Artificial Intelligence

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Genetic Programming

Naive Bayes

Naive Bayes is first used to Classify Data before any other Algorithms are run. This is a simple probabilistic classifier based on applying Bayes theorem with independence assumptions. Naive Bayes can be trained very efficiently in a supervised learning. In many practical applications, parameter estimation for Naive Bayes models uses the method of maximum Probability; in other words, one can work with the naive Bayes model without believing in Bayesian probability or using any Bayesian methods.

Naive Bayes classifiers often work much better in many complex real-world situations than one might expect. Recently, careful analysis of the Bayesian classification problem has shown that there are some theoretical reasons for the apparently unreasonable efficacy of naive Bayes classifiers. An advantage of the Naive Bayes classifier is that it requires a small amount of training data to estimate the parameters necessary for classification. Because independent variables are assumed, only the variances of the variables for each class need to be determined and not the entire covariance matrix.

Naive Bayes can be used after Text Mining to Classify Documents under different Search Vectors. On data warehouse applications this is first used before the clustering or decision trees.

Recom Systems can convert your Data bases into information reservoirs to convert the information into extremely useful Forecast Models.

Bayes Theorem

Let X be the data record (case) whose class label is unknown. Let H be some hypothesis, such as "data record X belongs to a specified class C." For classification, we want to determine P (H|X) -- the probability that the hypothesis H holds, given the observed data record X.

P (H|X) is the posterior probability of H conditioned on X. For example, the probability that a fruit is an apple, given the condition that it is red and round.  In contrast, P(H) is the prior probability, or apriori probability, of H. In this example P(H) is the probability that any given data record is an apple, regardless of how the data record looks. The posterior probability, P (H|X), is based on more information (such as background knowledge) than the prior probability, P(H), which is independent of X.

Similarly, P (X|H) is posterior probability of X conditioned on H. That is, it is the probability that X is red and round given that we know that it is true that X is an apple. P(X) is the prior probability of X,  i.e., it is the probability that a data record from our set of fruits is red and round. Bayes theorem is useful in that it provides a way of calculating the posterior probability, P(H|X), from P(H), P(X), and P(X|H). Bayes theorem is

P (H|X)  =  P(X|H) P(H) / P(X)

Studies comparing classification algorithms have found the Naive Bayesian classifier to be comparable in performance with classification trees and with neural network classifiers.  They have also exhibited high accuracy and speed when applied to large databases.

The Naive Bayesian Classifier (NBC) is used as the learning algorithm for diagnosing and evaluating one of the most hard-to-distinguish categories of diseases.