*What is Naive Bayesian Algorithms?*

During this lesson the following topics are covered:

Naïve Bayesian Classifier

Theoretical foundations of the classifier

Use cases

Evaluating the effectiveness of the classifier

The Reasons to Choose (+) and Cautions (-) with the use of the classifier

*Classification:** assign labels to objects.*

*Usually supervised:** training set of pre-classified examples.*

Our examples:

Naïve Bayesian

Decision Trees

(and Logistic Regression)

*Naïve Bayesian Classifier*

- Determine the most probable class label for each object

Based on the observed object attributes

- __Naïvely__ assumed to be conditionally independent of each other

Example:

- Based on the objects attributes {shape, color, weight}

- A given object that is {spherical, yellow, < 60 grams}, may be classified (labeled) as a tennis ball

Class label probabilities are determined using Bayes’ Law

- Input variables are discrete

- Output:

Probability score – proportional to the true probability

Class label – based on the highest probability score

*Naïve Bayesian Classifier - Use Cases*

- Preferred method for many text classification problems.

Try this first; if it doesn't work, try something more complicated

- Use cases

Spam filtering, other text classification tasks

Fraud detection

*Technical Description - Bayes' Law*

- C is the class label:

C ϵ {C1, C2, … Cn}

- A is the observed object attributes

A = (a1, a2, … am)

- P(C | A) is the probability of C given A is observed

4Called the conditional probability

*Apply the Naïve Assumption and Remove a Constant *

- For observed attributes A = (a1, a2, … am), we want to compute.

and assign the classifier, Ci, with the largest P(Ci|A).

- Two simplifications to the calculations

Apply naïve assumption - each aj is conditionally independent of each other, then

Denominator P(a1,a2,…am) is a constant and can be ignored.

*Building a Naïve Bayesian Classifier*

- Applying the two simplifications

- To build a Naïve Bayesian Classifier, collect the following statistics from the training data:

P(Ci) for all the class labels.

P(aj| Ci) for all possible aj and Ci

Assign the classifier label, Ci, that maximizes the value of

*Example:** **Weather data set*

Weather data, frequency according to class:

**Weather example: solving our example**

*P***(***O, T , H, W ***| Play) = ***P***(***O ***| Play) · ***P***(***T ***| Play). P(***H ***| Play) · ***P***(***W ***| Play)**

**Weather example when play = Yes or No:**

*P***(***Play=Y***| x) = ***P***(***Play=Y***) · [***P***(O=s| Play=Y) . ***P***(T=c| Play=Y) . ***P***(H=h| Play=Y) . ***P***(W=t| Play=Y)**

**Weather example when play = Yes:**

*P***(***Play=Y***| x) = ***P***(***Play=Y***) · [***P***(O=s| Play=Y) . ***P***(T=c| Play=Y) . ***P***(H=h| Play=Y) . ***P***(W=t| Play=Y)**

Weather example when play = No:

*P*(*Play=N*| x) = *P*(*Play=N*) · [*P*(O=s| Play=N) . *P*(T=c| Play=N) . *P*(H=h| Play=N) . *P*(W=t| Play=N)

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