Update naive-bayes.md

Updating some of the markdown equations. Please consider and please also review this under GSSOC and give this updations some level.

contrib/machine-learning/naive-bayes.md

@@ -93,13 +93,9 @@ $$
 
 - Rain:
 
-$$
-P(Rain|Yes) = \frac{2}{6}
-$$
+$$P(Rain|Yes) = \frac{2}{6}$$
 
-$$
-P(Rain|No) = \frac{4}{4}
-$$
+$$P(Rain|No) = \frac{4}{4}$$
 
 - Overcast:
 
@@ -111,10 +107,7 @@ $$
 $$
 
 
-Here, we can see that
-  $$
-    P(Overcast|No)  = 0
-  $$
+Here, we can see that P(Overcast|No)  = 0
 This is a zero probability error! 
 
 Since probability is 0, naive bayes model fails to predict.
@@ -124,13 +117,9 @@ Since probability is 0, naive bayes model fails to predict.
   In Laplace's correction, we scale the values for 1000 instances.
   - **Calculate prior probabilities**
 
-  $$
-     P(Yes)  =  \frac{600}{1002} 
-  $$
+  $$P(Yes)  =  \frac{600}{1002}$$
   
-  $$
-     P(No)  =  \frac{402}{1002} 
-  $$
+  $$P(No)  =  \frac{402}{1002}$$
 
 - **Calculate likelihoods**
 
@@ -151,21 +140,13 @@ Since probability is 0, naive bayes model fails to predict.
 
     - **Rain:**
 
-  $$
-     P(Rain|Yes)  =  \frac{200}{600} 
-  $$
-  $$
-     P(Rain|No)  =  \frac{401}{402} 
-  $$
+  $$P(Rain|Yes)  =  \frac{200}{600}$$
+  $$P(Rain|No)  =  \frac{401}{402}$$
 
   - **Overcast:**
 
-  $$
-     P(Overcast|Yes)  =  \frac{400}{600} 
-  $$
-  $$
-     P(Overcast|No)  =  \frac{1}{402}
-  $$
+  $$P(Overcast|Yes)  =  \frac{400}{600}$$
+  $$P(Overcast|No)  =  \frac{1}{402}$$
 
 
   2. **Wind (B):** 
@@ -181,49 +162,27 @@ Since probability is 0, naive bayes model fails to predict.
 
     - **Weak:**
 
-    $$
-       P(Weak|Yes)  =  \frac{500}{600} 
-    $$
-    $$
-       P(Weak|No)  =  \frac{200}{400} 
-    $$
+    $$P(Weak|Yes)  =  \frac{500}{600}$$
+    $$P(Weak|No)  =  \frac{200}{400}$$
 
     - **Strong:**
 
-    $$
-       P(Strong|Yes)  =  \frac{100}{600} 
-    $$
-    $$
-       P(Strong|No)  =  \frac{200}{400}
-    $$
+    $$P(Strong|Yes)  =  \frac{100}{600}$$
+    $$P(Strong|No)  =  \frac{200}{400}$$
 
   - **Calculting probabilities:**
   
-  $$
-     P(PlayTennis|Yes)  =  P(Yes) * P(Overcast|Yes) * P(Weak|Yes)
-  $$
-  $$
-                 =  \frac{600}{1002} * \frac{400}{600} * \frac{500}{600} 
-  $$
-  $$
-                 =  0.3326
-  $$
+  $$P(PlayTennis|Yes)  =  P(Yes) * P(Overcast|Yes) * P(Weak|Yes)$$
+  $$=  \frac{600}{1002} * \frac{400}{600} * \frac{500}{600}$$
+  $$=  0.3326$$
 
-  $$
-     P(PlayTennis|No)  =  P(No) * P(Overcast|No) * P(Weak|No)
-  $$
-  $$
-                 =  \frac{402}{1002} * \frac{1}{402} * \frac{200}{400} 
-  $$
-  $$
-                 =  0.000499 =  0.0005
-  $$
+  $$P(PlayTennis|No)  =  P(No) * P(Overcast|No) * P(Weak|No)$$
+  $$=  \frac{402}{1002} * \frac{1}{402} * \frac{200}{400}$$
+  $$=  0.000499 =  0.0005$$
 
 
 Since ,
-$$
-     P(PlayTennis|Yes)  >  P(PlayTennis|No) 
-$$
+$$P(PlayTennis|Yes)  >  P(PlayTennis|No)$$
 we can conclude that tennis can be played if outlook is overcast and wind is weak.
 
 
@@ -366,4 +325,4 @@ print("Confusion matrix: \n",confusion_matrix(y_train,y_pred))
 ## Conclusion
 
  We can conclude that naive bayes may limit in some cases due to the assumption that the features are independent of each other but still reliable in many cases. Naive Bayes is an efficient classifier and works even on small datasets.
-  
+