Merge overleaf-2024-10-31-1327 into master

slides/supervised-classification/slides-classification-basicdefs.tex

@@ -14,7 +14,7 @@
 }{% Relative path to title page image: Can be empty but must not start with slides/
   figure/db_examples
 }{% Learning goals, wrapped inside itemize environment
-  \item Understand why classification models have a score / probability as output and not a class
+  \item Understand why classifiers output a score / probability and not a class
   \item Understand the difference between scoring and probabilistic classifiers
   \item Know the concept of decision regions and boundaries
   \item Know the difference between generative and discriminant approach
@@ -82,12 +82,12 @@
 \begin{vbframe}{Probabilistic Classifiers}
 \begin{itemize}
 % \item Probabilistic classifiers assume the output variable to be 0/1-encoded, i. e. $\Yspace = \{0, 1\}$
-\item Construct $g$ \textbf{probability functions} $\pi_1, ..., \pi_g: \Xspace \to [0, 1],~\sum_i \pi_i = 1$ 
+\item Construct $g$ \textbf{probability functions} $\pi_1, ..., \pi_g: \Xspace \to [0, 1],~\sum_{k = 1}^g \pi_k = 1$ 
 \item Probabilities $\pi_1(\xv), \ldots, \pikx[g]$ are transformed into labels by predicting the class with the maximum probability
 $$
 \hx = \argmax_{k \in \gset} \pikx
 $$ 
-\item For $g = 2$ one $\pix$ is constructed (note that it would be natural here to label the classes with $\setzo$)
+\item For $g = 2$ a single $\pix$ is constructed (note that it would be natural here to label the classes with $\setzo$)
 \end{itemize}
 
 
@@ -100,9 +100,9 @@
 \begin{frame}{Thresholding}
 
 \begin{itemize}
-\item Both scoring and probabilistic classifiers can also output classes by thresholding
-\item Thresholding: $\hx:= [\pix \ge c]$ or $\hx = [\fx \ge c]$ for some threshold $c$.
-\item Usually $c = 0.5$ for probabilistic, $c = 0$ for scoring classifiers.
+\item Convert scores or probabilities to class outputs by thresholding: \\[0.5ex]
+$\hx:= [\pix \ge c]$ or $\hx = [\fx \ge c]$ for some threshold $c$
+\item Standard thresholds: $c = 0.5$ for probabilities, $c = 0$ for scores
 \item There are also versions of thresholding for the multiclass case
 
 \end{itemize}
@@ -187,7 +187,7 @@
 \begin{vbframe}{Generative approach}
 
 The \textbf{generative approach}
-models $\pdfxyk$, usually by making some assumptions about the structure of these distributions, and employs the Bayes theorem:
+models $\pdfxyk$, usually by making some assumptions about the structure of these distributions, and employs the Bayes' theorem:
 $$\pikx = \postk = \frac{\P(\xv | y = k) \P(y = k)}{\P(\xv)} = \frac{\pdfxyk \pik}{\sumjg \pdfxyk[j] \pi_j}$$
 
 The prior probabilities, $\pi_k = \P(y = k)$, for each class $k$ can be estimated from the training data as the relative frequency of each class: