This commit is contained in:
mhjensen
2020-09-18 06:13:34 +02:00
parent 59a9e35caf
commit f3a24115ea
9 changed files with 116 additions and 227 deletions
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@@ -217,7 +217,7 @@ in the data set (see the full example below).
One simple way to get a discrete output is to have sign
functions that map the output of a linear regressor to values \( \{0,1\} \),
\( f(s_i)=sign(s_i)=1 \) if \( s_i\ge 0 \) and 0 if otherwise.
We will encounter this model in our first demonstration of neural networks. Historically it is called the "perceptron" model in the machine learning
We will encounter this model in our first demonstration of neural networks. Historically it is called the ``perceptron" model in the machine learning
literature. This model is extremely simple. However, in many cases it is more
favorable to use a ``soft" classifier that outputs
the probability of a given category. This leads us to the logistic function.
+1 -1
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@@ -206,7 +206,7 @@ MathJax.Hub.Config({
<h2 id="___sec26" class="anchor">Simple example </h2>
<p>
The following example on data for coronary heart disease (CHD) as function of age may serve as an illustration. In the code here we read and plot for whether a person has had CHD (output = 1) or not (output = 0) is plotted against age. Clearly, the figure shows that attempting to make a standard lineae regression fit may not be very meaningful.
The following example on data for coronary heart disease (CHD) as function of age may serve as an illustration. In the code here we read and plot whether a person has had CHD (output = 1) or not (output = 0). This ouput is plotted the person's against age. Clearly, the figure shows that attempting to make a standard linear regression fit may not be very meaningful.
<p>
+1 -1
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@@ -207,7 +207,7 @@ MathJax.Hub.Config({
<p>
Another widely studied model, is the so-called
perceptron model, which is an example of a ``hard classification&quot; model. We
perceptron model, which is an example of a &quot;hard classification&quot; model. We
will encounter this model when we discuss neural networks as
well. Each datapoint is deterministically assigned to a category (i.e
\( y_i=0 \) or \( y_i=1 \)). In many cases, and the coronary heart disease data forms one of many such examples, it is favorable to have a &quot;soft&quot;
+1 -4
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@@ -242,12 +242,9 @@ plt<span style="color: #666666">.</span>show()
correlation_matrix <span style="color: #666666">=</span> cancerpd<span style="color: #666666">.</span>corr()<span style="color: #666666">.</span>round(<span style="color: #666666">1</span>)
<span style="color: #408080; font-style: italic"># use the heatmap function from seaborn to plot the correlation matrix</span>
<span style="color: #408080; font-style: italic"># annot = True to print the values inside the square</span>
plt<span style="color: #666666">.</span>figure(figsize<span style="color: #666666">=</span>(<span style="color: #666666">15</span>,<span style="color: #666666">8</span>))
sns<span style="color: #666666">.</span>heatmap(data<span style="color: #666666">=</span>correlation_matrix, annot<span style="color: #666666">=</span><span style="color: #008000">True</span>)
plt<span style="color: #666666">.</span>show()
<span style="color: #408080; font-style: italic">#print eigvalues of correlation matrix</span>
EigValues, EigVectors <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>eig(correlation_matrix)
<span style="color: #008000; font-weight: bold">print</span>(EigValues)
</pre></div>
<p>
<p>
+4 -7
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@@ -1333,7 +1333,7 @@ in the data set (see the full example below).
One simple way to get a discrete output is to have sign
functions that map the output of a linear regressor to values \( \{0,1\} \),
\( f(s_i)=sign(s_i)=1 \) if \( s_i\ge 0 \) and 0 if otherwise.
We will encounter this model in our first demonstration of neural networks. Historically it is called the &quot;perceptron" model in the machine learning
We will encounter this model in our first demonstration of neural networks. Historically it is called the ``perceptron" model in the machine learning
literature. This model is extremely simple. However, in many cases it is more
favorable to use a ``soft" classifier that outputs
the probability of a given category. This leads us to the logistic function.
@@ -1344,7 +1344,7 @@ the probability of a given category. This leads us to the logistic function.
<h2 id="___sec26">Simple example </h2>
<p>
The following example on data for coronary heart disease (CHD) as function of age may serve as an illustration. In the code here we read and plot for whether a person has had CHD (output = 1) or not (output = 0) is plotted against age. Clearly, the figure shows that attempting to make a standard lineae regression fit may not be very meaningful.
The following example on data for coronary heart disease (CHD) as function of age may serve as an illustration. In the code here we read and plot whether a person has had CHD (output = 1) or not (output = 0). This ouput is plotted the person's against age. Clearly, the figure shows that attempting to make a standard linear regression fit may not be very meaningful.
<p>
@@ -1453,7 +1453,7 @@ representing the probability for finding a value of \( y_i \) with a given
<p>
Another widely studied model, is the so-called
perceptron model, which is an example of a ``hard classification&quot; model. We
perceptron model, which is an example of a &quot;hard classification&quot; model. We
will encounter this model when we discuss neural networks as
well. Each datapoint is deterministically assigned to a category (i.e
\( y_i=0 \) or \( y_i=1 \)). In many cases, and the coronary heart disease data forms one of many such examples, it is favorable to have a &quot;soft&quot;
@@ -1852,12 +1852,9 @@ plt.show()
correlation_matrix = cancerpd.corr().round(<span style="color: #B452CD">1</span>)
<span style="color: #228B22"># use the heatmap function from seaborn to plot the correlation matrix</span>
<span style="color: #228B22"># annot = True to print the values inside the square</span>
plt.figure(figsize=(<span style="color: #B452CD">15</span>,<span style="color: #B452CD">8</span>))
sns.heatmap(data=correlation_matrix, annot=<span style="color: #658b00">True</span>)
plt.show()
<span style="color: #228B22">#print eigvalues of correlation matrix</span>
EigValues, EigVectors = np.linalg.eig(correlation_matrix)
<span style="color: #8B008B; font-weight: bold">print</span>(EigValues)
</pre></div>
</section>
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@@ -1265,7 +1265,7 @@ in the data set (see the full example below).
One simple way to get a discrete output is to have sign
functions that map the output of a linear regressor to values \( \{0,1\} \),
\( f(s_i)=sign(s_i)=1 \) if \( s_i\ge 0 \) and 0 if otherwise.
We will encounter this model in our first demonstration of neural networks. Historically it is called the &quot;perceptron" model in the machine learning
We will encounter this model in our first demonstration of neural networks. Historically it is called the ``perceptron" model in the machine learning
literature. This model is extremely simple. However, in many cases it is more
favorable to use a ``soft" classifier that outputs
the probability of a given category. This leads us to the logistic function.
@@ -1276,7 +1276,7 @@ the probability of a given category. This leads us to the logistic function.
<h2 id="___sec26">Simple example </h2>
<p>
The following example on data for coronary heart disease (CHD) as function of age may serve as an illustration. In the code here we read and plot for whether a person has had CHD (output = 1) or not (output = 0) is plotted against age. Clearly, the figure shows that attempting to make a standard lineae regression fit may not be very meaningful.
The following example on data for coronary heart disease (CHD) as function of age may serve as an illustration. In the code here we read and plot whether a person has had CHD (output = 1) or not (output = 0). This ouput is plotted the person's against age. Clearly, the figure shows that attempting to make a standard linear regression fit may not be very meaningful.
<p>
@@ -1382,7 +1382,7 @@ representing the probability for finding a value of \( y_i \) with a given
<p>
Another widely studied model, is the so-called
perceptron model, which is an example of a ``hard classification&quot; model. We
perceptron model, which is an example of a &quot;hard classification&quot; model. We
will encounter this model when we discuss neural networks as
well. Each datapoint is deterministically assigned to a category (i.e
\( y_i=0 \) or \( y_i=1 \)). In many cases, and the coronary heart disease data forms one of many such examples, it is favorable to have a &quot;soft&quot;
@@ -1743,12 +1743,9 @@ plt.show()
correlation_matrix = cancerpd.corr().round(<span style="color: #B452CD">1</span>)
<span style="color: #228B22"># use the heatmap function from seaborn to plot the correlation matrix</span>
<span style="color: #228B22"># annot = True to print the values inside the square</span>
plt.figure(figsize=(<span style="color: #B452CD">15</span>,<span style="color: #B452CD">8</span>))
sns.heatmap(data=correlation_matrix, annot=<span style="color: #658b00">True</span>)
plt.show()
<span style="color: #228B22">#print eigvalues of correlation matrix</span>
EigValues, EigVectors = np.linalg.eig(correlation_matrix)
<span style="color: #8B008B; font-weight: bold">print</span>(EigValues)
</pre></div>
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
+4 -7
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@@ -1270,7 +1270,7 @@ in the data set (see the full example below).
One simple way to get a discrete output is to have sign
functions that map the output of a linear regressor to values \( \{0,1\} \),
\( f(s_i)=sign(s_i)=1 \) if \( s_i\ge 0 \) and 0 if otherwise.
We will encounter this model in our first demonstration of neural networks. Historically it is called the &quot;perceptron" model in the machine learning
We will encounter this model in our first demonstration of neural networks. Historically it is called the ``perceptron" model in the machine learning
literature. This model is extremely simple. However, in many cases it is more
favorable to use a ``soft" classifier that outputs
the probability of a given category. This leads us to the logistic function.
@@ -1281,7 +1281,7 @@ the probability of a given category. This leads us to the logistic function.
<h2 id="___sec26">Simple example </h2>
<p>
The following example on data for coronary heart disease (CHD) as function of age may serve as an illustration. In the code here we read and plot for whether a person has had CHD (output = 1) or not (output = 0) is plotted against age. Clearly, the figure shows that attempting to make a standard lineae regression fit may not be very meaningful.
The following example on data for coronary heart disease (CHD) as function of age may serve as an illustration. In the code here we read and plot whether a person has had CHD (output = 1) or not (output = 0). This ouput is plotted the person's against age. Clearly, the figure shows that attempting to make a standard linear regression fit may not be very meaningful.
<p>
@@ -1387,7 +1387,7 @@ representing the probability for finding a value of \( y_i \) with a given
<p>
Another widely studied model, is the so-called
perceptron model, which is an example of a ``hard classification&quot; model. We
perceptron model, which is an example of a &quot;hard classification&quot; model. We
will encounter this model when we discuss neural networks as
well. Each datapoint is deterministically assigned to a category (i.e
\( y_i=0 \) or \( y_i=1 \)). In many cases, and the coronary heart disease data forms one of many such examples, it is favorable to have a &quot;soft&quot;
@@ -1748,12 +1748,9 @@ plt<span style="color: #666666">.</span>show()
correlation_matrix <span style="color: #666666">=</span> cancerpd<span style="color: #666666">.</span>corr()<span style="color: #666666">.</span>round(<span style="color: #666666">1</span>)
<span style="color: #408080; font-style: italic"># use the heatmap function from seaborn to plot the correlation matrix</span>
<span style="color: #408080; font-style: italic"># annot = True to print the values inside the square</span>
plt<span style="color: #666666">.</span>figure(figsize<span style="color: #666666">=</span>(<span style="color: #666666">15</span>,<span style="color: #666666">8</span>))
sns<span style="color: #666666">.</span>heatmap(data<span style="color: #666666">=</span>correlation_matrix, annot<span style="color: #666666">=</span><span style="color: #008000">True</span>)
plt<span style="color: #666666">.</span>show()
<span style="color: #408080; font-style: italic">#print eigvalues of correlation matrix</span>
EigValues, EigVectors <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>eig(correlation_matrix)
<span style="color: #008000; font-weight: bold">print</span>(EigValues)
</pre></div>
<p>
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