From 101d4a02f162b057ec1a0e1ef196e887314cab55 Mon Sep 17 00:00:00 2001
From: sigjo290 <sigjo290@student.liu.se>
Date: Wed, 11 Dec 2024 10:04:25 +0100
Subject: [PATCH] Lab 3: Better answer on assignment 1.2

---
 lab3/lab-notes.md | 10 +++++++++-
 1 file changed, 9 insertions(+), 1 deletion(-)

diff --git a/lab3/lab-notes.md b/lab3/lab-notes.md
index 299a716..f521d14 100644
--- a/lab3/lab-notes.md
+++ b/lab3/lab-notes.md
@@ -8,7 +8,15 @@ This is known as the kernel trick:
 If x enters the model as 𝝓(x)^T𝝓(x') only, we can choose a kernel 𝜅(x, x') instead of chosing 𝝓(x). p. 194
 
 - In the literature, it is common to see a formulation of SVMs that makes use of a hyperparameter. What is the purpose of this hyperparameter?
-The purpose is to regularize. p. 211
+The hyperparameter C is the regularization term in the dual formulation of SVMs:
+\[
+\alpha = \arg \min_\alpha \left( \frac{1}{2} \alpha^T K(X, X) \alpha - \alpha^T y \right)
+\]
+\[
+\text{subject to } \lvert \alpha_i \rvert \leq \frac{1}{2n\lambda} \quad \text{and} \quad 0 \leq \alpha_i y
+\]
+with \[y(x^\star) = \operatorname{sign} \left( b + \alpha^T K(X, x^\star) \right)\].
+Here \[C = \frac{1}{2n\lambda}\]. p. 211
 
 
 - In neural networks, what do we mean by mini-batch and epoch?
-- 
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