add alternative IC for ROC metrics

exercises/evaluation-tex/ex_rnw/ex_roc-metrics-allocation.Rnw

@@ -1,8 +1,7 @@
 
 \begin{enumerate}
-    \item \textbf{Confusion Matrix Completion and Explanation}
-    \begin{enumerate}
-        \item Below is an empty confusion matrix for a binary classification problem. Assign the correct terms (\( \text{TP} \), \( \text{FP} \), \( \text{FN} \), \( \text{TN} \)) to fields (A), (B), (C), (D) and explain what each term represents. % and how it is used to evaluate model performance.
+    \item 
+    Below is an empty confusion matrix for a binary classification problem. Assign the correct terms (\( \text{TP} \), \( \text{FP} \), \( \text{FN} \), \( \text{TN} \)) to fields (A), (B), (C), (D) and explain what each term represents. % and how it is used to evaluate model performance.
 
         \[
         \begin{array}{c|c|c|}
@@ -14,9 +13,6 @@
             \hline
         \end{array}
         \]
-
-
-    \end{enumerate}
 
     \item Below is a table that incorrectly assigns 11 metrics derived from the confusion matrix to their corresponding formulas and descriptions.
     The table contains the following columns:

exercises/evaluation-tex/ex_rnw/sol_roc-metrics-allocation.Rnw

@@ -0,0 +1,65 @@
+\begin{enumerate}
+    \item \textbf{Confusion Matrix Completion and Explanation}
+
+        \[
+        \begin{array}{c|c|c|}
+            \multicolumn{1}{c}{} & \textbf{Actual Positive} & \textbf{Actual Negative} \\
+            \hline
+            \textbf{Predicted Positive} & \text{TP (True Positive)} & \text{FP (False Positive)} \\
+            \hline
+            \textbf{Predicted Negative} & \text{FN (False Negative)} & \text{TN (True Negative)} \\
+            \hline
+        \end{array}
+        \]
+
+        \begin{itemize}
+            \item TP: Cases where the model correctly predicts the positive class.
+            \item FP: Cases where the model incorrectly predicts the positive class for a negative actual value.
+            \item FN: Cases where the model incorrectly predicts the negative class for a positive actual value.
+            \item TN: Cases where the model correctly predicts the negative class.
+        \end{itemize}
+
+    \item 
+    Below a corrected table with properly assigned metric names, formulas, and descriptions:
+
+\begin{tabular}{|p{6cm}|l|p{6cm}|}
+\hline
+\textbf{Metric Name} & \textbf{Formula} & \textbf{Description} \\ \hline
+A) True Positive Rate (TPR) \newline B) Recall \newline C) Sensitivity & b) \( \frac{\text{TP}}{\text{TP} + \text{FN}} \) & 1) Proportion of actual positives correctly identified. \\ \hline
+
+% B) Recall & b) \( \frac{\text{TP}}{\text{TP} + \text{FN}} \) & 1) Proportion of actual positives correctly identified. \\ \hline
+% C) Sensitivity & b) \( \frac{\text{TP}}{\text{TP} + \text{FN}} \) & 1) Proportion of actual positives correctly identified. \\ \hline
+
+D) True Negative Rate (TNR) \newline 
+E) Specificity & c) \( \frac{\text{TN}}{\text{TN} + \text{FP}} \) & 2) Proportion of actual negatives correctly identified. \\ \hline
+
+%E) Specificity & c) \( \frac{\text{TN}}{\text{TN} + \text{FP}} \) & 2) Proportion of actual negatives correctly identified. \\ \hline
+
+F) Precision \newline
+G) Positive Predictive Value (PPV) & d) \( \frac{\text{TP}}{\text{TP} + \text{FP}} \) & 3) Proportion of positive predictions that are correct. \\ \hline
+%G) Positive Predictive Value (PPV) & d) \( \frac{\text{TP}}{\text{TP} + \text{FP}} \) & 3) Proportion of positive predictions that are correct. \\ \hline
+H) False Discovery Rate (FDR) & e) \( \frac{\text{FP}}{\text{TP} + \text{FP}} \) & 4) Proportion of positive predictions that are incorrect. \\ \hline
+I) False Positive Rate (FPR) & f) \( \frac{\text{FP}}{\text{FP} + \text{TN}} \) & 5) Proportion of actual negatives incorrectly classified as positive. \\ \hline
+J) False Negative Rate (FNR) & a) \( \frac{\text{FN}}{\text{TP} + \text{FN}} \) & 11) Proportion of actual positives incorrectly classified as negative. \\ \hline
+K) Negative Predictive Value (NPV) & k) \( \frac{\text{TN}}{\text{TN} + \text{FN}} \) & 9) Proportion of negative predictions that are correct. \\ \hline
+L) Accuracy & g) \( \frac{\text{TP} + \text{TN}}{\text{TP} + \text{FP} + \text{FN} + \text{TN}} \) & 6) Overall proportion of correct predictions. \\ \hline
+M) False Omission Rate (FOR) & l) \( \frac{\text{FN}}{\text{FN} + \text{TN}} \) & 10) Proportion of negative predictions that are incorrect. \\ \hline
+N) Prevalence & j) \( \frac{\text{TP} + \text{FN}}{\text{TP} + \text{FP} + \text{FN} + \text{TN}} \) & 8) Proportion of actual positives in the dataset. \\ \hline
+O) F1 Score & h) \( \frac{2 \cdot \text{Precision} \cdot \text{Recall}}{\text{Precision} + \text{Recall}} \) & 7) Combines precision and recall using their harmonic mean. \\ \hline
+\end{tabular}
+
+    Identified Synonyms:
+    \begin{itemize}
+        \item True Positive Rate (TPR), Recall, and Sensitivity refer to the same metric.
+        \item True Negative Rate (TNR) and Specificity refer to the same metric.
+        \item Precision and Positive Predictive Value (PPV) refer to the same metric.
+    \end{itemize}
+
+    Unassignable Formulas:
+    \begin{itemize}
+        \item \( i) \frac{2 \cdot (\text{Precision} + \text{Recall})}{\text{Precision} \cdot \text{Recall}} \)
+        \item \( o) \frac{\text{TP} - \text{FP}}{\text{TP} + \text{FN} + \text{FP} + \text{TN}} \)
+        \item \( n) \frac{\text{FN} + \text{FP}}{\text{TP} + \text{TN} + \text{FP} + \text{FN}} \)
+        \item \( m) \frac{\text{FN}}{\text{FP} + \text{FN}} \)
+    \end{itemize}
+\end{enumerate}

exercises/evaluation-tex/ic_sol_concepts_2.Rnw

@@ -0,0 +1,18 @@
+% !Rnw weave = knitr
+
+<<setup-child, include = FALSE>>=
+library('knitr')
+knitr::set_parent("../../style/preamble_ueb.Rnw")
+@
+
+
+\kopfic{6}{Evaluation}
+
+\aufgabe{}{
+<<child="ex_rnw/ex_roc-metrics-allocation.Rnw">>=
+@
+}
+\loesung{}{
+<<child="ex_rnw/sol_roc-metrics-allocation.Rnw">>=
+@
+}