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Naïve Bayesian Classifiers Project & Assignment Help | What is Naive Bayesian Algorithms?

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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