vault backup: 2025-03-16 18:59:42

AI & Data Mining/Week 3/Lecture 5 - Naive Bayes.md

@@ -55,13 +55,17 @@
 # Modified Probability Estimates
 
 - Consider attribute *outlook* for class *yes*
+
 # $\frac{2+\frac{1}{3}\mu}{9+\mu}$
+
 Sunny
 
 # $\frac{4+\frac{1}{3}\mu}{9+\mu}$
+
 Overcast
 
 # $\frac{3+\frac{1}{3}\mu}{9+\mu}$
+
 Rainy
 
 - Each value treated the same way
@@ -73,13 +77,16 @@ Rainy
 ## Fully Bayesian Formulation
 
 # $\frac{2+\frac{1}{3}\mu p_1}{9+\mu}$
+
 Sunny
 
 # $\frac{4+\frac{1}{3}\mu p_2}{9+\mu}$
+
 Overcast
 
 # $\frac{3+\frac{1}{3}\mu p_3}{9+\mu}$
+
 Rainy
 
-- Where $p_1 + p_2 + p_3 = 1$ 
-- $p_1, p_2, p_3$ are prior probabilities of outlook being sunny, overcast or rainy before seeing the training set. However, in practice it is not clear how these prior probabilities should be assigned.
+- Where $p_1 + p_2 + p_3 = 1$
+- $p_1, p_2, p_3$ are prior probabilities of outlook being sunny, overcast or rainy before seeing the training set. However, in practice it is not clear how these prior probabilities should be assigned.

AI & Data Mining/Week 3/Tutorial 3.md

@@ -27,20 +27,25 @@
 | High     | 2/5         | 1/9 | Red    | 3/5  | 2/9 |        |          |     |       |         |     |      |      |
 
 # Problem 1
+
 # $Pr[Diagnosis=N|E] = \frac{2}{5} \times \frac{2}{5} \times \frac{4}{5} \times \frac{3}{5} \times \frac{5}{14} = 0.027428571$
+
 # $Pr[Diagnosis = B|E] = \frac{3}{9} \times \frac{4}{9} \times \frac{3}{9} \times \frac{3}{9} \times \frac{9}{14} = 0.010582011$
 
 # $p(B) = \frac{0.0106}{0.0106+0.0274} = 0.2789$
 
-#  $p(N) = \frac{0.0274}{0.0106+0.0274} = 0.7211$
+# $p(N) = \frac{0.0274}{0.0106+0.0274} = 0.7211$
 
 Diagnosis N is much more likely than Diagnosis B
 
 # Problem 2
 
 # $Pr[Diagnosis = N|E] = \frac{2}{5} \times \frac{1}{5} \times \frac{3}{5} \times \frac{5}{14} = 0.0171$
+
 # $Pr[Diagnosis = B|E] = \frac{3}{9} \times \frac{6}{9} \times \frac{3}{9} \times \frac{9}{14} = 0.0476$
+
 # $p(N) = \frac{0.0171}{0.0171+0.0476} = 0.2643$
+
 # $p(B) = \frac{0.0474}{0.0476+0.0171} = 0.7357$
 
 Diagnosis B is much more likely than Diagnosis N
@@ -48,4 +53,5 @@ Diagnosis B is much more likely than Diagnosis N
 # Problem 3
 
 # $Pr[Diagnosis = N|E] = \frac{0}{5} \times \frac{2}{5} \times \frac{4}{5} \times \frac{3}{5} \times \frac{5}{14} = 0$
+
 # $Pr[Diagnosis = B|E] = \frac{5}{9} \times \frac{4}{9} \times \frac{3}{9} \times \frac{3}{9} \times \frac{9}{14} = 0.018$

AI & Data Mining/Week 3/Workshop 3.md

@@ -274,4 +274,4 @@ Root mean squared error                  0.3223
 Relative absolute error                 70.1487 %
 Root relative squared error             68.0965 %
 Total Number of Instances                3
-```
+```