From d6eabe1d2d1f46b4642ecec52314a7173dd7337d Mon Sep 17 00:00:00 2001 From: mhjensen Date: Thu, 20 Aug 2020 05:47:13 +0200 Subject: [PATCH] revised intro slides --- .../Introduction/html/Introduction-bs.html | 314 ++++++++++++++---- .../html/Introduction-reveal.html | 286 ++++++++++++---- .../html/Introduction-solarized.html | 297 +++++++++++++---- doc/pub/Introduction/html/Introduction.html | 297 +++++++++++++---- .../ipynb/ipynb-Introduction-src.tar.gz | Bin 193 -> 193 bytes .../Introduction/pdf/Introduction-minted.pdf | Bin 214706 -> 237127 bytes doc/src/Introduction/Introduction.do.txt | 214 +++++++++--- 7 files changed, 1086 insertions(+), 322 deletions(-) diff --git a/doc/pub/Introduction/html/Introduction-bs.html b/doc/pub/Introduction/html/Introduction-bs.html index b66e0c3fc..2cee96b01 100644 --- a/doc/pub/Introduction/html/Introduction-bs.html +++ b/doc/pub/Introduction/html/Introduction-bs.html @@ -43,16 +43,49 @@ Automatically generated HTML file from DocOnce source {'highest level': 2, 'sections': [('Introduction', 2, None, '___sec0'), ('Learning outcomes', 2, None, '___sec1'), - ('Types of Machine Learning', 2, None, '___sec2'), - ('Choice of programming language', 2, None, '___sec3'), + ('Machine Learning, short overview', 2, None, '___sec2'), + ('Machine Learning, a small (and probably biased) introduction', + 2, + None, + '___sec3'), + ('Machine Learning, an extremely rich field', 2, None, '___sec4'), + ('A multidisciplinary approach', 2, None, '___sec5'), + ('Types of Machine Learning', 2, None, '___sec6'), + ('Essential elements of ML', 2, None, '___sec7'), + ('An optimization/minimization problem', 2, None, '___sec8'), + ('A Frequentist approach to data analysis', 2, None, '___sec9'), + ('What is a good model?', 2, None, '___sec10'), + ('What is a good model? Can we define it?', 2, None, '___sec11'), + ('Practicalities, choice of programming language and other ' + 'computational issues', + 2, + None, + '___sec12'), + ('Choice of Programming Language', 2, None, '___sec13'), ('Data handling, machine learning and ethical aspects', 2, None, - '___sec4')]} + '___sec14')]} end of tocinfo --> + + + + + + +
@@ -72,9 +105,19 @@ end of tocinfo --> @@ -108,11 +151,14 @@ end of tocinfo -->
[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

-

Aug 19, 2020

+

Aug 20, 2020


+

+ +

Introduction

@@ -251,7 +297,69 @@ and the jackknife methods and the infamous bias-variance tradeoff. The second part of the material covers several algorithms used in machine learning. -

Types of Machine Learning

+

+ + +

+ + +

Machine Learning, short overview

+ +

+ + +

Machine Learning, a small (and probably biased) introduction

+ +

+Ideally, machine learning represents the science of giving computers +the ability to learn without being explicitly programmed. The idea is +that there exist generic algorithms which can be used to find patterns +in a broad class of data sets without having to write code +specifically for each problem. The algorithm will build its own logic +based on the data. You should however always keep in mind that +machines and algorithms are to a large extent developed by humans. The +insights and knowledge we have about a specific system, play a central +role when we develop a specific machine learning algorithm. + +

+ + +

Machine Learning, an extremely rich field

+ +

+Machine learning is an extremely rich field, in spite of its young +age. The increases we have seen during the last decades in +computational capabilities have been followed by developments of +methods and techniques for analyzing and handling large date sets, +relying heavily on statistics, computer science and mathematics. The +field is rather new and developing rapidly. Popular software libraries +written in Python for machine learning like +Scikit-learn, +Tensorflow, +PyTorch and Keras, all +freely available at their respective GitHub sites, encompass +communities of developers in the thousands or more. And the number of +code developers and contributors keeps increasing. + +

+ + +

A multidisciplinary approach

+ +

+Not all the +algorithms and methods can be given a rigorous mathematical +justification (for example decision trees and random forests), opening up thereby large rooms for experimenting and +trial and error and thereby exciting new developments. However, a +solid command of linear algebra, multivariate theory, probability +theory, statistical data analysis, understanding errors and Monte +Carlo methods are central elements in a proper understanding of many +of the algorithms and methods we will discuss. + +

+ + +

Types of Machine Learning

The approaches to machine learning are many, but are often split into @@ -268,43 +376,144 @@ solely from rewards and punishment. Another way to categorize machine learning tasks is to consider the desired output of a system. Some of the most common tasks are: +

+ +

+ + +

+ + +

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 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. + + +

An optimization/minimization problem

-Here we will build our machine learning approach on elements of the -statistical foundation discussed above, with elements from data -analysis, stochastic processes etc. We will discuss the following -machine learning algorithms +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. -

    -
  1. Linear regression and its variants
    2. -
  2. Decision tree algorithms, from single trees to random forests
    3. -
  3. Bayesian statistics and regression
    4. -
  4. Support vector machines and finally various variants of
    5. -
  5. Artifical neural networks and deep learning, including convolutional neural networks and Bayesian neural networks
    6. -
  6. Networks for unsupervised learning using for example reduced Boltzmann machines.
    7. -
+

+ -

Choice of programming language

+

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 set of lectures. + +

+ + +

Practicalities, choice of programming language and other computational issues

+ +

+ + +

Choice of Programming Language

Python plays nowadays a central role in the development of machine @@ -316,43 +525,14 @@ Jupyter notebook framework with the possibility to run R codes or compiled programs written in C++, and much more made our choice of programming language for this series of lectures easy. However, since the focus here is not only on using existing Python libraries such -as Scikit-Learn or Tensorflow, but also on developing your own +as Scikit-Learn, Tensorflow and Pytorch, but also on developing your own algorithms and codes, we will as far as possible present many of these algorithms either as a Python codes or C++ or Fortran (or other languages) codes.

-The reason we also focus on compiled languages like C++ (or -Fortran), is that Python is still notoriously slow when we do not -utilize highly streamlined computational libraries like -Lapack or other numerical libraries -written in compiled languages (many of these libraries are written in -Fortran). Although a project like Numba -holds great promise for speeding up the unrolling of lengthy loops, C++ -and Fortran are presently still the performance winners. Numba gives -you potentially the power to speed up your applications with high -performance functions written directly in Python. In particular, -array-oriented and math-heavy Python code can achieve similar -performance to C, C++ and Fortran. However, even with these speed-ups, -for codes involving heavy Markov Chain Monte Carlo analyses and -optimizations of cost functions, C++/C or Fortran codes tend to -outperform Python codes. + -

-Presently thus, the community tends to let -code written in C++/C or Fortran do the heavy duty numerical -number crunching and leave the post-analysis of the data to the above -mentioned Python modules or software packages. However, with the developments taking place in for example the Python community, and seen -the changes during the last decade, the above situation may change swiftly in the not too distant future. - -

-Many of the examples we discuss in this series of lectures come with -existing data files or provide code examples which produce the data to -be analyzed. Most of the applications we will discuss deal with -small data sets (less than a terabyte of information) and can easily -be analyzed and tested on standard off the shelf laptops you find in general -stores. - -

Data handling, machine learning and ethical aspects

+

Data handling, machine learning and ethical aspects

In most of the cases we will study, we will either generate the data diff --git a/doc/pub/Introduction/html/Introduction-reveal.html b/doc/pub/Introduction/html/Introduction-reveal.html index 87b5520da..0be274cd8 100644 --- a/doc/pub/Introduction/html/Introduction-reveal.html +++ b/doc/pub/Introduction/html/Introduction-reveal.html @@ -107,6 +107,22 @@ td.padding { + + + + + + + @@ -132,9 +148,17 @@ td.padding {

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

 
-

Aug 19, 2020

+

Aug 20, 2020


+

+

+ © 1999-2020, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license +
+ + + +

Introduction

@@ -215,12 +239,6 @@ solid command of linear algebra, multivariate theory, probability theory, statistical data analysis, understanding errors and Monte Carlo methods are central elements in a proper understanding of many of algorithms and methods we will discuss. - -

- -

- © 1999-2020, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license -
@@ -279,8 +297,71 @@ and the jackknife methods and the infamous bias-variance tradeoff.

The second part of the material covers several algorithms used in machine learning. + -

Types of Machine Learning

+ +
+
+ + +
+

Machine Learning, short overview

+
+ + +
+

Machine Learning, a small (and probably biased) introduction

+ +

+Ideally, machine learning represents the science of giving computers +the ability to learn without being explicitly programmed. The idea is +that there exist generic algorithms which can be used to find patterns +in a broad class of data sets without having to write code +specifically for each problem. The algorithm will build its own logic +based on the data. You should however always keep in mind that +machines and algorithms are to a large extent developed by humans. The +insights and knowledge we have about a specific system, play a central +role when we develop a specific machine learning algorithm. +

+ + +
+

Machine Learning, an extremely rich field

+ +

+Machine learning is an extremely rich field, in spite of its young +age. The increases we have seen during the last decades in +computational capabilities have been followed by developments of +methods and techniques for analyzing and handling large date sets, +relying heavily on statistics, computer science and mathematics. The +field is rather new and developing rapidly. Popular software libraries +written in Python for machine learning like +Scikit-learn, +Tensorflow, +PyTorch and Keras, all +freely available at their respective GitHub sites, encompass +communities of developers in the thousands or more. And the number of +code developers and contributors keeps increasing. +

+ + +
+

A multidisciplinary approach

+ +

+Not all the +algorithms and methods can be given a rigorous mathematical +justification (for example decision trees and random forests), opening up thereby large rooms for experimenting and +trial and error and thereby exciting new developments. However, a +solid command of linear algebra, multivariate theory, probability +theory, statistical data analysis, understanding errors and Monte +Carlo methods are central elements in a proper understanding of many +of the algorithms and methods we will discuss. +

+ + +
+

Types of Machine Learning

The approaches to machine learning are many, but are often split into @@ -298,46 +379,136 @@ Another way to categorize machine learning tasks is to consider the desired output of a system. Some of the most common tasks are:

-

+

+ +
+

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. + + +

+
+ + +
+

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 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

-Here we will build our machine learning approach on elements of the -statistical foundation discussed above, with elements from data -analysis, stochastic processes etc. We will discuss the following -machine learning algorithms +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 \( A \). -

    -

  1. Linear regression and its variants
    2. -

  2. Decision tree algorithms, from single trees to random forests
    3. -

  3. Bayesian statistics and regression
    4. -

  4. Support vector machines and finally various variants of
    5. -

  5. Artifical neural networks and deep learning, including convolutional neural networks and Bayesian neural networks
    6. -

  6. Networks for unsupervised learning using for example reduced Boltzmann machines.
    7. -
+

+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. -

Choice of programming language

+

+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 set of lectures. +

+ + +
+

Practicalities, choice of programming language and other computational issues

+
+ + +
+

Choice of Programming Language

Python plays nowadays a central role in the development of machine @@ -349,43 +520,14 @@ Jupyter notebook framework with the possibility to run R codes or compiled programs written in C++, and much more made our choice of programming language for this series of lectures easy. However, since the focus here is not only on using existing Python libraries such -as Scikit-Learn or Tensorflow, but also on developing your own +as Scikit-Learn, Tensorflow and Pytorch, but also on developing your own algorithms and codes, we will as far as possible present many of these algorithms either as a Python codes or C++ or Fortran (or other languages) codes. +

-

-The reason we also focus on compiled languages like C++ (or -Fortran), is that Python is still notoriously slow when we do not -utilize highly streamlined computational libraries like -Lapack or other numerical libraries -written in compiled languages (many of these libraries are written in -Fortran). Although a project like Numba -holds great promise for speeding up the unrolling of lengthy loops, C++ -and Fortran are presently still the performance winners. Numba gives -you potentially the power to speed up your applications with high -performance functions written directly in Python. In particular, -array-oriented and math-heavy Python code can achieve similar -performance to C, C++ and Fortran. However, even with these speed-ups, -for codes involving heavy Markov Chain Monte Carlo analyses and -optimizations of cost functions, C++/C or Fortran codes tend to -outperform Python codes. -

-Presently thus, the community tends to let -code written in C++/C or Fortran do the heavy duty numerical -number crunching and leave the post-analysis of the data to the above -mentioned Python modules or software packages. However, with the developments taking place in for example the Python community, and seen -the changes during the last decade, the above situation may change swiftly in the not too distant future. - -

-Many of the examples we discuss in this series of lectures come with -existing data files or provide code examples which produce the data to -be analyzed. Most of the applications we will discuss deal with -small data sets (less than a terabyte of information) and can easily -be analyzed and tested on standard off the shelf laptops you find in general -stores. - -

Data handling, machine learning and ethical aspects

+
+

Data handling, machine learning and ethical aspects

In most of the cases we will study, we will either generate the data diff --git a/doc/pub/Introduction/html/Introduction-solarized.html b/doc/pub/Introduction/html/Introduction-solarized.html index c8a49b06e..84e2ea615 100644 --- a/doc/pub/Introduction/html/Introduction-solarized.html +++ b/doc/pub/Introduction/html/Introduction-solarized.html @@ -37,16 +37,49 @@ div { text-align: justify; text-justify: inter-word; } {'highest level': 2, 'sections': [('Introduction', 2, None, '___sec0'), ('Learning outcomes', 2, None, '___sec1'), - ('Types of Machine Learning', 2, None, '___sec2'), - ('Choice of programming language', 2, None, '___sec3'), + ('Machine Learning, short overview', 2, None, '___sec2'), + ('Machine Learning, a small (and probably biased) introduction', + 2, + None, + '___sec3'), + ('Machine Learning, an extremely rich field', 2, None, '___sec4'), + ('A multidisciplinary approach', 2, None, '___sec5'), + ('Types of Machine Learning', 2, None, '___sec6'), + ('Essential elements of ML', 2, None, '___sec7'), + ('An optimization/minimization problem', 2, None, '___sec8'), + ('A Frequentist approach to data analysis', 2, None, '___sec9'), + ('What is a good model?', 2, None, '___sec10'), + ('What is a good model? Can we define it?', 2, None, '___sec11'), + ('Practicalities, choice of programming language and other ' + 'computational issues', + 2, + None, + '___sec12'), + ('Choice of Programming Language', 2, None, '___sec13'), ('Data handling, machine learning and ethical aspects', 2, None, - '___sec4')]} + '___sec14')]} end of tocinfo --> + + + + + + + @@ -68,8 +101,10 @@ end of tocinfo -->

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

-

Aug 19, 2020

+

Aug 20, 2020


+

+









Introduction

@@ -209,7 +244,69 @@ and the jackknife methods and the infamous bias-variance tradeoff. The second part of the material covers several algorithms used in machine learning. -

Types of Machine Learning

+

+









+ +

+









+ +

Machine Learning, short overview

+ +

+









+ +

Machine Learning, a small (and probably biased) introduction

+ +

+Ideally, machine learning represents the science of giving computers +the ability to learn without being explicitly programmed. The idea is +that there exist generic algorithms which can be used to find patterns +in a broad class of data sets without having to write code +specifically for each problem. The algorithm will build its own logic +based on the data. You should however always keep in mind that +machines and algorithms are to a large extent developed by humans. The +insights and knowledge we have about a specific system, play a central +role when we develop a specific machine learning algorithm. + +

+









+ +

Machine Learning, an extremely rich field

+ +

+Machine learning is an extremely rich field, in spite of its young +age. The increases we have seen during the last decades in +computational capabilities have been followed by developments of +methods and techniques for analyzing and handling large date sets, +relying heavily on statistics, computer science and mathematics. The +field is rather new and developing rapidly. Popular software libraries +written in Python for machine learning like +Scikit-learn, +Tensorflow, +PyTorch and Keras, all +freely available at their respective GitHub sites, encompass +communities of developers in the thousands or more. And the number of +code developers and contributors keeps increasing. + +

+









+ +

A multidisciplinary approach

+ +

+Not all the +algorithms and methods can be given a rigorous mathematical +justification (for example decision trees and random forests), opening up thereby large rooms for experimenting and +trial and error and thereby exciting new developments. However, a +solid command of linear algebra, multivariate theory, probability +theory, statistical data analysis, understanding errors and Monte +Carlo methods are central elements in a proper understanding of many +of the algorithms and methods we will discuss. + +

+









+ +

Types of Machine Learning

The approaches to machine learning are many, but are often split into @@ -226,43 +323,144 @@ solely from rewards and punishment. Another way to categorize machine learning tasks is to consider the desired output of a system. Some of the most common tasks are: +

+ +

+ + +

+









+ +

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 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. +









+ +

An optimization/minimization problem

-Here we will build our machine learning approach on elements of the -statistical foundation discussed above, with elements from data -analysis, stochastic processes etc. We will discuss the following -machine learning algorithms +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. -

    -
  1. Linear regression and its variants
    2. -
  2. Decision tree algorithms, from single trees to random forests
    3. -
  3. Bayesian statistics and regression
    4. -
  4. Support vector machines and finally various variants of
    5. -
  5. Artifical neural networks and deep learning, including convolutional neural networks and Bayesian neural networks
    6. -
  6. Networks for unsupervised learning using for example reduced Boltzmann machines.
    7. -
+

+









-

Choice of programming language

+

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 set of lectures. + +

+









+ +

Practicalities, choice of programming language and other computational issues

+ +

+









+ +

Choice of Programming Language

Python plays nowadays a central role in the development of machine @@ -274,43 +472,14 @@ Jupyter notebook framework with the possibility to run R codes or compiled programs written in C++, and much more made our choice of programming language for this series of lectures easy. However, since the focus here is not only on using existing Python libraries such -as Scikit-Learn or Tensorflow, but also on developing your own +as Scikit-Learn, Tensorflow and Pytorch, but also on developing your own algorithms and codes, we will as far as possible present many of these algorithms either as a Python codes or C++ or Fortran (or other languages) codes.

-The reason we also focus on compiled languages like C++ (or -Fortran), is that Python is still notoriously slow when we do not -utilize highly streamlined computational libraries like -Lapack or other numerical libraries -written in compiled languages (many of these libraries are written in -Fortran). Although a project like Numba -holds great promise for speeding up the unrolling of lengthy loops, C++ -and Fortran are presently still the performance winners. Numba gives -you potentially the power to speed up your applications with high -performance functions written directly in Python. In particular, -array-oriented and math-heavy Python code can achieve similar -performance to C, C++ and Fortran. However, even with these speed-ups, -for codes involving heavy Markov Chain Monte Carlo analyses and -optimizations of cost functions, C++/C or Fortran codes tend to -outperform Python codes. +









-

-Presently thus, the community tends to let -code written in C++/C or Fortran do the heavy duty numerical -number crunching and leave the post-analysis of the data to the above -mentioned Python modules or software packages. However, with the developments taking place in for example the Python community, and seen -the changes during the last decade, the above situation may change swiftly in the not too distant future. - -

-Many of the examples we discuss in this series of lectures come with -existing data files or provide code examples which produce the data to -be analyzed. Most of the applications we will discuss deal with -small data sets (less than a terabyte of information) and can easily -be analyzed and tested on standard off the shelf laptops you find in general -stores. - -

Data handling, machine learning and ethical aspects

+

Data handling, machine learning and ethical aspects

In most of the cases we will study, we will either generate the data diff --git a/doc/pub/Introduction/html/Introduction.html b/doc/pub/Introduction/html/Introduction.html index 6bc3b2fd4..6196c545b 100644 --- a/doc/pub/Introduction/html/Introduction.html +++ b/doc/pub/Introduction/html/Introduction.html @@ -42,16 +42,49 @@ div { text-align: justify; text-justify: inter-word; } {'highest level': 2, 'sections': [('Introduction', 2, None, '___sec0'), ('Learning outcomes', 2, None, '___sec1'), - ('Types of Machine Learning', 2, None, '___sec2'), - ('Choice of programming language', 2, None, '___sec3'), + ('Machine Learning, short overview', 2, None, '___sec2'), + ('Machine Learning, a small (and probably biased) introduction', + 2, + None, + '___sec3'), + ('Machine Learning, an extremely rich field', 2, None, '___sec4'), + ('A multidisciplinary approach', 2, None, '___sec5'), + ('Types of Machine Learning', 2, None, '___sec6'), + ('Essential elements of ML', 2, None, '___sec7'), + ('An optimization/minimization problem', 2, None, '___sec8'), + ('A Frequentist approach to data analysis', 2, None, '___sec9'), + ('What is a good model?', 2, None, '___sec10'), + ('What is a good model? Can we define it?', 2, None, '___sec11'), + ('Practicalities, choice of programming language and other ' + 'computational issues', + 2, + None, + '___sec12'), + ('Choice of Programming Language', 2, None, '___sec13'), ('Data handling, machine learning and ethical aspects', 2, None, - '___sec4')]} + '___sec14')]} end of tocinfo --> + + + + + + + @@ -73,8 +106,10 @@ end of tocinfo -->

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

-

Aug 19, 2020

+

Aug 20, 2020


+

+









Introduction

@@ -214,7 +249,69 @@ and the jackknife methods and the infamous bias-variance tradeoff. The second part of the material covers several algorithms used in machine learning. -

Types of Machine Learning

+

+









+ +

+









+ +

Machine Learning, short overview

+ +

+









+ +

Machine Learning, a small (and probably biased) introduction

+ +

+Ideally, machine learning represents the science of giving computers +the ability to learn without being explicitly programmed. The idea is +that there exist generic algorithms which can be used to find patterns +in a broad class of data sets without having to write code +specifically for each problem. The algorithm will build its own logic +based on the data. You should however always keep in mind that +machines and algorithms are to a large extent developed by humans. The +insights and knowledge we have about a specific system, play a central +role when we develop a specific machine learning algorithm. + +

+









+ +

Machine Learning, an extremely rich field

+ +

+Machine learning is an extremely rich field, in spite of its young +age. The increases we have seen during the last decades in +computational capabilities have been followed by developments of +methods and techniques for analyzing and handling large date sets, +relying heavily on statistics, computer science and mathematics. The +field is rather new and developing rapidly. Popular software libraries +written in Python for machine learning like +Scikit-learn, +Tensorflow, +PyTorch and Keras, all +freely available at their respective GitHub sites, encompass +communities of developers in the thousands or more. And the number of +code developers and contributors keeps increasing. + +

+









+ +

A multidisciplinary approach

+ +

+Not all the +algorithms and methods can be given a rigorous mathematical +justification (for example decision trees and random forests), opening up thereby large rooms for experimenting and +trial and error and thereby exciting new developments. However, a +solid command of linear algebra, multivariate theory, probability +theory, statistical data analysis, understanding errors and Monte +Carlo methods are central elements in a proper understanding of many +of the algorithms and methods we will discuss. + +

+









+ +

Types of Machine Learning

The approaches to machine learning are many, but are often split into @@ -231,43 +328,144 @@ solely from rewards and punishment. Another way to categorize machine learning tasks is to consider the desired output of a system. Some of the most common tasks are: +

+ +

+ + +

+









+ +

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 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. +









+ +

An optimization/minimization problem

-Here we will build our machine learning approach on elements of the -statistical foundation discussed above, with elements from data -analysis, stochastic processes etc. We will discuss the following -machine learning algorithms +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. -

    -
  1. Linear regression and its variants
    2. -
  2. Decision tree algorithms, from single trees to random forests
    3. -
  3. Bayesian statistics and regression
    4. -
  4. Support vector machines and finally various variants of
    5. -
  5. Artifical neural networks and deep learning, including convolutional neural networks and Bayesian neural networks
    6. -
  6. Networks for unsupervised learning using for example reduced Boltzmann machines.
    7. -
+

+









-

Choice of programming language

+

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 set of lectures. + +

+









+ +

Practicalities, choice of programming language and other computational issues

+ +

+









+ +

Choice of Programming Language

Python plays nowadays a central role in the development of machine @@ -279,43 +477,14 @@ Jupyter notebook framework with the possibility to run R codes or compiled programs written in C++, and much more made our choice of programming language for this series of lectures easy. However, since the focus here is not only on using existing Python libraries such -as Scikit-Learn or Tensorflow, but also on developing your own +as Scikit-Learn, Tensorflow and Pytorch, but also on developing your own algorithms and codes, we will as far as possible present many of these algorithms either as a Python codes or C++ or Fortran (or other languages) codes.

-The reason we also focus on compiled languages like C++ (or -Fortran), is that Python is still notoriously slow when we do not -utilize highly streamlined computational libraries like -Lapack or other numerical libraries -written in compiled languages (many of these libraries are written in -Fortran). Although a project like Numba -holds great promise for speeding up the unrolling of lengthy loops, C++ -and Fortran are presently still the performance winners. Numba gives -you potentially the power to speed up your applications with high -performance functions written directly in Python. In particular, -array-oriented and math-heavy Python code can achieve similar -performance to C, C++ and Fortran. However, even with these speed-ups, -for codes involving heavy Markov Chain Monte Carlo analyses and -optimizations of cost functions, C++/C or Fortran codes tend to -outperform Python codes. +









-

-Presently thus, the community tends to let -code written in C++/C or Fortran do the heavy duty numerical -number crunching and leave the post-analysis of the data to the above -mentioned Python modules or software packages. However, with the developments taking place in for example the Python community, and seen -the changes during the last decade, the above situation may change swiftly in the not too distant future. - -

-Many of the examples we discuss in this series of lectures come with -existing data files or provide code examples which produce the data to -be analyzed. Most of the applications we will discuss deal with -small data sets (less than a terabyte of information) and can easily -be analyzed and tested on standard off the shelf laptops you find in general -stores. - -

Data handling, machine learning and ethical aspects

+

Data handling, machine learning and ethical aspects

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zQ=E|(bhwt-lUgj?!q}5sW)-Dh(S|rzIF76IBPkSFh~$`@5KagmIvt&qvNZaC028d> A;Q#;t diff --git a/doc/src/Introduction/Introduction.do.txt b/doc/src/Introduction/Introduction.do.txt index e29c6ff91..390446e12 100644 --- a/doc/src/Introduction/Introduction.do.txt +++ b/doc/src/Introduction/Introduction.do.txt @@ -3,7 +3,7 @@ AUTHOR: Morten Hjorth-Jensen {copyright, 1999-present|CC BY-NC} at Department of DATE: today - +!split ===== Introduction ===== During the last two decades there has been a swift and amazing @@ -131,9 +131,59 @@ machine learning. +!split + +!split +===== Machine Learning, short overview ===== + + +!split +===== Machine Learning, a small (and probably biased) introduction ===== + + +Ideally, machine learning represents the science of giving computers +the ability to learn without being explicitly programmed. The idea is +that there exist generic algorithms which can be used to find patterns +in a broad class of data sets without having to write code +specifically for each problem. The algorithm will build its own logic +based on the data. You should however always keep in mind that +machines and algorithms are to a large extent developed by humans. The +insights and knowledge we have about a specific system, play a central +role when we develop a specific machine learning algorithm. + +!split +===== Machine Learning, an extremely rich field ===== + +Machine learning is an extremely rich field, in spite of its young +age. The increases we have seen during the last decades in +computational capabilities have been followed by developments of +methods and techniques for analyzing and handling large date sets, +relying heavily on statistics, computer science and mathematics. The +field is rather new and developing rapidly. Popular software libraries +written in Python for machine learning like +"Scikit-learn":"http://scikit-learn.org/stable/", +"Tensorflow":"https://www.tensorflow.org/", +"PyTorch":"http://pytorch.org/" and "Keras":"https://keras.io/", all +freely available at their respective GitHub sites, encompass +communities of developers in the thousands or more. And the number of +code developers and contributors keeps increasing. + +!split +===== A multidisciplinary approach ===== + +Not all the +algorithms and methods can be given a rigorous mathematical +justification (for example decision trees and random forests), opening up thereby large rooms for experimenting and +trial and error and thereby exciting new developments. However, a +solid command of linear algebra, multivariate theory, probability +theory, statistical data analysis, understanding errors and Monte +Carlo methods are central elements in a proper understanding of many +of the algorithms and methods we will discuss. + +!split ===== Types of Machine Learning ===== @@ -150,42 +200,120 @@ solely from rewards and punishment. Another way to categorize machine learning tasks is to consider the desired output of a system. Some of the most common tasks are: - * Classification: Outputs are divided into two or more classes. The goal is to produce a model that assigns inputs into one of these classes. An example is to identify digits based on pictures of hand-written ones. Classification is typically supervised learning. +!bpop +* Classification: Outputs are divided into two or more classes. The goal is to produce a model that assigns inputs into one of these classes. An example is to identify digits based on pictures of hand-written ones. Classification is often supervised learning. - * Regression: Finding a functional relationship between an input data set and a reference data set. The goal is to construct a function that maps input data to continuous output values. +* Regression: Finding a functional relationship between an input data set and a reference data set. The goal is to construct a function that maps input data to continuous output values. - * Clustering: Data are divided into groups with certain common traits, without knowing the different groups beforehand. It is thus a form of unsupervised learning. +* Clustering: Data are divided into groups with certain common traits, without knowing the different groups beforehand. It is thus a form of unsupervised learning. +!epop + +!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. 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. +!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 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. +* 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. -Here we will build our machine learning approach on elements of the -statistical foundation discussed above, with elements from data -analysis, stochastic processes etc. We will discuss the following -machine learning algorithms - -o Linear regression and its variants -o Decision tree algorithms, from single trees to random forests -o Bayesian statistics and regression -o Support vector machines and finally various variants of -o Artifical neural networks and deep learning, including convolutional neural networks and Bayesian neural networks -o Networks for unsupervised learning using for example reduced Boltzmann machines. +* The last ingredient is a so-called _cost/loss_ function (or error function) which allows us to present an estimate on how good our model is in reproducing the data it is supposed to train. +!epop -===== Choice of programming language ===== + +!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 set of lectures. + +!split +===== Practicalities, choice of programming language and other computational issues ===== + +!split +===== Choice of Programming Language ===== Python plays nowadays a central role in the development of machine learning techniques and tools for data analysis. In particular, seen @@ -196,39 +324,13 @@ Jupyter notebook framework with the possibility to run _R_ codes or compiled programs written in C++, and much more made our choice of programming language for this series of lectures easy. However, since the focus here is not only on using existing Python libraries such -as _Scikit-Learn_ or _Tensorflow_, but also on developing your own +as _Scikit-Learn_, _Tensorflow_ and _Pytorch_, but also on developing your own algorithms and codes, we will as far as possible present many of these algorithms either as a Python codes or C++ or Fortran (or other languages) codes. -The reason we also focus on compiled languages like C++ (or -Fortran), is that Python is still notoriously slow when we do not -utilize highly streamlined computational libraries like -"Lapack":"http://www.netlib.org/lapack/" or other numerical libraries -written in compiled languages (many of these libraries are written in -Fortran). Although a project like "Numba":"https://numba.pydata.org/" -holds great promise for speeding up the unrolling of lengthy loops, C++ -and Fortran are presently still the performance winners. Numba gives -you potentially the power to speed up your applications with high -performance functions written directly in Python. In particular, -array-oriented and math-heavy Python code can achieve similar -performance to C, C++ and Fortran. However, even with these speed-ups, -for codes involving heavy Markov Chain Monte Carlo analyses and -optimizations of cost functions, C++/C or Fortran codes tend to -outperform Python codes. -Presently thus, the community tends to let -code written in C++/C or Fortran do the heavy duty numerical -number crunching and leave the post-analysis of the data to the above -mentioned Python modules or software packages. However, with the developments taking place in for example the Python community, and seen -the changes during the last decade, the above situation may change swiftly in the not too distant future. - -Many of the examples we discuss in this series of lectures come with -existing data files or provide code examples which produce the data to -be analyzed. Most of the applications we will discuss deal with -small data sets (less than a terabyte of information) and can easily -be analyzed and tested on standard off the shelf laptops you find in general -stores. +!split ===== Data handling, machine learning and ethical aspects ===== In most of the cases we will study, we will either generate the data @@ -324,3 +426,5 @@ society. + +