update

doc/LectureNotes/_build/html/chapter1.html

@@ -644,7 +644,7 @@ role when we develop a specific machine learning algorithm.</p>
 <p>Machine learning is an extremely rich field, in spite of its young
 age. The increases we have seen during the last three decades in
 computational capabilities have been followed by developments of
-methods and techniques for analyzing and handling large date sets,
+methods and techniques for analyzing and handling large data sets,
 relying heavily on statistics, computer science and mathematics.  The
 field is rather new and developing rapidly. Popular software packages
 written in Python for machine learning like
@@ -666,7 +666,7 @@ 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
 hand, <em>unsupervised learning</em> is a method for finding patterns and
 relationship in data sets without any prior knowledge of the system.
-Some authours also operate with a third category, namely
+Some authors also operate with a third category, namely
 <em>reinforcement learning</em>. This is a paradigm of learning inspired by
 behavioral psychology, where learning is achieved by trial-and-error,
 solely from rewards and punishment.</p>
@@ -714,13 +714,13 @@ what is the likelihood of finding <span class="math notranslate nohighlight">\(B
 <h3><span class="section-number">3.2.2. </span>What is a good model?<a class="headerlink" href="#what-is-a-good-model" title="Permalink to this headline">¶</a></h3>
 <p>In science and engineering we often end up in situations where we want to infer (or learn) a
 quantitative model <span class="math notranslate nohighlight">\(M\)</span> for a given set of sample points <span class="math notranslate nohighlight">\(\boldsymbol{X} \in [x_1, x_2,\dots x_N]\)</span>.</p>
-<p>As we will see repeatedely in these lectures, we could try to fit these data points to a model given by a
+<p>As we will see repeatedly 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.</p>
 <p>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.</p>
+correlations that relate interesting physics interpretations.</p>
 <p>In addition, it can simplify the representation of the given data set and help
 us in making predictions about  future data samples.</p>
 <p>A first important consideration to keep in mind is that inferring the <em>correct</em> model
@@ -843,7 +843,7 @@ y = 10x+0.01 \times N(0,1),
 <p>where <span class="math notranslate nohighlight">\(x\)</span> is defined as before.  Does the fit look better? Indeed, by
 reducing the role of the noise given by the normal distribution we see immediately that
 our linear prediction seemingly reproduces better the training
-set. However, this testing ‘by the eye’ is obviouly not satisfactory in the
+set. However, this testing ‘by the eye’ is obviously not satisfactory in the
 long run. Here we have only defined the training data and our model, and
 have not discussed a more rigorous approach to the <strong>cost</strong> function.</p>
 <p>We need more rigorous criteria in defining whether we have succeeded or
@@ -957,13 +957,13 @@ example of the functionality of <strong>Scikit-Learn</strong>.</p>
 </div>
 <div class="cell_output docutils container">
 <div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>The intercept alpha: 
- [2.02408959]
+ [2.03523311]
 Coefficient beta : 
- [[4.92811987]]
-Mean squared error: 0.25
-Variance score: 0.89
+ [[4.99498108]]
+Mean squared error: 0.27
+Variance score: 0.87
 Mean squared log error: 0.01
-Mean absolute error: 0.39
+Mean absolute error: 0.41
 </pre></div>
 </div>
 <img alt="_images/chapter1_19_1.png" src="_images/chapter1_19_1.png" />
@@ -1063,7 +1063,7 @@ a linear <span class="math notranslate nohighlight">\(x\)</span>-dependence we s
 </div>
 <div class="cell_output docutils container">
 <img alt="_images/chapter1_33_0.png" src="_images/chapter1_33_0.png" />
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.005
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.00499999999999999
 </pre></div>
 </div>
 </div>