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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