README.md

Naive Bayes

• Thomas Bayes (1701 – 1761) was an English statistician and philosopher

• Bayes is known for formulating a specific case of the theorem that bears his name: Bayes' theorem.

• In machine learning, Naïve Bayes classifiers are a family of simple "probabilistic classifiers" based on applying Bayes' theorem with strong (naïve) independence assumptions between the features.

    Possible k outcomes = {C1, C2, ..., Ck}

    i =  1, 2, ..., k

                   P(Ci) P(x | Ci)
    P(Ci | x) =  -------------------
                       P(x)

• P(A | B) stands for "the conditional probability of A given B", or "the probability of A under the condition B", i.e. the probability of some event A under the assumption that the event B took place.

• P(A | B) = P (A and B) / P(B)

• P(B) can not be ZERO since B has happened

• Conditional probability answers the question: how does the probability of an event change if we have extra information

• Independent Events: Events A and B are independent whenever P(A | B) = P(A).

• Equivalently, events A and B are independent whenever P(B | A) = P(B)

• When two events A and B are independent, we can use the multiplication rule for independent events : P(A and B) = P(A) x P(B)

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Proof!!!

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Probability, Conditional Probability: foundation for Naive Bayes

1. Probability Theory 101 for Dummies like Me

2. Probability 101, CS 2800: Discrete Structures

3. Probability: Terminology and Examples

4. Lesson slides: Understand conditional probability using scenarios -- 8 slides

5. Conditional Probability

6. Conditional Probability, Independence and Bayes’ Theorem

7. Conditional Probability, Independence, Bayes’ Theorem -- MIT slides

8. Section 5.3 - Conditional Probability and Independence

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Naive Bayes Videos

1. An Introduction to Conditional Probability: 12 minutes video

2. Naive Bayes Classifier With Example : 43 minutes

3. Naive Bayes Classifier in Python : 30 minutes

4. Naive Bayes Classifier - Stanford University Course: 10 minutes

5. Introduction to Naive Bayes Theorem, ML Classification: 10 minutes

6. Naive Bayes classifier: A friendly approach: 20 minutes

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Naive Bayes -- Introduction

1. Introduction to Naive Bayes -- slide 37 (pages)

2. Naive Bayes Classifier 37 (pages)

3. Naive Bayesian (with example)

4. Naïve Bayes and Logistic Regression, by Tom M. Mitchell

5. Naive Bayes Classification using Scikit-learn

6. Naive Bayes Classifiers (Golf Example)

7. Naive Bayes Classifier From Scratch in Python

8. Naive Bayes Tutorial for Machine Learning

9. Naive Bayes Classifier Explained Step by Step

10. How Naive Bayes Algorithm Works? (with example and full code)

11. Python Machine Learning Tutorial: Naive Bayes Classifier

12. Naive Bayes Classifier: Learning Naive Bayes with Python

13. Pure Python Solution: An Introduction to Naïve Bayes Classifier

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Naive Bayes classification algorithms

1. Comparing a variety of Naive Bayes classification algorithms

Naive Bayes Deep Understandings

1. In Depth: Naive Bayes Classification

2. How to Develop a Naive Bayes Classifier from Scratch in Python: by Jason Brownlee

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Spark-ML for Naive Bayes

1. PySpark + Naive Bayes: worked example

2. Naive Bayes Classifier - ML Pipelines

3. How to implement Naive Bayes with Spark MLlib

4. Multi-Class Text Classification with PySpark

   • Multi-Class Text Classification with PySpark -- blog
   • PySpark solutions: Logistic Regression, Naive Bayes
   • San Francisco Crime Classification Data download

5. Pyspark – Classification with Naive Bayes