From 4da18852c42ea569e6b923b3d5802e981ced8192 Mon Sep 17 00:00:00 2001 From: Morten Hjorth-Jensen Date: Tue, 24 Aug 2021 22:52:34 +0200 Subject: [PATCH] updating week 35 --- doc/pub/week34/html/week34-bs.html | 2 +- doc/pub/week34/html/week34-reveal.html | 56 +++++++++------- doc/pub/week34/html/week34-solarized.html | 56 +++++++++------- doc/pub/week34/html/week34.html | 56 +++++++++------- .../ipynb/Results/FigureFiles/Masses2016.png | Bin 16191 -> 16565 bytes .../Results/FigureFiles/Masses2016Trees.png | Bin 21619 -> 21472 bytes doc/pub/week34/ipynb/ipynb-week34-src.tar.gz | Bin 103349 -> 103349 bytes doc/pub/week34/ipynb/week34.ipynb | 62 +++++++++++------- doc/src/week34/week34.do.txt | 56 +++++++++------- 9 files changed, 174 insertions(+), 114 deletions(-) diff --git a/doc/pub/week34/html/week34-bs.html b/doc/pub/week34/html/week34-bs.html index 7e1e9edca..93dca0db3 100644 --- a/doc/pub/week34/html/week34-bs.html +++ b/doc/pub/week34/html/week34-bs.html @@ -239,7 +239,7 @@ MathJax.Hub.Config({
[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

-

Aug 23, 2021

+

Aug 24, 2021


diff --git a/doc/pub/week34/html/week34-reveal.html b/doc/pub/week34/html/week34-reveal.html index 44723bd74..947448e2a 100644 --- a/doc/pub/week34/html/week34-reveal.html +++ b/doc/pub/week34/html/week34-reveal.html @@ -148,7 +148,7 @@ MathJax.Hub.Config({

[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

 
-

Aug 23, 2021

+

Aug 24, 2021


@@ -334,7 +334,7 @@ Projects are handed in using Canvas. We use Github as repository for code

-In addition to the electure notes, we recommend the books of Bishop and Goodfellow et al. We will follow these texts closely and the weekly reading assignments refer to these two texts. The text by Hastie et al is also widely used in the Machine Learning community. Finally, we also recommend the hands-on text by Geron, see below. +In addition to the lecture notes, we recommend the books of Bishop and Goodfellow et al. We will follow these texts closely and the weekly reading assignments refer to these two texts. The text by Hastie et al is also widely used in the Machine Learning community. Finally, we also recommend the hands-on text by Geron, see below.

  1. Christopher M. Bishop, Pattern Recognition and Machine Learning, Springer, https://www.springer.com/gp/book/9780387310732.
    2. @@ -374,7 +374,19 @@ Python is the recurring programming language.

    -This course aims at giving you insights and knowledge about many of the central algorithms used in Data Analysis and Machine Learning. The course is project based and through various numerical projects, normally three, you will be exposed to fundamental research problems in these fields, with the aim to reproduce state of the art scientific results. Both supervised and unsupervised methods will be covered. The emphasis is on a frequentist approach, although we will try to link it with a Bayesian approach as well. You will learn to develop and structure large codes for studying different cases where Machine Learning is applied to, get acquainted with computing facilities and learn to handle large scientific projects. A good scientific and ethical conduct is emphasized throughout the course. More specifically, after this course you will +This course aims at giving you insights and knowledge about many of +the central algorithms used in Data Analysis and Machine Learning. +The course is project based and through various numerical projects, +normally three, you will be exposed to fundamental research problems +in these fields, with the aim to reproduce state of the art scientific +results. Both supervised and unsupervised methods will be covered. The +emphasis is on a frequentist approach, although we will try to link it +with a Bayesian approach as well. You will learn to develop and +structure large codes for studying different cases where Machine +Learning is applied to, get acquainted with computing facilities and +learn to handle large scientific projects. A good scientific and +ethical conduct is emphasized throughout the course. More +specifically, after this course you will

    • Learn about basic data analysis, statistical analysis, Bayesian statistics, Monte Carlo sampling, data optimization and machine learning;
      • @@ -386,7 +398,7 @@ This course aims at giving you insights and knowledge about many of the central

    • Learn about support vector machines and kernel transformations;

    • Reduction of data sets, from PCA to clustering;

    • Autoencoders and Reinforcement Learning;
      • -

    • Work on numerical projects to illustrate the theory. The projects play a central role and you are expected to know modern programming languages like Python or C++ and/or Fortran (Fortran2003 or later).
      • +

    • Work on numerical projects to illustrate the theory. The projects play a central role and you are expected to know modern programming languages like Python or C++ and/or Fortran (Fortran2003 or later) or Julia or other.
    @@ -441,7 +453,7 @@ The following topics will be covered

  2. Support vector machines

  3. Bayesian linear and logistic regression

  4. Boltzmann Machines
    5. -

  5. Unsupervised learning Dimensionality reduction, from PCA to cluster models
    6. +

  6. Unsupervised learning Dimensionality reduction, from PCA to clustering

    7. @@ -462,7 +474,7 @@ Hands-on demonstrations, exercises and projects aim at deepening your understand

  7. GIT for version control, and GitHub or GitLab as repositories, highly recommended. This will be discussed during the first exercise session
    8. -

  8. Anaconda and other Python environments, see intro slides and first exercise session
    9. +

  9. Anaconda and other Python environments, see intro slides and links to programming resources at https://computationalscienceuio.github.io/RefreshProgrammingSkills/intro.html
    10. @@ -476,7 +488,7 @@ The link here STK2100 Machine learning and statistical methods for prediction and classification. -

  10. IN3050 Introduction to Artificial Intelligence and Machine Learning. Introductory course in machine learning and AI with an algorithmic approach.
    11. +

  11. IN3050/4050 Introduction to Artificial Intelligence and Machine Learning. Introductory course in machine learning and AI with an algorithmic approach.

  12. STK-INF3000/4000 Selected Topics in Data Science. The course provides insight into selected contemporary relevant topics within Data Science.

  13. IN4080 Natural Language Processing. Probabilistic and machine learning techniques applied to natural language processing.

  14. STK-IN4300 Statistical learning methods in Data Science. An advanced introduction to statistical and machine learning. For students with a good mathematics and statistics background.
    15. @@ -862,14 +874,14 @@ $$

    - + - - - - - + + + + +
    Relations Name matrix elements
    Relations Name matrix elements
    \( A=A^{T} \) symmetric \( a_{ij}=a_{ji} \)
    \( A=\left (A^{T} \right )^{-1} \) real orthogonal \( \sum_k a_{ik}a_{jk}=\sum_k a_{ki} a_{kj} = \delta_{ij} \)
    \( A=A^{ * } \) real matrix \( a_{ij}=a_{ij}^{ * } \)
    \( A=A^{\dagger} \) hermitian \( a_{ij}=a_{ji}^{ * } \)
    \( A=\left (A^{\dagger} \right )^{-1} \) unitary \( \sum_k a_{ik}a_{jk}^{ * }=\sum_k a_{ki}^{ * } a_{kj}=\delta_{ij} \)
    \( A=A^{T} \) symmetric \( a_{ij}=a_{ji} \)
    \( A=\left (A^{T}\right )^{-1} \) real orthogonal \( \sum_k a_{ik}a_{jk}=\sum_k a_{ki} a_{kj}=\delta_{ij} \)
    \( A=A^{ * } \) real matrix \( a_{ij}=a_{ij}^{ < em>} \)
    \( A=A^{\dagger} \) hermitian \( a_{ij}=a_{ji}^{ < /em>} \)
    \( A=\left(A^{\dagger}\right )^{-1} \) unitary \( \sum_k a_{ik}a_{jk}^{ < em>}=\sum_k a_{ki}^{ < /em> } a_{kj}=\delta_{ij} \)
    @@ -885,17 +897,17 @@ $$

  15. Diagonal if \( a_{ij}=0 \) for \( i\ne j \)
    16. -

  16. Upper triangular if \( a_{ij}=0 \) for \( i > j \)
    17. +

  17. Upper triangular if \( a_{ij}=0 \) for \( i>j \)

  18. Lower triangular if \( a_{ij}=0 \) for \( i < j \)
    19. -

  19. Upper Hessenberg if \( a_{ij}=0 \) for \( i > j+1 \)
    20. +

  20. Upper Hessenberg if \( a_{ij}=0 \) for \( i>j+1 \)

  21. Lower Hessenberg if \( a_{ij}=0 \) for \( i < j+1 \)
    22. -

  22. Tridiagonal if \( a_{ij}=0 \) for \( |i -j| > 1 \)
    23. +

  23. Tridiagonal if \( a_{ij}=0 \) for \( |i -j|>1 \)
    24. -

  24. Lower banded with bandwidth \( p \): \( a_{ij}=0 \) for \( i > j+p \)
    25. +

  25. Lower banded with bandwidth \( p \): \( a_{ij}=0 \) for \( i>j+p \)

  26. Upper banded with bandwidth \( p \): \( a_{ij}=0 \) for \( i < j+p \)
    27. @@ -1005,7 +1017,7 @@ or simply write them as double precision numbers (Python uses 64 bits as default 
    import numpy as np
-x = np.log(np.array([4.0, 7.0, 8.0])
+x = np.log(np.array([4.0, 7.0, 8.0]))
 print(x)

    @@ -1014,7 +1026,7 @@ To check the number of bytes (remember that one byte contains eight bits for dou 

    import numpy as np
-x = np.log(np.array([4.0, 7.0, 8.0])
+x = np.log(np.array([4.0, 7.0, 8.0]))
 print(x.itemsize)
    @@ -1327,7 +1339,7 @@ pretty close the basic mathematical expressions.

    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 simply as an example here of a data set. +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 @@ -1571,7 +1583,7 @@ plt.show()

    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 +\( \alpha \). 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, @@ -1642,7 +1654,7 @@ ways of dealing with outliers. The Huber cost function is defined as

     
    $$ -H_{\delta}(a)={\begin{cases}{\frac {1}{2}}{a^{2}}&{\text{for }}|a|\leq \delta ,\\\delta (|a|-{\frac {1}{2}}\delta ),&{\text{otherwise.}}\end{cases}}}. +H_{\delta}(a)=\left\{\begin{array}\frac{1}{2}{a^{2}}&{\text{for }}|a|\leq \delta ,\\ \delta (|a|-{\frac {1}{2}}\delta ),&{\text{otherwise.}\end{array}\right. $$

     
    diff --git a/doc/pub/week34/html/week34-solarized.html b/doc/pub/week34/html/week34-solarized.html index 2589481a4..292477361 100644 --- a/doc/pub/week34/html/week34-solarized.html +++ b/doc/pub/week34/html/week34-solarized.html @@ -191,7 +191,7 @@ MathJax.Hub.Config({

    [2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

    -

    Aug 23, 2021

    +

    Aug 24, 2021












    @@ -366,7 +366,7 @@ Projects are handed in using Canvas. We use Github as repository for code

  27. The lecture notes are collected as a jupyter-book at https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/intro.html.
-In addition to the electure notes, we recommend the books of Bishop and Goodfellow et al. We will follow these texts closely and the weekly reading assignments refer to these two texts. The text by Hastie et al is also widely used in the Machine Learning community. Finally, we also recommend the hands-on text by Geron, see below. +In addition to the lecture notes, we recommend the books of Bishop and Goodfellow et al. We will follow these texts closely and the weekly reading assignments refer to these two texts. The text by Hastie et al is also widely used in the Machine Learning community. Finally, we also recommend the hands-on text by Geron, see below.
  1. Christopher M. Bishop, Pattern Recognition and Machine Learning, Springer, https://www.springer.com/gp/book/9780387310732.
    2. @@ -406,7 +406,19 @@ Python is the recurring programming language.

    -This course aims at giving you insights and knowledge about many of the central algorithms used in Data Analysis and Machine Learning. The course is project based and through various numerical projects, normally three, you will be exposed to fundamental research problems in these fields, with the aim to reproduce state of the art scientific results. Both supervised and unsupervised methods will be covered. The emphasis is on a frequentist approach, although we will try to link it with a Bayesian approach as well. You will learn to develop and structure large codes for studying different cases where Machine Learning is applied to, get acquainted with computing facilities and learn to handle large scientific projects. A good scientific and ethical conduct is emphasized throughout the course. More specifically, after this course you will +This course aims at giving you insights and knowledge about many of +the central algorithms used in Data Analysis and Machine Learning. +The course is project based and through various numerical projects, +normally three, you will be exposed to fundamental research problems +in these fields, with the aim to reproduce state of the art scientific +results. Both supervised and unsupervised methods will be covered. The +emphasis is on a frequentist approach, although we will try to link it +with a Bayesian approach as well. You will learn to develop and +structure large codes for studying different cases where Machine +Learning is applied to, get acquainted with computing facilities and +learn to handle large scientific projects. A good scientific and +ethical conduct is emphasized throughout the course. More +specifically, after this course you will

    @@ -476,7 +488,7 @@ The following topics will be covered
  2. Support vector machines
  3. Bayesian linear and logistic regression
  4. Boltzmann Machines
    5. -
  5. Unsupervised learning Dimensionality reduction, from PCA to cluster models
    6. +
  6. Unsupervised learning Dimensionality reduction, from PCA to clustering
    7. Hands-on demonstrations, exercises and projects aim at deepening your understanding of these topics. @@ -497,7 +509,7 @@ Hands-on demonstrations, exercises and projects aim at deepening your understand @@ -512,7 +524,7 @@ The link here STK2100 Machine learning and statistical methods for prediction and classification. -
  7. IN3050 Introduction to Artificial Intelligence and Machine Learning. Introductory course in machine learning and AI with an algorithmic approach.
    8. +
  8. IN3050/4050 Introduction to Artificial Intelligence and Machine Learning. Introductory course in machine learning and AI with an algorithmic approach.
  9. STK-INF3000/4000 Selected Topics in Data Science. The course provides insight into selected contemporary relevant topics within Data Science.
  10. IN4080 Natural Language Processing. Probabilistic and machine learning techniques applied to natural language processing.
  11. STK-IN4300 Statistical learning methods in Data Science. An advanced introduction to statistical and machine learning. For students with a good mathematics and statistics background.
    12. @@ -880,14 +892,14 @@ $$

    - + - - - - - + + + + +
    Relations Name matrix elements
    Relations Name matrix elements
    \( A=A^{T} \) symmetric \( a_{ij}=a_{ji} \)
    \( A=\left (A^{T} \right )^{-1} \) real orthogonal \( \sum_k a_{ik}a_{jk}=\sum_k a_{ki} a_{kj} = \delta_{ij} \)
    \( A=A^{ * } \) real matrix \( a_{ij}=a_{ij}^{ * } \)
    \( A=A^{\dagger} \) hermitian \( a_{ij}=a_{ji}^{ * } \)
    \( A=\left (A^{\dagger} \right )^{-1} \) unitary \( \sum_k a_{ik}a_{jk}^{ * }=\sum_k a_{ki}^{ * } a_{kj}=\delta_{ij} \)
    \( A=A^{T} \) symmetric \( a_{ij}=a_{ji} \)
    \( A=\left (A^{T}\right )^{-1} \) real orthogonal \( \sum_k a_{ik}a_{jk}=\sum_k a_{ki} a_{kj}=\delta_{ij} \)
    \( A=A^{ * } \) real matrix \( a_{ij}=a_{ij}^{ < em>} \)
    \( A=A^{\dagger} \) hermitian \( a_{ij}=a_{ji}^{ < /em>} \)
    \( A=\left(A^{\dagger}\right )^{-1} \) unitary \( \sum_k a_{ik}a_{jk}^{ < em>}=\sum_k a_{ki}^{ < /em> } a_{kj}=\delta_{ij} \)
    @@ -901,12 +913,12 @@ $$

    @@ -1007,7 +1019,7 @@ or simply write them as double precision numbers (Python uses 64 bits as default 
    import numpy as np
-x = np.log(np.array([4.0, 7.0, 8.0])
+x = np.log(np.array([4.0, 7.0, 8.0]))
 print(x)

    @@ -1016,7 +1028,7 @@ To check the number of bytes (remember that one byte contains eight bits for dou 

    import numpy as np
-x = np.log(np.array([4.0, 7.0, 8.0])
+x = np.log(np.array([4.0, 7.0, 8.0]))
 print(x.itemsize)

    @@ -1321,7 +1333,7 @@ pretty close the basic mathematical expressions.

    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 simply as an example here of a data set. +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 @@ -1556,7 +1568,7 @@ plt.show()

    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 +\( \alpha \). 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 $$ MSE(\hat{y},\hat{\tilde{y}}) = \frac{1}{n} \sum_{i=0}^{n-1}(y_i-\tilde{y}_i)^2, $$ @@ -1616,7 +1628,7 @@ ways of dealing with outliers.

    The Huber cost function is defined as $$ -H_{\delta}(a)={\begin{cases}{\frac {1}{2}}{a^{2}}&{\text{for }}|a|\leq \delta ,\\\delta (|a|-{\frac {1}{2}}\delta ),&{\text{otherwise.}}\end{cases}}}. +H_{\delta}(a)=\left\{\begin{array}\frac{1}{2}{a^{2}}&{\text{for }}|a|\leq \delta ,\\ \delta (|a|-{\frac {1}{2}}\delta ),&{\text{otherwise.}\end{array}\right. $$ Here \( a=\boldsymbol{y} - \boldsymbol{\tilde{y}} \). diff --git a/doc/pub/week34/html/week34.html b/doc/pub/week34/html/week34.html index e90b09b95..59e5c7f86 100644 --- a/doc/pub/week34/html/week34.html +++ b/doc/pub/week34/html/week34.html @@ -196,7 +196,7 @@ MathJax.Hub.Config({

    [2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

    -

    Aug 23, 2021

    +

    Aug 24, 2021












    @@ -371,7 +371,7 @@ Projects are handed in using Canvas. We use Github as repository for code

  12. The lecture notes are collected as a jupyter-book at https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/intro.html.
-In addition to the electure notes, we recommend the books of Bishop and Goodfellow et al. We will follow these texts closely and the weekly reading assignments refer to these two texts. The text by Hastie et al is also widely used in the Machine Learning community. Finally, we also recommend the hands-on text by Geron, see below. +In addition to the lecture notes, we recommend the books of Bishop and Goodfellow et al. We will follow these texts closely and the weekly reading assignments refer to these two texts. The text by Hastie et al is also widely used in the Machine Learning community. Finally, we also recommend the hands-on text by Geron, see below.
  1. Christopher M. Bishop, Pattern Recognition and Machine Learning, Springer, https://www.springer.com/gp/book/9780387310732.
    2. @@ -411,7 +411,19 @@ Python is the recurring programming language.

    -This course aims at giving you insights and knowledge about many of the central algorithms used in Data Analysis and Machine Learning. The course is project based and through various numerical projects, normally three, you will be exposed to fundamental research problems in these fields, with the aim to reproduce state of the art scientific results. Both supervised and unsupervised methods will be covered. The emphasis is on a frequentist approach, although we will try to link it with a Bayesian approach as well. You will learn to develop and structure large codes for studying different cases where Machine Learning is applied to, get acquainted with computing facilities and learn to handle large scientific projects. A good scientific and ethical conduct is emphasized throughout the course. More specifically, after this course you will +This course aims at giving you insights and knowledge about many of +the central algorithms used in Data Analysis and Machine Learning. +The course is project based and through various numerical projects, +normally three, you will be exposed to fundamental research problems +in these fields, with the aim to reproduce state of the art scientific +results. Both supervised and unsupervised methods will be covered. The +emphasis is on a frequentist approach, although we will try to link it +with a Bayesian approach as well. You will learn to develop and +structure large codes for studying different cases where Machine +Learning is applied to, get acquainted with computing facilities and +learn to handle large scientific projects. A good scientific and +ethical conduct is emphasized throughout the course. More +specifically, after this course you will

    @@ -481,7 +493,7 @@ The following topics will be covered
  2. Support vector machines
  3. Bayesian linear and logistic regression
  4. Boltzmann Machines
    5. -
  5. Unsupervised learning Dimensionality reduction, from PCA to cluster models
    6. +
  6. Unsupervised learning Dimensionality reduction, from PCA to clustering
    7. Hands-on demonstrations, exercises and projects aim at deepening your understanding of these topics. @@ -502,7 +514,7 @@ Hands-on demonstrations, exercises and projects aim at deepening your understand @@ -517,7 +529,7 @@ The link here STK2100 Machine learning and statistical methods for prediction and classification. -
  7. IN3050 Introduction to Artificial Intelligence and Machine Learning. Introductory course in machine learning and AI with an algorithmic approach.
    8. +
  8. IN3050/4050 Introduction to Artificial Intelligence and Machine Learning. Introductory course in machine learning and AI with an algorithmic approach.
  9. STK-INF3000/4000 Selected Topics in Data Science. The course provides insight into selected contemporary relevant topics within Data Science.
  10. IN4080 Natural Language Processing. Probabilistic and machine learning techniques applied to natural language processing.
  11. STK-IN4300 Statistical learning methods in Data Science. An advanced introduction to statistical and machine learning. For students with a good mathematics and statistics background.
    12. @@ -885,14 +897,14 @@ $$

    - + - - - - - + + + + +
    Relations Name matrix elements
    Relations Name matrix elements
    \( A=A^{T} \) symmetric \( a_{ij}=a_{ji} \)
    \( A=\left (A^{T} \right )^{-1} \) real orthogonal \( \sum_k a_{ik}a_{jk}=\sum_k a_{ki} a_{kj} = \delta_{ij} \)
    \( A=A^{ * } \) real matrix \( a_{ij}=a_{ij}^{ * } \)
    \( A=A^{\dagger} \) hermitian \( a_{ij}=a_{ji}^{ * } \)
    \( A=\left (A^{\dagger} \right )^{-1} \) unitary \( \sum_k a_{ik}a_{jk}^{ * }=\sum_k a_{ki}^{ * } a_{kj}=\delta_{ij} \)
    \( A=A^{T} \) symmetric \( a_{ij}=a_{ji} \)
    \( A=\left (A^{T}\right )^{-1} \) real orthogonal \( \sum_k a_{ik}a_{jk}=\sum_k a_{ki} a_{kj}=\delta_{ij} \)
    \( A=A^{ * } \) real matrix \( a_{ij}=a_{ij}^{ < em>} \)
    \( A=A^{\dagger} \) hermitian \( a_{ij}=a_{ji}^{ < /em>} \)
    \( A=\left(A^{\dagger}\right )^{-1} \) unitary \( \sum_k a_{ik}a_{jk}^{ < em>}=\sum_k a_{ki}^{ < /em> } a_{kj}=\delta_{ij} \)
    @@ -906,12 +918,12 @@ $$

    @@ -1012,7 +1024,7 @@ or simply write them as double precision numbers (Python uses 64 bits as default 
    import numpy as np
-x = np.log(np.array([4.0, 7.0, 8.0])
+x = np.log(np.array([4.0, 7.0, 8.0]))
 print(x)

    @@ -1021,7 +1033,7 @@ To check the number of bytes (remember that one byte contains eight bits for dou 

    import numpy as np
-x = np.log(np.array([4.0, 7.0, 8.0])
+x = np.log(np.array([4.0, 7.0, 8.0]))
 print(x.itemsize)

    @@ -1326,7 +1338,7 @@ pretty close the basic mathematical expressions.

    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 simply as an example here of a data set. +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 @@ -1561,7 +1573,7 @@ plt.show()

    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 +\( \alpha \). 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 $$ MSE(\hat{y},\hat{\tilde{y}}) = \frac{1}{n} \sum_{i=0}^{n-1}(y_i-\tilde{y}_i)^2, $$ @@ -1621,7 +1633,7 @@ ways of dealing with outliers.

    The Huber cost function is defined as $$ -H_{\delta}(a)={\begin{cases}{\frac {1}{2}}{a^{2}}&{\text{for }}|a|\leq \delta ,\\\delta (|a|-{\frac {1}{2}}\delta ),&{\text{otherwise.}}\end{cases}}}. +H_{\delta}(a)=\left\{\begin{array}\frac{1}{2}{a^{2}}&{\text{for }}|a|\leq \delta ,\\ \delta (|a|-{\frac {1}{2}}\delta ),&{\text{otherwise.}\end{array}\right. $$ Here \( a=\boldsymbol{y} - \boldsymbol{\tilde{y}} \). diff --git a/doc/pub/week34/ipynb/Results/FigureFiles/Masses2016.png b/doc/pub/week34/ipynb/Results/FigureFiles/Masses2016.png index 10b85e2caf3c0429bc45761f2959f7a731bfa9a4..b8976c975be470aba5146a39aa9335f0d7f94c32 100644 GIT binary patch literal 16565 zcmeIabx>Ac_%Hgtlz?=13y6SpmxO?nG)Q-MH-dDDC`f~V2ucakDXDaKcX!uaFMiK& z=FZ%iGiT=B|L*9X4eq`6T2FnRSkE%zwW2gSDhVnC0zsFRkyL>|;KU#hXf!es_!kZ> za#L{Qca_p|Rdq0T^)PZagD4oeI@&t8+FBV?xtlq=SUK2pvVuR%RFfwi5DT%Ly=_SO(yeVJHEP?!7o zv^c_~B*7C&s>hQIf9N<9CX>p2llu4LI6417T7ImjCLDX~60R`2^!XkoC;J*4-`OUz zcTmyL(5Oi5d?S7M!5&o%_PZNiproW^?iM2?B0OAXR2hPUjU8W@1EB*C)uo{_;9+4b z-23qGa5Zv7Dr{`*0)hX3;Qx&|q;BxBZhCsb(mM?#Bts`>v1DcEf*A!R7_nE|&HvrV zpZkr@=;FHJ{uRg1;&9eu*rHcMI~{FN4j||IUpIBL|8wSB(n zFv%S~9@}J~Gp(Uf>>Djf)AGHf@%OsOIU)he8{dgtA^its zAq(oHym#p1U-zZ(J9$CCTEAI3Uy_p(EP9n=V`-HvuB619dC|tI$GqD>HR%xkbb zrqd*+I!tHZbenm(e}DI!wdv;7)U?OYz(Ci^9~RuXXUK4{XEm#d0UecgtPLm5WYVPE zdvY)}WE!IFw=>!xNA2}W>VoC}sN);K1}~oWAW*+ zV!dGY&_@*2apKfUc6Q{Nx`&Ijd8uWsMCBU+=lcB>o@)eCS#bfNK@f`W1g?jr8~g4*EnZzkNp^t6OPI&lDN zdLQ`lxOjJaW1@Y#q^ZN;cC^>DT>Ea#q46a%!7@DM#lqm`d(>PAT_>IiT8Z71#Qt-4 z97^QL(ni8i_?h~U1YSNb$H#^~hS#BX{=Ai#Pbn*}{j{hJ4KedXbpm(I!^yv%+}Ra} zkXE(4oti@E2o)z982S9=D{Jhh(y|Xc?n6ws$>0Y9cjuGCk1^?PrR6;C<|qB{#&E(V z7sZ}&OSdK{i70X;8!vb8Mzk9X9d!l!-W}iL25t^pK;HL`vDv-ZbXQP7r=`scR^hdq z5(7fpvYNTI=c8a66X+WmJ;NDBpFo#~$3Duv`%=OXOZC`E9$J6pycDWHaMN3h0^&l7* zhpdP3#Y)Y%F+E*O^nd!jCo#I9^AgS6$mxc#%l<4<#^fi3nl2iWKYXuw2&`KOr)(vPF;1O z@+M@@OgN1nja1S-r9(@9@%AgRm5PGX**htDoJtRj@*

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    *%{YO1^`h52L}KE diff --git a/doc/pub/week34/ipynb/week34.ipynb b/doc/pub/week34/ipynb/week34.ipynb index 9ff666182..9cfc3d56e 100644 --- a/doc/pub/week34/ipynb/week34.ipynb +++ b/doc/pub/week34/ipynb/week34.ipynb @@ -10,7 +10,7 @@ " \n", "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University\n", "\n", - "Date: **Aug 23, 2021**\n", + "Date: **Aug 24, 2021**\n", "\n", "Copyright 1999-2021, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license\n", "\n", @@ -151,7 +151,7 @@ "\n", "1. The lecture notes are collected as a jupyter-book at \n", "\n", - "In addition to the electure notes, we recommend the books of Bishop and Goodfellow et al. We will follow these texts closely and the weekly reading assignments refer to these two texts. The text by Hastie et al is also widely used in the Machine Learning community. Finally, we also recommend the hands-on text by Geron, see below.\n", + "In addition to the lecture notes, we recommend the books of Bishop and Goodfellow et al. We will follow these texts closely and the weekly reading assignments refer to these two texts. The text by Hastie et al is also widely used in the Machine Learning community. Finally, we also recommend the hands-on text by Geron, see below.\n", "\n", "1. Christopher M. Bishop, Pattern Recognition and Machine Learning, Springer, \n", "\n", @@ -181,7 +181,19 @@ "\n", "\n", "\n", - "This course aims at giving you insights and knowledge about many of the central algorithms used in Data Analysis and Machine Learning. The course is project based and through various numerical projects, normally three, you will be exposed to fundamental research problems in these fields, with the aim to reproduce state of the art scientific results. Both supervised and unsupervised methods will be covered. The emphasis is on a frequentist approach, although we will try to link it with a Bayesian approach as well. You will learn to develop and structure large codes for studying different cases where Machine Learning is applied to, get acquainted with computing facilities and learn to handle large scientific projects. A good scientific and ethical conduct is emphasized throughout the course. More specifically, after this course you will\n", + "This course aims at giving you insights and knowledge about many of\n", + "the central algorithms used in Data Analysis and Machine Learning.\n", + "The course is project based and through various numerical projects,\n", + "normally three, you will be exposed to fundamental research problems\n", + "in these fields, with the aim to reproduce state of the art scientific\n", + "results. Both supervised and unsupervised methods will be covered. The\n", + "emphasis is on a frequentist approach, although we will try to link it\n", + "with a Bayesian approach as well. You will learn to develop and\n", + "structure large codes for studying different cases where Machine\n", + "Learning is applied to, get acquainted with computing facilities and\n", + "learn to handle large scientific projects. A good scientific and\n", + "ethical conduct is emphasized throughout the course. More\n", + "specifically, after this course you will\n", "\n", "* Learn about basic data analysis, statistical analysis, Bayesian statistics, Monte Carlo sampling, data optimization and machine learning;\n", "\n", @@ -201,7 +213,7 @@ "\n", "* Autoencoders and Reinforcement Learning;\n", "\n", - "* Work on numerical projects to illustrate the theory. The projects play a central role and you are expected to know modern programming languages like Python or C++ and/or Fortran (Fortran2003 or later).\n", + "* Work on numerical projects to illustrate the theory. The projects play a central role and you are expected to know modern programming languages like Python or C++ and/or Fortran (Fortran2003 or later) or Julia or other.\n", "\n", "\n", "\n", @@ -251,7 +263,7 @@ "\n", "* Boltzmann Machines\n", "\n", - "* Unsupervised learning Dimensionality reduction, from PCA to cluster models\n", + "* Unsupervised learning Dimensionality reduction, from PCA to clustering\n", "\n", "Hands-on demonstrations, exercises and projects aim at deepening your understanding of these topics.\n", "\n", @@ -264,7 +276,7 @@ "\n", " * GIT for version control, and GitHub or GitLab as repositories, highly recommended. This will be discussed during the first exercise session\n", "\n", - " * Anaconda and other Python environments, see intro slides and first exercise session\n", + " * Anaconda and other Python environments, see intro slides and links to programming resources at \n", "\n", "\n", "\n", @@ -278,7 +290,7 @@ "\n", "1. [STK2100 Machine learning and statistical methods for prediction and classification](http://www.uio.no/studier/emner/matnat/math/STK2100/index-eng.html). \n", "\n", - "2. [IN3050 Introduction to Artificial Intelligence and Machine Learning](https://www.uio.no/studier/emner/matnat/ifi/IN3050/index-eng.html). Introductory course in machine learning and AI with an algorithmic approach. \n", + "2. [IN3050/4050 Introduction to Artificial Intelligence and Machine Learning](https://www.uio.no/studier/emner/matnat/ifi/IN3050/index-eng.html). Introductory course in machine learning and AI with an algorithmic approach. \n", "\n", "3. [STK-INF3000/4000 Selected Topics in Data Science](http://www.uio.no/studier/emner/matnat/math/STK-INF3000/index-eng.html). The course provides insight into selected contemporary relevant topics within Data Science. \n", "\n", @@ -638,14 +650,14 @@ "source": [ "\n", "\n", - "\n", + "\n", "\n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "
    Relations Name matrix elements
    Relations Name matrix elements
    $A=A^{T}$ symmetric $a_{ij}=a_{ji}$
    $A=\\left (A^{T} \\right )^{-1}$ real orthogonal $\\sum_k a_{ik}a_{jk}=\\sum_k a_{ki} a_{kj} = \\delta_{ij}$
    $A=A^{ * }$ real matrix $a_{ij}=a_{ij}^{ * }$
    $A=A^{\\dagger}$ hermitian $a_{ij}=a_{ji}^{ * }$
    $A=\\left (A^{\\dagger} \\right )^{-1}$ unitary $\\sum_k a_{ik}a_{jk}^{ * }=\\sum_k a_{ki}^{ * } a_{kj}=\\delta_{ij}$
    $A=A^{T}$ symmetric $a_{ij}=a_{ji}$
    $A=\\left (A^{T}\\right )^{-1}$ real orthogonal $\\sum_k a_{ik}a_{jk}=\\sum_k a_{ki} a_{kj}=\\delta_{ij}$
    $A=A^{ * }$ real matrix $a_{ij}=a_{ij}^{*}$
    $A=A^{\\dagger}$ hermitian $a_{ij}=a_{ji}^{*}$
    $A=\\left(A^{\\dagger}\\right )^{-1}$ unitary $\\sum_k a_{ik}a_{jk}^{*}=\\sum_k a_{ki}^{ * } a_{kj}=\\delta_{ij}$
    \n", "\n", @@ -655,19 +667,19 @@ "\n", " * Diagonal if $a_{ij}=0$ for $i\\ne j$\n", "\n", - " * Upper triangular if $a_{ij}=0$ for $i > j$\n", + " * Upper triangular if $a_{ij}=0$ for $i>j$\n", "\n", - " * Lower triangular if $a_{ij}=0$ for $i < j$\n", + " * Lower triangular if $a_{ij}=0$ for $i j+1$\n", + " * Upper Hessenberg if $a_{ij}=0$ for $i>j+1$\n", "\n", - " * Lower Hessenberg if $a_{ij}=0$ for $i < j+1$\n", + " * Lower Hessenberg if $a_{ij}=0$ for $i 1$\n", + " * Tridiagonal if $a_{ij}=0$ for $|i -j|>1$\n", "\n", - " * Lower banded with bandwidth $p$: $a_{ij}=0$ for $i > j+p$\n", + " * Lower banded with bandwidth $p$: $a_{ij}=0$ for $i>j+p$\n", "\n", - " * Upper banded with bandwidth $p$: $a_{ij}=0$ for $i < j+p$\n", + " * Upper banded with bandwidth $p$: $a_{ij}=0$ for $i j$ - * Lower triangular if $a_{ij}=0$ for $i < j$ - * Upper Hessenberg if $a_{ij}=0$ for $i > j+1$ - * Lower Hessenberg if $a_{ij}=0$ for $i < j+1$ - * Tridiagonal if $a_{ij}=0$ for $|i -j| > 1$ - * Lower banded with bandwidth $p$: $a_{ij}=0$ for $i > j+p$ - * Upper banded with bandwidth $p$: $a_{ij}=0$ for $i < j+p$ + * Upper triangular if $a_{ij}=0$ for $i>j$ + * Lower triangular if $a_{ij}=0$ for $ij+1$ + * Lower Hessenberg if $a_{ij}=0$ for $i1$ + * Lower banded with bandwidth $p$: $a_{ij}=0$ for $i>j+p$ + * Upper banded with bandwidth $p$: $a_{ij}=0$ for $i