Adding a definition for p instead of j

05-supervisedLearning.Rmd

@@ -680,7 +680,7 @@ Training accuracy is $1$, so training error is $0$, and nothing is misclassified
 ### Regularization in order to avoid overfitting
 If \index{regularization}we can limit the flexibility of the model, this might help with performance on the unseen, new data sets. Generally, any modification of the learning method to improve performance on the unseen datasets is called regularization. We need regularization to introduce bias to the model and to decrease the variance. This can be achieved by modifying the loss function with a penalty term which effectively shrinks the estimates of the coefficients. Therefore these types of methods within the framework of regression are also called "shrinkage" methods or "penalized regression" methods.\index{overfitting} 
 
-One way to ensure shrinkage is to add the penalty term, $\lambda\sum{\beta_j}^2$, to the loss function. This penalty term is also known as the L2 norm or L2 penalty. It is calculated as the square root of the sum of the squared vector values. This term will help shrink the coefficients in the regression towards zero. The new loss function is as follows, where $j$ is the number of parameters/coefficients in the model and $L_{log}$ is the log loss function in Eq. \@ref(eq:llog).
+One way to ensure shrinkage is to add the penalty term, $\lambda\sum{\beta_j}^2$, to the loss function. This penalty term is also known as the L2 norm or L2 penalty. It is calculated as the square root of the sum of the squared vector values. This term will help shrink the coefficients in the regression towards zero. The new loss function is as follows, where $p$ is the total number of parameters/coefficients in the model and $L_{log}$ is the log loss function in Eq. \@ref(eq:llog).
 
 \begin{equation}
 L_{log}+\lambda\sum_{j=1}^p{\beta_j}^2
@@ -1021,4 +1021,4 @@ ameth=readRDS(fileMethAge)
 2. Split 20% of the methylation-age data as test data and run elastic net regression on the training portion to tune parameters and test it on the test portion. [Difficulty: **Intermediate**] 
 
 3. Run an ensemble model for regression using the **caretEnsemble** or **mlr** package and compare the results with the elastic net and random forest model. Did the test accuracy increase?
-**HINT:** You need to install these extra packages and learn how to use them in the context of ensemble models. [Difficulty: **Advanced**] 
+**HINT:** You need to install these extra packages and learn how to use them in the context of ensemble models. [Difficulty: **Advanced**]