Naive Bayes Explained | Medium

1. What’s it?

— A statistical technique for classifying based mostly on Bayes Theorem. Supervised Studying. It assumes independence between options.

2. Why did we’d like that?

— For simplicity, multi-class prediction issues and restricted coaching information are wanted.

3. When to make use of it?

— Restricted coaching information, multi-class classification, high-dimensional information, and real-time purposes.

4. The place is it generally utilized?

— Spam filtering, textual content classification, recommender methods.

5. How one can apply it?

If crucial, convert textual content information into numerical options utilizing strategies like CountVectorizer, which tokenizes sentences and counts phrase frequency.
Create a Naive Bayes classifier utilizing MultinominalNB or GaussianNB, it relies upon
Match the coaching information utilizing match()
Make a prediction utilizing predict()
Efficiency metrics.

6. Key phrases

System:

The Formula of Naive Bayes — The System of Naive Bayes

Ck is the k-th class
x=(x1,…,xn)x=(x1,…,xn) is the characteristic vector
P(Ck∣x) is the posterior likelihood of sophistication Ck given x
P(Ck) is the prior likelihood of sophistication Ck
P(xi∣Ck) is the probability of characteristic xi given class Ck
P(x) is the proof (which might be ignored because it’s fixed for all courses)

Numerical Instance:

Suppose we wish to predict whether or not it’s going to rain based mostly on two options: temperature (Scorching or Cool) and humidity (Excessive or Regular). We’ve got a small coaching dataset:

Step 1: Calculate prior chances
P(Rain=Sure) = 3/5 = 0.6
P(Rain=No) = 2/5 = 0.4

Step 2: Calculate conditional chances
P(Cool|Rain=Sure) = 1/3
P(Cool|Rain=No) = 2/2 = 1
P(Excessive|Rain=Sure) = 3/3 = 1
P(Excessive|Rain=No) = 0/2 = 0

Step 3: Apply Naive Bayes method
P(Rain=Sure|Cool,Excessive) ∝ P(Rain=Sure) * P(Cool|Rain=Sure) * P(Excessive|Rain=Sure)
= 0.6 * (1/3) * 1 = 0.2

P(Rain=No|Cool,Excessive) ∝ P(Rain=No) * P(Cool|Rain=No) * P(Excessive|Rain=No)
= 0.4 * 1 * 0 = 0

Step 4: Normalize chances
Whole = 0.2 + 0 = 0.2
P(Rain=Sure|Cool,Excessive) = 0.2 / 0.2 = 1
P(Rain=No|Cool,Excessive) = 0 / 0.2 = 0

Due to this fact, the mannequin predicts that it’s going to rain with a likelihood of 100%.