Lab 1: Ridge function fix

lab1/assignment2.R

@@ -61,7 +61,7 @@ log_likelihood <- function(theta, sigma) {
 
 # Ridge
 ridge <- function(theta, sigma, lambda) {
-  ridge <- lambda * sum(theta ^ 2) - log_likelihood(theta, sigma)
+  ridge <- - log_likelihood(theta, sigma) + lambda * sum(theta ^ 2) 
   return(ridge)
 }
 

lab1/lab-notes.md

@@ -105,7 +105,7 @@ Confusion matrix o misclassification error e framtana.
 3. The functions where implemented using the following formulas:
 
    - _Loglikelihood_: $$\log P(T | \theta, \sigma) = -\frac{n}{2} \log(2 \pi \sigma^2) - \frac{1}{2 \sigma^2} \sum_{i=1}^{n} (T_i - \mathbf{X}_i \boldsymbol{\theta})^2$$
-   - _Ridge_: $$\mathcal{L}_{\text{ridge}}(\theta, \sigma, \lambda) = \lambda \sum_{j=1}^{p} \theta_j^2 - \log P(T | \theta, \sigma)$$
+   - _Ridge_: $$\mathcal{L}_{\text{ridge}}(\theta, \sigma, \lambda) = - \log P(T | \theta, \sigma) + \lambda \sum_{j=1}^{p} \theta_j^2$$
    - _RidgeOpt_: $$\hat{\theta}, \hat{\sigma} = \arg \min_{\theta, \sigma} \mathcal{L}_{\text{ridge}}(\theta, \sigma, \lambda)$$
    - _DF_: $$\text{df}(\lambda) = \text{tr}\left( X \left( X^T X + \lambda I \right)^{-1} X^T \right)$$