Machine Learning Naive Bayes
Those who have learned the probability must know Bayes' theorem and have an unparalleled position in the field of information. Bayesian algorithm is a kind of algorithm based on Bayes' theorem, which is mainly used to solve the classification and regression problems.
The two most widely used classification models for machine learning in artificial intelligence are 1) Decision Tree Model and 2) Naive Bayesian Model.
Today we focus on naive Bayes (NB). Note that NB is not cattle X but Naive Bayesian. ^_^
Naive Bayes is one of the classic machine learning algorithms and is one of the few classification algorithms based on probability theory. Naive Bayes' principle is simple and easy to implement. It is mostly used for text classification, spam filtering, and sentiment analysis.
In a paper published by Thomas Bayes in 1763, the British mathematician first proposed Bayes' Theorem.
The application of Bayes' Theorem requires a lot of calculations, so it has not been widely used for a long time in history. Only after the birth of the computer did it gain real importance. It has been found that many statistics cannot be objectively judged in advance, and the large data sets that emerged in the Internet era, coupled with high-speed computing capabilities, provide convenience for verifying these statistics and create conditions for the application of Bayes' theorem. Its power is increasingly apparent.
Concepts and definitions:
Naive Bayes method is a classification method based on Bayesian theorem and independent conditions of feature conditions. Naive Bayes Classifier (NBC) originated from classical mathematical theory, has a solid mathematical foundation, and stable classification efficiency. Naive Bayes classifier (NBC) models require few parameters to estimate, are less sensitive to missing data, and are relatively simple in algorithm. In theory, the NBC model has the smallest error rate compared to other classification methods. However, this is not always the case. This is because the NBC model assumes that the attributes are independent of each other. This hypothesis is often not true in practical applications. This has brought certain influence on the correct classification of the NBC model.
Bayesian classification is a general term for a series of classification algorithms. All of these algorithms are based on Bayes' theorem and are collectively referred to as Bayesian classification. Naive Bayes classification is the simplest and most common classification method in Bayesian classification.
Theoretical basis:
The most central part of Naive Bayes is the Bayesian rule, and the cornerstone of the Bayesian rule is the conditional probability. Bayes' rule is as follows:
Here, C denotes a category, enters the data to be judged, and the formula gives the probability of a certain class of solutions.
The naive Bayes classifier is based on a simple assumption that when a given target value is given, the attributes are independent of each other.
Naive Bayes classifier model:
Vmap=arg maxP( Vj | a1, a2...an) Vj belongs to the V set, where Vmap is the given most likely target value given an example. Where a1. . . An is the attribute in this example. The Vmap target value is the one with the highest probability calculated later. So use max to indicate.
The Bayesian formula is applied to P(Vj|a1, a2...an). Vmap = arg max P(a1,a2...an |Vj) P(Vj)/P(a1,a2...an) is available. And because the naive Bayes classifier defaults to a1. . . An independent. So P(a1, a2...an) is not useful for the result. Vmap= arg max P(a1,a2...an |Vj ) P( Vj ) is available.
"The naive Bayes classifier is based on a simple assumption that when a given target value is given, the conditions are independent of each other. In other words, this hypothesis states the target value for a given instance. Observed for the joint a1, a2...an The probability is exactly the product of the probabilities for each individual attribute: P(a1,a2...an |Vj) =Î i P(ai| Vj )
Therefore, the naive Bayes classifier model: Vnb=arg max P( Vj ) Î iP ( ai | Vj )
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