Week 34: Introduction to the course, Logistics and Practicalities
+TITLE: Week 35: Introduction to the course, Logistics and Practicalities
AUTHOR: Morten Hjorth-Jensen {copyright, 1999-present|CC BY-NC} at Department of Physics, University of Oslo & Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University
DATE: today
@@ -187,7 +187,7 @@ These topics will be scattered thorughout the course and may not necessarily be
!bblock Statistical analysis and optimization of data
-The following topics will be covered
+We plan to cover the following topics:
* Basic concepts, expectation values, variance, covariance, correlation functions and errors;
* Simpler models, binomial distribution, the Poisson distribution, simple and multivariate normal distributions;
* Central elements of Bayesian statistics and modeling;
@@ -376,16 +376,106 @@ desired output of a system. Some of the most common tasks are:
* Clustering: Data are divided into groups with certain common traits, without knowing the different groups beforehand. It is thus a form of unsupervised learning.
-The methods we cover have three main topics in common, irrespective of
-whether we deal with supervised or unsupervised learning. The first
-ingredient is normally our data set (which can be subdivided into
-training and test data), the second item is a model which is normally a
-function of some parameters. The model reflects our knowledge of the system (or lack thereof). As an example, if we know that our data show a behavior similar to what would be predicted by a polynomial, fitting our data to a polynomial of some degree would then determin our model.
+!split
+===== Essential elements of ML =====
+
+The methods we cover have three main topics in common, irrespective of
+whether we deal with supervised or unsupervised learning.
+!bpop
+* The first ingredient is normally our data set (which can be subdivided into training, validation and test data). Many find the most difficult part of using Machine Learning to be the set up of your data in a meaningful way.
+
+* The second item is a model which is normally a function of some parameters. The model reflects our knowledge of the system (or lack thereof). As an example, if we know that our data show a behavior similar to what would be predicted by a polynomial, fitting our data to a polynomial of some degree would then determin our model.
+
+* The last ingredient is a so-called _cost/loss_ function (or error or risk function) which allows us to present an estimate on how good our model is in reproducing the data it is supposed to train.
+!epop
+
+
+
+
+!split
+===== An optimization/minimization problem =====
+
+At the heart of basically all Machine Learning algorithms we will encounter so-called minimization or optimization algorithms. A large family of such methods are so-called _gradient methods_.
+
+!split
+===== A Frequentist approach to data analysis =====
+
+When you hear phrases like _predictions and estimations_ and
+_correlations and causations_, what do you think of? May be you think
+of the difference between classifying new data points and generating
+new data points.
+Or perhaps you consider that correlations represent some kind of symmetric statements like
+if $A$ is correlated with $B$, then $B$ is correlated with
+$A$. Causation on the other hand is directional, that is if $A$ causes $B$, $B$ does not
+necessarily cause $A$.
+
+These concepts are in some sense the difference between machine
+learning and statistics. In machine learning and prediction based
+tasks, we are often interested in developing algorithms that are
+capable of learning patterns from given data in an automated fashion,
+and then using these learned patterns to make predictions or
+assessments of newly given data. In many cases, our primary concern
+is the quality of the predictions or assessments, and we are less
+concerned about the underlying patterns that were learned in order
+to make these predictions.
+
+In machine learning we normally use "a so-called frequentist approach":"https://en.wikipedia.org/wiki/Frequentist_inference",
+where the aim is to make predictions and find correlations. We focus
+less on for example extracting a probability distribution function (PDF). The PDF can be
+used in turn to make estimations and find causations such as given $A$
+what is the likelihood of finding $B$.
+
+
+!split
+===== What is a good model? =====
+
+In science and engineering we often end up in situations where we want to infer (or learn) a
+quantitative model $M$ for a given set of sample points $\bm{X} \in [x_1, x_2,\dots x_N]$.
+
+As we will see repeatedely in these lectures, we could try to fit these data points to a model given by a
+straight line, or if we wish to be more sophisticated to a more complex
+function.
+
+The reason for inferring such a model is that it
+serves many useful purposes. On the one hand, the model can reveal information
+encoded in the data or underlying mechanisms from which the data were generated. For instance, we could discover important
+corelations that relate interesting physics interpretations.
+
+In addition, it can simplify the representation of the given data set and help
+us in making predictions about future data samples.
+
+A first important consideration to keep in mind is that inferring the *correct* model
+for a given data set is an elusive, if not impossible, task. The fundamental difficulty
+is that if we are not specific about what we mean by a *correct* model, there
+could easily be many different models that fit the given data set *equally well*.
+
+
+!split
+===== What is a good model? Can we define it? =====
+
+
+The central question is this: what leads us to say that a model is correct or
+optimal for a given data set? To make the model inference problem well posed, i.e.,
+to guarantee that there is a unique optimal model for the given data, we need to
+impose additional assumptions or restrictions on the class of models considered. To
+this end, we should not be looking for just any model that can describe the data.
+Instead, we should look for a _model_ $M$ that is the best among a restricted class
+of models. In addition, to make the model inference problem computationally
+tractable, we need to specify how restricted the class of models needs to be. A
+common strategy is to start
+with the simplest possible class of models that is just necessary to describe the data
+or solve the problem at hand. More precisely, the model class should be rich enough
+to contain at least one model that can fit the data to a desired accuracy and yet be
+restricted enough that it is relatively simple to find the best model for the given data.
+
+Thus, the most popular strategy is to start from the
+simplest class of models and increase the complexity of the models only when the
+simpler models become inadequate. For instance, if we work with a regression problem to fit a set of sample points, one
+may first try the simplest class of models, namely linear models, followed obviously by more complex models.
+
+How to evaluate which model fits best the data is something we will come back to over and over again in these sets of lectures.
+
-The last ingredient is a so-called _cost_
-function which allows us to present an estimate on how good our model
-is in reproducing the data it is supposed to train.
-At the heart of basically all ML algorithms there are so-called minimization algorithms, often we end up with various variants of _gradient_ methods.
@@ -897,9 +987,9 @@ For multidimensional arrays, we recommend strongly "xarray":"http://xarray.pydat
!split
-===== Friday August 21 =====
+===== Friday August 27 =====
-"Video of Lecture":"https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h20/forelesningsvideoer/LectureAug21.mp4?vrtx=view-as-webpage" and "Handwritten notes":"https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/NotesAugust21.pdf"
+"Video of Lecture from fall 2020":"https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h20/forelesningsvideoer/LectureAug21.mp4?vrtx=view-as-webpage" and "Handwritten notes":"https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/NotesAugust21.pdf"
@@ -1599,5 +1689,146 @@ Machine Learning algorithms for supervised learning. Later we will meet _Tensorf
Now it is time to dive more into the details of various methods. We will start with linear regression and try to take a deeper look at what it entails.
+!split
+===== Exercise: Setting up various Python environments =====
+
+The first exercise here is of a mere technical art. We want you to have
+* git as a version control software and to establish a user account on a provider like GitHub. Other providers like GitLab etc are equally fine. You can also use the University of Oslo "GitHub facilities":"https://www.uio.no/tjenester/it/maskin/filer/versjonskontroll/github.html".
+* Install various Python packages
+
+We will make extensive use of Python as programming language and its
+myriad of available libraries. You will find
+IPython/Jupyter notebooks invaluable in your work. You can run _R_
+codes in the Jupyter/IPython notebooks, with the immediate benefit of
+visualizing your data. You can also use compiled languages like C++,
+Rust, Fortran etc if you prefer. The focus in these lectures will be
+on Python.
+
+If you have Python installed (we recommend Python3) and you feel
+pretty familiar with installing different packages, we recommend that
+you install the following Python packages via _pip_ as
+
+o pip install numpy scipy matplotlib ipython scikit-learn sympy pandas pillow
+
+For _Tensorflow_, we recommend following the instructions in the text of
+"Aurelien Geron, Hands‑On Machine Learning with Scikit‑Learn and TensorFlow, O'Reilly":"http://shop.oreilly.com/product/0636920052289.do"
+
+We will come back to _tensorflow_ later.
+
+For Python3, replace _pip_ with _pip3_.
+
+For OSX users we recommend, after having installed Xcode, to
+install _brew_. Brew allows for a seamless installation of additional
+software via for example
+
+o brew install python3
+
+For Linux users, with its variety of distributions like for example the widely popular Ubuntu distribution,
+you can use _pip_ as well and simply install Python as
+
+o sudo apt-get install python3 (or python for Python2.7)
+
+If you don't want to perform these operations separately and venture
+into the hassle of exploring how to set up dependencies and paths, we
+recommend two widely used distrubutions which set up all relevant
+dependencies for Python, namely
+
+* "Anaconda":"https://docs.anaconda.com/",
+
+which is an open source
+distribution of the Python and R programming languages for large-scale
+data processing, predictive analytics, and scientific computing, that
+aims to simplify package management and deployment. Package versions
+are managed by the package management system _conda_.
+
+* "Enthought canopy":"https://www.enthought.com/product/canopy/"
+
+is a Python
+distribution for scientific and analytic computing distribution and
+analysis environment, available for free and under a commercial
+license.
+
+We recommend using _Anaconda_.
+
+
+===== Exercise: making your own data and exploring scikit-learn =====
+
+
+We will generate our own dataset for a function $y(x)$ where $x \in [0,1]$ and defined by random numbers computed with the uniform distribution. The function $y$ is a quadratic polynomial in $x$ with added stochastic noise according to the normal distribution $\cal {N}(0,1)$.
+The following simple Python instructions define our $x$ and $y$ values (with 100 data points).
+!bc pycod
+x = np.random.rand(100,1)
+y = 2.0+5*x*x+0.1*np.random.randn(100,1)
+!ec
+
+o Write your own code (following the examples under the "regression slides":"https://compphysics.github.io/MachineLearningECT/doc/pub/Day1/html/Day1-bs.html") for computing the parametrization of the data set fitting a second-order polynomial.
+o Use thereafter _scikit-learn_ (see again the examples in the regression slides) and compare with your own code.
+o Using scikit-learn, compute also the mean square error, a risk metric corresponding to the expected value of the squared (quadratic) error defined as
+!bt
+\[ MSE(\hat{y},\hat{\tilde{y}}) = \frac{1}{n}
+\sum_{i=0}^{n-1}(y_i-\tilde{y}_i)^2,
+\]
+!et
+and the $R^2$ score function.
+If $\tilde{\hat{y}}_i$ is the predicted value of the $i-th$ sample and $y_i$ is the corresponding true value, then the score $R^2$ is defined as
+!bt
+\[
+R^2(\hat{y}, \tilde{\hat{y}}) = 1 - \frac{\sum_{i=0}^{n - 1} (y_i - \tilde{y}_i)^2}{\sum_{i=0}^{n - 1} (y_i - \bar{y})^2},
+\]
+!et
+where we have defined the mean value of $\hat{y}$ as
+!bt
+\[
+\bar{y} = \frac{1}{n} \sum_{i=0}^{n - 1} y_i.
+\]
+!et
+You can use the functionality included in scikit-learn. If you feel for it, you can use your own program and define functions which compute the above two functions.
+Discuss the meaning of these results. Try also to vary the coefficient in front of the added stochastic noise term and discuss the quality of the fits.
+
+!bsol
+The code here is an example of where we define our own design matrix and fit parameters $\beta$.
+!bc pycod
+import os
+import numpy as np
+import pandas as pd
+import matplotlib.pyplot as plt
+from sklearn.model_selection import train_test_split
+
+def save_fig(fig_id):
+ plt.savefig(image_path(fig_id) + ".png", format='png')
+
+def R2(y_data, y_model):
+ return 1 - np.sum((y_data - y_model) ** 2) / np.sum((y_data - np.mean(y_data)) ** 2)
+def MSE(y_data,y_model):
+ n = np.size(y_model)
+ return np.sum((y_data-y_model)**2)/n
+
+x = np.random.rand(100)
+y = 2.0+5*x*x+0.1*np.random.randn(100)
+
+
+# The design matrix now as function of a given polynomial
+X = np.zeros((len(x),3))
+X[:,0] = 1.0
+X[:,1] = x
+X[:,2] = x**2
+# We split the data in test and training data
+X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)
+# matrix inversion to find beta
+beta = np.linalg.inv(X_train.T @ X_train) @ X_train.T @ y_train
+print(beta)
+# and then make the prediction
+ytilde = X_train @ beta
+print("Training R2")
+print(R2(y_train,ytilde))
+print("Training MSE")
+print(MSE(y_train,ytilde))
+ypredict = X_test @ beta
+print("Test R2")
+print(R2(y_test,ypredict))
+print("Test MSE")
+print(MSE(y_test,ypredict))
+!ec
+!esol
