principle
Naive Bayes ( Naive Bayes ) method is based on the assumption independence Bayes' theorem and characteristic condition (which is a strong assumption, although making the process easier, but sometimes at the expense of a certain classification accuracy) classification belonging generated ( the Generative approach one) method.
Why is it belongs to the generation methods?
It is through the joint probability distribution of the training data set learning , so we can represent the distribution of data from a statistical point of view, reflects the similarity of similar data itself.
Specifically , our goal is to seek posterior probability , i.e., a known input value, the output request Probability, the probability of which the largest is the classification results.
And by the conditional probability formula:
Where the prior probability distribution K = 1,2, ... n-can be obtained directly from the training data.
For the conditional probability
Launched as the following, it is found that there is exponential parameters, it is virtually impossible to estimate. :
Here reflect naive Bayes method is simple (simple) features: We conditional probability distribution of here to do aconditional independenceassumptions.
Here is assumed independence assumptions mean that the conditionscharacteristic for classification at the class of conditional independence are determined.
Our goal
in the denominator launched by the P (X) total probability formula is:
then brought aboveconditional independence assumptions formula:
and we chose the biggest result of probability, the Bayesian classifier can be expressed as:
noted denominator for all
They are the same, so in fact the final classification only requirements:
Real
To be added
reference
This article is a blogger summarized in "statistical learning methods" "machine learning real."