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<head>
<meta charset="utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>15. Getting started, our first data and Machine Learning encounters &#8212; Applied Machine Learning and Data Analysis</title>
<title>2. Getting started, our first data and Machine Learning encounters &#8212; Applied Machine Learning and Data Analysis</title>
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/all.min.css" integrity="sha384-KA6wR/X5RY4zFAHpv/CnoG2UW1uogYfdnP67Uv7eULvTveboZJg0qUpmJZb5VqzN" crossorigin="anonymous">
<link href="_static/css/index.css" rel="stylesheet">
<link rel="stylesheet" href="_static/sphinx-book-theme.css" type="text/css" />
@@ -38,7 +38,7 @@
<script async="async" src="_static/sphinx-thebe.js"></script>
<link rel="index" title="Index" href="genindex.html" />
<link rel="search" title="Search" href="search.html" />
<link rel="next" title="16. Linear Regression and more Advanced Regression Analysis" href="chapter4.html" />
<link rel="next" title="3. Linear Regression and more Advanced Regression Analysis" href="chapter4.html" />
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<meta name="viewport" content="width=device-width, initial-scale=1">
@@ -90,99 +90,34 @@
1. Elements of Probability Theory and Statistical Data Analysis
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="chapter2.html#random-numbers">
2. Random Numbers
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="chapter2.html#random-numbers-better-name-pseudo-random-numbers">
3. Random Numbers, better name: pseudo random numbers
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="chapter2.html#random-number-generator-rng">
4. Random number generator RNG
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="chapter2.html#random-number-generator-rng-and-periodic-outputs">
5. Random number generator RNG and periodic outputs
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="chapter2.html#random-number-generator-rng-and-its-period">
6. Random number generator RNG and its period
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="chapter2.html#random-number-generator-rng-other-examples">
7. Random number generator RNG, other examples
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="chapter2.html#id9">
8. Random number generator RNG, other examples
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="chapter2.html#random-number-generator-rng-ran0">
9. Random number generator RNG, RAN0
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="chapter2.html#id10">
10. Random number generator RNG, RAN0
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="chapter2.html#id11">
11. Random number generator RNG, RAN0
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="chapter2.html#id12">
12. Random number generator RNG, RAN0
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="chapter2.html#random-number-generator-rng-ran0-code">
13. Random number generator RNG, RAN0 code
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="chapter2.html#which-rng-should-i-use">
14. Which RNG should I use?
</a>
</li>
<li class="toctree-l1 current active">
<a class="current reference internal" href="#">
15. Getting started, our first data and Machine Learning encounters
2. Getting started, our first data and Machine Learning encounters
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="chapter4.html">
16. Linear Regression and more Advanced Regression Analysis
3. Linear Regression and more Advanced Regression Analysis
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="chapter5.html">
17. Logistic Regression
4. Logistic Regression
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="chapter6.html">
18. Neural networks, from the simple perceptron to deep learning
5. Neural networks, from the simple perceptron to deep learning
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="chapter7.html">
19. Support Vector Machines, overarching aims
6. Support Vector Machines, overarching aims
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="chapter8.html">
20. Dimensionality Reduction
7. Dimensionality Reduction
</a>
</li>
</ul>
@@ -257,89 +192,89 @@
<ul class="nav section-nav flex-column">
<li class="toc-h2 nav-item toc-entry">
<a class="reference internal nav-link" href="#introduction">
15.1. Introduction
2.1. Introduction
</a>
</li>
<li class="toc-h2 nav-item toc-entry">
<a class="reference internal nav-link" href="#what-is-machine-learning">
15.2. What is Machine Learning?
2.2. What is Machine Learning?
</a>
</li>
<li class="toc-h2 nav-item toc-entry">
<a class="reference internal nav-link" href="#types-of-machine-learning">
15.3. Types of Machine Learning
2.3. Types of Machine Learning
</a>
</li>
<li class="toc-h2 nav-item toc-entry">
<a class="reference internal nav-link" href="#software-and-needed-installations">
15.4. Software and needed installations
2.4. Software and needed installations
</a>
</li>
<li class="toc-h2 nav-item toc-entry">
<a class="reference internal nav-link" href="#python-installers">
15.5. Python installers
2.5. Python installers
</a>
</li>
<li class="toc-h2 nav-item toc-entry">
<a class="reference internal nav-link" href="#useful-python-libraries">
15.6. Useful Python libraries
2.6. Useful Python libraries
</a>
</li>
<li class="toc-h2 nav-item toc-entry">
<a class="reference internal nav-link" href="#installing-r-c-cython-or-julia">
15.7. Installing R, C++, cython or Julia
2.7. Installing R, C++, cython or Julia
</a>
</li>
<li class="toc-h2 nav-item toc-entry">
<a class="reference internal nav-link" href="#installing-r-c-cython-numba-etc">
15.8. Installing R, C++, cython, Numba etc
2.8. Installing R, C++, cython, Numba etc
</a>
</li>
<li class="toc-h2 nav-item toc-entry">
<a class="reference internal nav-link" href="#numpy-examples-and-important-matrix-and-vector-handling-packages">
15.9. Numpy examples and Important Matrix and vector handling packages
2.9. Numpy examples and Important Matrix and vector handling packages
</a>
</li>
<li class="toc-h2 nav-item toc-entry">
<a class="reference internal nav-link" href="#basic-matrix-features">
15.10. Basic Matrix Features
2.10. Basic Matrix Features
</a>
<ul class="nav section-nav flex-column">
<li class="toc-h3 nav-item toc-entry">
<a class="reference internal nav-link" href="#some-famous-matrices">
15.10.1. Some famous Matrices
2.10.1. Some famous Matrices
</a>
</li>
<li class="toc-h3 nav-item toc-entry">
<a class="reference internal nav-link" href="#more-basic-matrix-features">
15.10.2. More Basic Matrix Features
2.10.2. More Basic Matrix Features
</a>
</li>
</ul>
</li>
<li class="toc-h2 nav-item toc-entry">
<a class="reference internal nav-link" href="#numpy-and-arrays">
15.11. Numpy and arrays
2.11. Numpy and arrays
</a>
</li>
<li class="toc-h2 nav-item toc-entry">
<a class="reference internal nav-link" href="#matrices-in-python">
15.12. Matrices in Python
2.12. Matrices in Python
</a>
</li>
<li class="toc-h2 nav-item toc-entry">
<a class="reference internal nav-link" href="#meet-the-pandas">
15.13. Meet the Pandas
2.13. Meet the Pandas
</a>
</li>
<li class="toc-h2 nav-item toc-entry">
<a class="reference internal nav-link" href="#reading-data-and-fitting">
15.14. Reading Data and fitting
2.14. Reading Data and fitting
</a>
<ul class="nav section-nav flex-column">
<li class="toc-h3 nav-item toc-entry">
<a class="reference internal nav-link" href="#simple-linear-regression-model-using-scikit-learn">
15.14.1. Simple linear regression model using
2.14.1. Simple linear regression model using
<strong>
scikit-learn
</strong>
@@ -347,29 +282,29 @@
</li>
<li class="toc-h3 nav-item toc-entry">
<a class="reference internal nav-link" href="#to-our-real-data-nuclear-binding-energies-brief-reminder-on-masses-and-binding-energies">
15.14.2. To our real data: nuclear binding energies. Brief reminder on masses and binding energies
2.14.2. To our real data: nuclear binding energies. Brief reminder on masses and binding energies
</a>
</li>
<li class="toc-h3 nav-item toc-entry">
<a class="reference internal nav-link" href="#organizing-our-data">
15.14.3. Organizing our data
2.14.3. Organizing our data
</a>
</li>
<li class="toc-h3 nav-item toc-entry">
<a class="reference internal nav-link" href="#seeing-the-wood-for-the-trees">
15.14.4. Seeing the wood for the trees
2.14.4. Seeing the wood for the trees
</a>
</li>
<li class="toc-h3 nav-item toc-entry">
<a class="reference internal nav-link" href="#and-what-about-using-neural-networks">
15.14.5. And what about using neural networks?
2.14.5. And what about using neural networks?
</a>
</li>
</ul>
</li>
<li class="toc-h2 nav-item toc-entry">
<a class="reference internal nav-link" href="#a-first-summary">
15.15. A first summary
2.15. A first summary
</a>
</li>
</ul>
@@ -383,9 +318,9 @@
<div>
<div class="section" id="getting-started-our-first-data-and-machine-learning-encounters">
<h1><span class="section-number">15. </span>Getting started, our first data and Machine Learning encounters<a class="headerlink" href="#getting-started-our-first-data-and-machine-learning-encounters" title="Permalink to this headline"></a></h1>
<h1><span class="section-number">2. </span>Getting started, our first data and Machine Learning encounters<a class="headerlink" href="#getting-started-our-first-data-and-machine-learning-encounters" title="Permalink to this headline"></a></h1>
<div class="section" id="introduction">
<h2><span class="section-number">15.1. </span>Introduction<a class="headerlink" href="#introduction" title="Permalink to this headline"></a></h2>
<h2><span class="section-number">2.1. </span>Introduction<a class="headerlink" href="#introduction" title="Permalink to this headline"></a></h2>
<p>Our emphasis throughout this series of lectures<br />
is on understanding the mathematical aspects of
different algorithms used in the fields of data analysis and machine learning.</p>
@@ -417,7 +352,7 @@ well as allowing you to set up models and produce your own data and
get started with programming.</p>
</div>
<div class="section" id="what-is-machine-learning">
<h2><span class="section-number">15.2. </span>What is Machine Learning?<a class="headerlink" href="#what-is-machine-learning" title="Permalink to this headline"></a></h2>
<h2><span class="section-number">2.2. </span>What is Machine Learning?<a class="headerlink" href="#what-is-machine-learning" title="Permalink to this headline"></a></h2>
<p>Statistics, data science and machine learning form important fields of
research in modern science. They describe how to learn and make
predictions from data, as well as allowing us to extract important
@@ -478,7 +413,7 @@ Carlo methods are central elements in a proper understanding of many
of algorithms and methods we will discuss.</p>
</div>
<div class="section" id="types-of-machine-learning">
<h2><span class="section-number">15.3. </span>Types of Machine Learning<a class="headerlink" href="#types-of-machine-learning" title="Permalink to this headline"></a></h2>
<h2><span class="section-number">2.3. </span>Types of Machine Learning<a class="headerlink" href="#types-of-machine-learning" title="Permalink to this headline"></a></h2>
<p>The approaches to machine learning are many, but are often split into
two main categories. In <em>supervised learning</em> we know the answer to a
problem, and let the computer deduce the logic behind it. On the other
@@ -506,7 +441,7 @@ is in reproducing the data it is supposed to train.<br />
At the heart of basically all ML algorithms there are so-called minimization algorithms, often we end up with various variants of <strong>gradient</strong> methods.</p>
</div>
<div class="section" id="software-and-needed-installations">
<h2><span class="section-number">15.4. </span>Software and needed installations<a class="headerlink" href="#software-and-needed-installations" title="Permalink to this headline"></a></h2>
<h2><span class="section-number">2.4. </span>Software and needed installations<a class="headerlink" href="#software-and-needed-installations" title="Permalink to this headline"></a></h2>
<p>We will make extensive use of Python as programming language and its
myriad of available libraries. You will find
Jupyter notebooks invaluable in your work. You can run <strong>R</strong>
@@ -535,7 +470,7 @@ you can use <strong>pip</strong> as well and simply install Python as</p>
<p>etc etc.</p>
</div>
<div class="section" id="python-installers">
<h2><span class="section-number">15.5. </span>Python installers<a class="headerlink" href="#python-installers" title="Permalink to this headline"></a></h2>
<h2><span class="section-number">2.5. </span>Python installers<a class="headerlink" href="#python-installers" title="Permalink to this headline"></a></h2>
<p>If you don’t want to perform these operations separately and venture
into the hassle of exploring how to set up dependencies and paths, we
recommend two widely used distrubutions which set up all relevant
@@ -559,7 +494,7 @@ license.</p>
no setup and runs entirely in the cloud. Try it out!</p>
</div>
<div class="section" id="useful-python-libraries">
<h2><span class="section-number">15.6. </span>Useful Python libraries<a class="headerlink" href="#useful-python-libraries" title="Permalink to this headline"></a></h2>
<h2><span class="section-number">2.6. </span>Useful Python libraries<a class="headerlink" href="#useful-python-libraries" title="Permalink to this headline"></a></h2>
<p>Here we list several useful Python libraries we strongly recommend (if you use anaconda many of these are already there)</p>
<ul class="simple">
<li><p><a class="reference external" href="https://www.numpy.org/">NumPy</a> is a highly popular library for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays</p></li>
@@ -576,7 +511,7 @@ no setup and runs entirely in the cloud. Try it out!</p>
</ul>
</div>
<div class="section" id="installing-r-c-cython-or-julia">
<h2><span class="section-number">15.7. </span>Installing R, C++, cython or Julia<a class="headerlink" href="#installing-r-c-cython-or-julia" title="Permalink to this headline"></a></h2>
<h2><span class="section-number">2.7. </span>Installing R, C++, cython or Julia<a class="headerlink" href="#installing-r-c-cython-or-julia" title="Permalink to this headline"></a></h2>
<p>You will also find it convenient to utilize <strong>R</strong>. We will mainly
use Python during our lectures and in various projects and exercises.
Those of you
@@ -591,7 +526,7 @@ lectures.</p>
<a class="reference external" href="https://mpacer.org/maths/r-kernel-for-ipython-notebook">follow the link here</a></p>
</div>
<div class="section" id="installing-r-c-cython-numba-etc">
<h2><span class="section-number">15.8. </span>Installing R, C++, cython, Numba etc<a class="headerlink" href="#installing-r-c-cython-numba-etc" title="Permalink to this headline"></a></h2>
<h2><span class="section-number">2.8. </span>Installing R, C++, cython, Numba etc<a class="headerlink" href="#installing-r-c-cython-numba-etc" title="Permalink to this headline"></a></h2>
<p>For the C++ aficionados, Jupyter/IPython notebook allows you also to
install C++ and run codes written in this language interactively in
the browser. Since we will emphasize writing many of the algorithms
@@ -616,7 +551,7 @@ further processing. For example, convert to latex as</p>
formats, ipython notebooks, latex files, pdf files etc with minimal edits. These lectures were generated using <strong>doconce</strong>.</p>
</div>
<div class="section" id="numpy-examples-and-important-matrix-and-vector-handling-packages">
<h2><span class="section-number">15.9. </span>Numpy examples and Important Matrix and vector handling packages<a class="headerlink" href="#numpy-examples-and-important-matrix-and-vector-handling-packages" title="Permalink to this headline"></a></h2>
<h2><span class="section-number">2.9. </span>Numpy examples and Important Matrix and vector handling packages<a class="headerlink" href="#numpy-examples-and-important-matrix-and-vector-handling-packages" title="Permalink to this headline"></a></h2>
<p>There are several central software libraries for linear algebra and eigenvalue problems. Several of the more
popular ones have been wrapped into ofter software packages like those from the widely used text <strong>Numerical Recipes</strong>. The original source codes in many of the available packages are often taken from the widely used
software package LAPACK, which follows two other popular packages
@@ -628,7 +563,7 @@ developed in the 1970s, namely EISPACK and LINPACK. We describe them shortly he
</ul>
</div>
<div class="section" id="basic-matrix-features">
<h2><span class="section-number">15.10. </span>Basic Matrix Features<a class="headerlink" href="#basic-matrix-features" title="Permalink to this headline"></a></h2>
<h2><span class="section-number">2.10. </span>Basic Matrix Features<a class="headerlink" href="#basic-matrix-features" title="Permalink to this headline"></a></h2>
<p><strong>Matrix properties reminder.</strong></p>
<div class="math notranslate nohighlight">
\[\begin{split}
@@ -663,7 +598,7 @@ developed in the 1970s, namely EISPACK and LINPACK. We describe them shortly he
</tbody>
</table>
<div class="section" id="some-famous-matrices">
<h3><span class="section-number">15.10.1. </span>Some famous Matrices<a class="headerlink" href="#some-famous-matrices" title="Permalink to this headline"></a></h3>
<h3><span class="section-number">2.10.1. </span>Some famous Matrices<a class="headerlink" href="#some-famous-matrices" title="Permalink to this headline"></a></h3>
<ul class="simple">
<li><p>Diagonal if <span class="math notranslate nohighlight">\(a_{ij}=0\)</span> for <span class="math notranslate nohighlight">\(i\ne j\)</span></p></li>
<li><p>Upper triangular if <span class="math notranslate nohighlight">\(a_{ij}=0\)</span> for <span class="math notranslate nohighlight">\(i &gt; j\)</span></p></li>
@@ -677,7 +612,7 @@ developed in the 1970s, namely EISPACK and LINPACK. We describe them shortly he
</ul>
</div>
<div class="section" id="more-basic-matrix-features">
<h3><span class="section-number">15.10.2. </span>More Basic Matrix Features<a class="headerlink" href="#more-basic-matrix-features" title="Permalink to this headline"></a></h3>
<h3><span class="section-number">2.10.2. </span>More Basic Matrix Features<a class="headerlink" href="#more-basic-matrix-features" title="Permalink to this headline"></a></h3>
<p><strong>Some Equivalent Statements.</strong></p>
<p>For an <span class="math notranslate nohighlight">\(N\times N\)</span> matrix <span class="math notranslate nohighlight">\(\mathbf{A}\)</span> the following properties are all equivalent</p>
<ul class="simple">
@@ -691,7 +626,7 @@ developed in the 1970s, namely EISPACK and LINPACK. We describe them shortly he
</div>
</div>
<div class="section" id="numpy-and-arrays">
<h2><span class="section-number">15.11. </span>Numpy and arrays<a class="headerlink" href="#numpy-and-arrays" title="Permalink to this headline"></a></h2>
<h2><span class="section-number">2.11. </span>Numpy and arrays<a class="headerlink" href="#numpy-and-arrays" title="Permalink to this headline"></a></h2>
<p><a class="reference external" href="http://www.numpy.org/">Numpy</a> provides an easy way to handle arrays in Python. The standard way to import this library is as</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
@@ -818,7 +753,7 @@ The attentive reader will also notice that the output is <span class="math notra
</div>
</div>
<div class="section" id="matrices-in-python">
<h2><span class="section-number">15.12. </span>Matrices in Python<a class="headerlink" href="#matrices-in-python" title="Permalink to this headline"></a></h2>
<h2><span class="section-number">2.12. </span>Matrices in Python<a class="headerlink" href="#matrices-in-python" title="Permalink to this headline"></a></h2>
<p>Having defined vectors, we are now ready to try out matrices. We can
define a <span class="math notranslate nohighlight">\(3 \times 3 \)</span> real matrix <span class="math notranslate nohighlight">\(\hat{A}\)</span> as (recall that we user
lowercase letters for vectors and uppercase letters for matrices)</p>
@@ -963,7 +898,7 @@ covariance matrix through the <strong>np.linalg.eig()</strong> function.</p>
</div>
</div>
<div class="section" id="meet-the-pandas">
<h2><span class="section-number">15.13. </span>Meet the Pandas<a class="headerlink" href="#meet-the-pandas" title="Permalink to this headline"></a></h2>
<h2><span class="section-number">2.13. </span>Meet the Pandas<a class="headerlink" href="#meet-the-pandas" title="Permalink to this headline"></a></h2>
<!-- dom:FIGURE: [fig/pandas.jpg, width=600 frac=0.8] -->
<!-- begin figure -->
<p></p>
@@ -1091,7 +1026,7 @@ As we will see below it leads also to a very concice code close to the mathemati
For multidimensional arrays, we recommend strongly <a class="reference external" href="http://xarray.pydata.org/en/stable/">xarray</a>. <strong>xarray</strong> has much of the same flexibility as <strong>pandas</strong>, but allows for the extension to higher dimensions than two. We will see examples later of the usage of both <strong>pandas</strong> and <strong>xarray</strong>.</p>
</div>
<div class="section" id="reading-data-and-fitting">
<h2><span class="section-number">15.14. </span>Reading Data and fitting<a class="headerlink" href="#reading-data-and-fitting" title="Permalink to this headline"></a></h2>
<h2><span class="section-number">2.14. </span>Reading Data and fitting<a class="headerlink" href="#reading-data-and-fitting" title="Permalink to this headline"></a></h2>
<p>In order to study various Machine Learning algorithms, we need to
access data. Acccessing data is an essential step in all machine
learning algorithms. In particular, setting up the so-called <strong>design
@@ -1117,7 +1052,7 @@ you can easily implement other algorithms like decision trees and random forests
<p>But before we really start with nuclear physics data, let’s just look at some simpler polynomial fitting cases, such as,
(don’t be offended) fitting straight lines!</p>
<div class="section" id="simple-linear-regression-model-using-scikit-learn">
<h3><span class="section-number">15.14.1. </span>Simple linear regression model using <strong>scikit-learn</strong><a class="headerlink" href="#simple-linear-regression-model-using-scikit-learn" title="Permalink to this headline"></a></h3>
<h3><span class="section-number">2.14.1. </span>Simple linear regression model using <strong>scikit-learn</strong><a class="headerlink" href="#simple-linear-regression-model-using-scikit-learn" title="Permalink to this headline"></a></h3>
<p>We start with perhaps our simplest possible example, using <strong>Scikit-Learn</strong> to perform linear regression analysis on a data set produced by us.</p>
<p>What follows is a simple Python code where we have defined a function
<span class="math notranslate nohighlight">\(y\)</span> in terms of the variable <span class="math notranslate nohighlight">\(x\)</span>. Both are defined as vectors with <span class="math notranslate nohighlight">\(100\)</span> entries.
@@ -1400,7 +1335,7 @@ a linear <span class="math notranslate nohighlight">\(x\)</span>-dependence we s
</div>
</div>
<div class="section" id="to-our-real-data-nuclear-binding-energies-brief-reminder-on-masses-and-binding-energies">
<h3><span class="section-number">15.14.2. </span>To our real data: nuclear binding energies. Brief reminder on masses and binding energies<a class="headerlink" href="#to-our-real-data-nuclear-binding-energies-brief-reminder-on-masses-and-binding-energies" title="Permalink to this headline"></a></h3>
<h3><span class="section-number">2.14.2. </span>To our real data: nuclear binding energies. Brief reminder on masses and binding energies<a class="headerlink" href="#to-our-real-data-nuclear-binding-energies-brief-reminder-on-masses-and-binding-energies" title="Permalink to this headline"></a></h3>
<p>Let us now dive into nuclear physics and remind ourselves briefly about some basic features about binding
energies. A basic quantity which can be measured for the ground
states of nuclei is the atomic mass <span class="math notranslate nohighlight">\(M(N, Z)\)</span> of the neutral atom with
@@ -1463,7 +1398,7 @@ arises from the tendency of proton pairs and neutron pairs to
occur. An even number of particles is more stable than an odd number.</p>
</div>
<div class="section" id="organizing-our-data">
<h3><span class="section-number">15.14.3. </span>Organizing our data<a class="headerlink" href="#organizing-our-data" title="Permalink to this headline"></a></h3>
<h3><span class="section-number">2.14.3. </span>Organizing our data<a class="headerlink" href="#organizing-our-data" title="Permalink to this headline"></a></h3>
<p>Let us start with reading and organizing our data.
We start with the compilation of masses and binding energies from 2016.
After having downloaded this file to our own computer, we are now ready to read the file and start structuring our data.</p>
@@ -1650,7 +1585,7 @@ Now we can print measures of how our fit is doing, the coefficients from the fit
</div>
</div>
<div class="section" id="seeing-the-wood-for-the-trees">
<h3><span class="section-number">15.14.4. </span>Seeing the wood for the trees<a class="headerlink" href="#seeing-the-wood-for-the-trees" title="Permalink to this headline"></a></h3>
<h3><span class="section-number">2.14.4. </span>Seeing the wood for the trees<a class="headerlink" href="#seeing-the-wood-for-the-trees" title="Permalink to this headline"></a></h3>
<p>As a teaser, let us now see how we can do this with decision trees using <strong>scikit-learn</strong>. Later we will switch to so-called <strong>random forests</strong>!</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
@@ -1689,7 +1624,7 @@ Now we can print measures of how our fit is doing, the coefficients from the fit
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</div>
<div class="section" id="and-what-about-using-neural-networks">
<h3><span class="section-number">15.14.5. </span>And what about using neural networks?<a class="headerlink" href="#and-what-about-using-neural-networks" title="Permalink to this headline"></a></h3>
<h3><span class="section-number">2.14.5. </span>And what about using neural networks?<a class="headerlink" href="#and-what-about-using-neural-networks" title="Permalink to this headline"></a></h3>
<p>The <strong>seaborn</strong> package allows us to visualize data in an efficient way. Note that we use <strong>scikit-learn</strong>’s multi-layer perceptron (or feed forward neural network)
functionality.</p>
<div class="cell docutils container">
@@ -1730,7 +1665,7 @@ functionality.</p>
</div>
</div>
<div class="section" id="a-first-summary">
<h2><span class="section-number">15.15. </span>A first summary<a class="headerlink" href="#a-first-summary" title="Permalink to this headline"></a></h2>
<h2><span class="section-number">2.15. </span>A first summary<a class="headerlink" href="#a-first-summary" title="Permalink to this headline"></a></h2>
<p>The aim behind these introductory words was to present to you various
Python libraries and their functionalities, in particular libraries like
<strong>numpy</strong>, <strong>pandas</strong>, <strong>xarray</strong> and <strong>matplotlib</strong> and other that make our life much easier
@@ -1771,7 +1706,7 @@ Now it is time to dive more into the details of various methods. We will start w
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