Some selected typos

doc/pub/Regression/html/._Regression-bs102.html

@@ -403,7 +403,7 @@ classes).
 <p>
 The goal is to predict the
 output classes from the design matrix \( X\in\mathbb{R}^{n\times p} \)
-made of \( n \) samples, each of which bears \( p \) features. Of cours e the
+made of \( n \) samples, each of which bears \( p \) features. The
 primary goal is to identify the classes to which new unseen samples
 belong.
 

doc/pub/Regression/html/._Regression-bs104.html

@@ -396,7 +396,18 @@ MathJax.Hub.Config({
 <h2 id="___sec103" class="anchor">Some selected properties </h2>
 
 <p>
-This function takes values on the entire real axis. In the case of logistic regression, however, the labels \( y_i \) are discrete variables. One simple way to get a discrete output is to have sign functions that map the output of a linear regressor to \( \{0,1\} \),  \( f(s_i)= \) sign$(s_i) = 1$ if \( s_i\ge 0 \) and 0 if otherwise. Indeed, this is commonly known as the &quot;perceptron" in the machine learning literature. This model is extremely simple, and it is favorable in many cases (e.g. noisy data) to have a ``soft" classifier that outputs the probability of a given category. For example, given \( \mathbf{x}_i \), the classifier outputs the probability of being in category \( m \). One such function is the logistic (or sigmoid) function:
+This function takes values on the entire real axis. In the case of
+logistic regression, however, the labels \( y_i \) are discrete
+variables. One simple way to get a discrete output is to have sign
+functions that map the output of a linear regressor to \( \{0,1\} \),
+\( f(s_i)=sign(s_i)=1 \) if \( s_i\ge 0 \) and 0 if otherwise. Indeed,
+this is commonly known as the &quot;perceptron" in the machine learning
+literature. This model is extremely simple, and it is favorable in
+many cases (e.g. noisy data) to have a ``soft" classifier that outputs
+the probability of a given category. For example, given
+\( \mathbf{x}_i \), the classifier outputs the probability of being in
+category \( m \). One such function is the logistic (or sigmoid) function:
+
 $$
 \begin{equation}
 f(s) = \frac{1}{1+\mathrm e^{-s}}.

doc/pub/Regression/html/Regression-reveal.html

@@ -3488,7 +3488,7 @@ classes).
 <p>
 The goal is to predict the
 output classes from the design matrix \( X\in\mathbb{R}^{n\times p} \)
-made of \( n \) samples, each of which bears \( p \) features. Of cours e the
+made of \( n \) samples, each of which bears \( p \) features. The
 primary goal is to identify the classes to which new unseen samples
 belong.
 </section>
@@ -3517,7 +3517,18 @@ where we use the short-hand notation
 <h2 id="___sec103">Some selected properties </h2>
 
 <p>
-This function takes values on the entire real axis. In the case of logistic regression, however, the labels \( y_i \) are discrete variables. One simple way to get a discrete output is to have sign functions that map the output of a linear regressor to \( \{0,1\} \),  \( f(s_i)= \) sign$(s_i) = 1$ if \( s_i\ge 0 \) and 0 if otherwise. Indeed, this is commonly known as the &quot;perceptron" in the machine learning literature. This model is extremely simple, and it is favorable in many cases (e.g. noisy data) to have a ``soft" classifier that outputs the probability of a given category. For example, given \( \mathbf{x}_i \), the classifier outputs the probability of being in category \( m \). One such function is the logistic (or sigmoid) function:
+This function takes values on the entire real axis. In the case of
+logistic regression, however, the labels \( y_i \) are discrete
+variables. One simple way to get a discrete output is to have sign
+functions that map the output of a linear regressor to \( \{0,1\} \),
+\( f(s_i)=sign(s_i)=1 \) if \( s_i\ge 0 \) and 0 if otherwise. Indeed,
+this is commonly known as the &quot;perceptron" in the machine learning
+literature. This model is extremely simple, and it is favorable in
+many cases (e.g. noisy data) to have a ``soft" classifier that outputs
+the probability of a given category. For example, given
+\( \mathbf{x}_i \), the classifier outputs the probability of being in
+category \( m \). One such function is the logistic (or sigmoid) function:
+
 <p>&nbsp;<br>
 $$
 \begin{equation}

doc/pub/Regression/html/Regression-solarized.html

@@ -3431,7 +3431,7 @@ classes).
 <p>
 The goal is to predict the
 output classes from the design matrix \( X\in\mathbb{R}^{n\times p} \)
-made of \( n \) samples, each of which bears \( p \) features. Of cours e the
+made of \( n \) samples, each of which bears \( p \) features. The
 primary goal is to identify the classes to which new unseen samples
 belong.
 
@@ -3458,7 +3458,18 @@ where we use the short-hand notation
 <h2 id="___sec103">Some selected properties </h2>
 
 <p>
-This function takes values on the entire real axis. In the case of logistic regression, however, the labels \( y_i \) are discrete variables. One simple way to get a discrete output is to have sign functions that map the output of a linear regressor to \( \{0,1\} \),  \( f(s_i)= \) sign$(s_i) = 1$ if \( s_i\ge 0 \) and 0 if otherwise. Indeed, this is commonly known as the &quot;perceptron" in the machine learning literature. This model is extremely simple, and it is favorable in many cases (e.g. noisy data) to have a ``soft" classifier that outputs the probability of a given category. For example, given \( \mathbf{x}_i \), the classifier outputs the probability of being in category \( m \). One such function is the logistic (or sigmoid) function:
+This function takes values on the entire real axis. In the case of
+logistic regression, however, the labels \( y_i \) are discrete
+variables. One simple way to get a discrete output is to have sign
+functions that map the output of a linear regressor to \( \{0,1\} \),
+\( f(s_i)=sign(s_i)=1 \) if \( s_i\ge 0 \) and 0 if otherwise. Indeed,
+this is commonly known as the &quot;perceptron" in the machine learning
+literature. This model is extremely simple, and it is favorable in
+many cases (e.g. noisy data) to have a ``soft" classifier that outputs
+the probability of a given category. For example, given
+\( \mathbf{x}_i \), the classifier outputs the probability of being in
+category \( m \). One such function is the logistic (or sigmoid) function:
+
 $$
 \begin{equation}
 f(s) = \frac{1}{1+\mathrm e^{-s}}.

doc/pub/Regression/html/Regression.html

@@ -3436,7 +3436,7 @@ classes).
 <p>
 The goal is to predict the
 output classes from the design matrix \( X\in\mathbb{R}^{n\times p} \)
-made of \( n \) samples, each of which bears \( p \) features. Of cours e the
+made of \( n \) samples, each of which bears \( p \) features. The
 primary goal is to identify the classes to which new unseen samples
 belong.
 
@@ -3463,7 +3463,18 @@ where we use the short-hand notation
 <h2 id="___sec103">Some selected properties </h2>
 
 <p>
-This function takes values on the entire real axis. In the case of logistic regression, however, the labels \( y_i \) are discrete variables. One simple way to get a discrete output is to have sign functions that map the output of a linear regressor to \( \{0,1\} \),  \( f(s_i)= \) sign$(s_i) = 1$ if \( s_i\ge 0 \) and 0 if otherwise. Indeed, this is commonly known as the &quot;perceptron" in the machine learning literature. This model is extremely simple, and it is favorable in many cases (e.g. noisy data) to have a ``soft" classifier that outputs the probability of a given category. For example, given \( \mathbf{x}_i \), the classifier outputs the probability of being in category \( m \). One such function is the logistic (or sigmoid) function:
+This function takes values on the entire real axis. In the case of
+logistic regression, however, the labels \( y_i \) are discrete
+variables. One simple way to get a discrete output is to have sign
+functions that map the output of a linear regressor to \( \{0,1\} \),
+\( f(s_i)=sign(s_i)=1 \) if \( s_i\ge 0 \) and 0 if otherwise. Indeed,
+this is commonly known as the &quot;perceptron" in the machine learning
+literature. This model is extremely simple, and it is favorable in
+many cases (e.g. noisy data) to have a ``soft" classifier that outputs
+the probability of a given category. For example, given
+\( \mathbf{x}_i \), the classifier outputs the probability of being in
+category \( m \). One such function is the logistic (or sigmoid) function:
+
 $$
 \begin{equation}
 f(s) = \frac{1}{1+\mathrm e^{-s}}.

doc/pub/Regression/ipynb/Regression.ipynb

@@ -4435,7 +4435,7 @@
     "\n",
     "The goal is to predict the\n",
     "output classes from the design matrix $X\\in\\mathbb{R}^{n\\times p}$\n",
-    "made of $n$ samples, each of which bears $p$ features. Of cours e the\n",
+    "made of $n$ samples, each of which bears $p$ features. The\n",
     "primary goal is to identify the classes to which new unseen samples\n",
     "belong.\n",
     "\n",
@@ -4469,7 +4469,17 @@
     "\n",
     "## Some selected properties\n",
     "\n",
-    "This function takes values on the entire real axis. In the case of logistic regression, however, the labels $y_i$ are discrete variables. One simple way to get a discrete output is to have sign functions that map the output of a linear regressor to $\\{0,1\\}$,  $f(s_i)=$ sign$(s_i) = 1$ if $s_i\\ge 0$ and 0 if otherwise. Indeed, this is commonly known as the \"perceptron\" in the machine learning literature. This model is extremely simple, and it is favorable in many cases (e.g. noisy data) to have a ``soft\" classifier that outputs the probability of a given category. For example, given $\\mathbf{x}_i$, the classifier outputs the probability of being in category $m$. One such function is the logistic (or sigmoid) function:"
+    "This function takes values on the entire real axis. In the case of\n",
+    "logistic regression, however, the labels $y_i$ are discrete\n",
+    "variables. One simple way to get a discrete output is to have sign\n",
+    "functions that map the output of a linear regressor to $\\{0,1\\}$,\n",
+    "$f(s_i)=sign(s_i)=1$ if $s_i\\ge 0$ and 0 if otherwise. Indeed,\n",
+    "this is commonly known as the \"perceptron\" in the machine learning\n",
+    "literature. This model is extremely simple, and it is favorable in\n",
+    "many cases (e.g. noisy data) to have a ``soft\" classifier that outputs\n",
+    "the probability of a given category. For example, given\n",
+    "$\\mathbf{x}_i$, the classifier outputs the probability of being in\n",
+    "category $m$. One such function is the logistic (or sigmoid) function:"
    ]
   },
   {

doc/src/Regression/Regression.do.txt

@@ -2830,7 +2830,7 @@ classes).
 
 The goal is to predict the
 output classes from the design matrix $X\in\mathbb{R}^{n\times p}$
-made of $n$ samples, each of which bears $p$ features. Of cours e the
+made of $n$ samples, each of which bears $p$ features. The
 primary goal is to identify the classes to which new unseen samples
 belong.
  
@@ -2850,7 +2850,18 @@ $\mathbf{x}_i = (1,\boldsymbol{x}_i)$ and $\mathbf{w}_i = (b_0,\boldsymbol{w}_i)
 !split
 ===== Some selected properties =====
 
-This function takes values on the entire real axis. In the case of logistic regression, however, the labels $y_i$ are discrete variables. One simple way to get a discrete output is to have sign functions that map the output of a linear regressor to $\{0,1\}$,  $f(s_i)=$ sign$(s_i) = 1$ if $s_i\ge 0$ and 0 if otherwise. Indeed, this is commonly known as the ``perceptron" in the machine learning literature. This model is extremely simple, and it is favorable in many cases (e.g. noisy data) to have a ``soft" classifier that outputs the probability of a given category. For example, given $\mathbf{x}_i$, the classifier outputs the probability of being in category $m$. One such function is the logistic (or sigmoid) function:
+This function takes values on the entire real axis. In the case of
+logistic regression, however, the labels $y_i$ are discrete
+variables. One simple way to get a discrete output is to have sign
+functions that map the output of a linear regressor to $\{0,1\}$,
+$f(s_i)=sign(s_i)=1$ if $s_i\ge 0$ and 0 if otherwise. Indeed,
+this is commonly known as the ``perceptron" in the machine learning
+literature. This model is extremely simple, and it is favorable in
+many cases (e.g. noisy data) to have a ``soft" classifier that outputs
+the probability of a given category. For example, given
+$\mathbf{x}_i$, the classifier outputs the probability of being in
+category $m$. One such function is the logistic (or sigmoid) function:
+
 !bt
 \begin{equation}
 f(s) = \frac{1}{1+\mathrm e^{-s}}.