Lab 1: Fixes

lab1/assignment2.R

@@ -54,14 +54,15 @@ print(paste("MSE on the test data:", mse(test_scaled$motor_UPDRS, test_pred)))
 # Loglikelihood
 log_likelihood <- function(theta, sigma) {
   n <- length(y_train)
-  ll <- -n / 2 * log(sqrt(2 * pi) * sigma) - (1 / (2 * sigma ^ 2)) * sum((y_train -
-                                                                            as.matrix(X_train) %*% theta) ^ 2)
+  ll <- -n / 2 * log(2 * pi) - n * log(sigma) - (1 / (2 * sigma ^ 2)) * sum((y_train -
+                                                                               as.matrix(X_train) %*% theta) ^
+                                                                              2)
   return(ll)
 }
 
 # Ridge
 ridge <- function(theta, sigma, lambda) {
-  ridge <- - log_likelihood(theta, sigma) + lambda * sum(theta ^ 2) 
+  ridge <- -log_likelihood(theta, sigma) + lambda * sum(theta ^ 2)
   return(ridge)
 }
 

lab1/lab-notes.md

@@ -112,16 +112,16 @@ Confusion matrix o misclassification error e framtana.
 4. Optimal $\bold{\theta}$ for $\lambda \in \{1,100,1000\}$:
 
    - $\lambda = 1$:
-     - $\text{MSE}_{\text{train}} = 0.878681448897974$:
-     - $\text{MSE}_{\text{test}} = 0.934684486872397$:
+     - $\text{MSE}_{\text{train}} = 0.878627075979604$:
+     - $\text{MSE}_{\text{test}} = 0.93499698041696$:
      - $df = 13.8607362829965$
    - $\lambda = 100$:
-     - $\text{MSE}_{\text{train}} = 0.889775499501371$
-     - $\text{MSE}_{\text{test}} = 0.934131808081541$
+     - $\text{MSE}_{\text{train}} = 0.884410431119223$
+     - $\text{MSE}_{\text{test}} = 0.932331719427938$
      - $df = 9.92488712829542$
    - $\lambda = 1000$:
-     - $\text{MSE}_{\text{train}} = 0.939949118364897$
-     - $\text{MSE}_{\text{test}} = 0.967756869359676$
+     - $\text{MSE}_{\text{train}} = 0.921107873074395$
+     - $\text{MSE}_{\text{test}} = 0.953955470516858$
      - $df = 5.6439254878463$
 
    $\lambda = 100$ seems to be the most suitable penalty parameter considering