1. The algorithm logic is simple , Easy to implement
2. The cost of time and space is small in the process of classification , High classification accuracy , Fast
3. Naive Bayesian model originated from classical mathematical theory , Stable classification efficiency
4. Less sensitive to missing data , The algorithm is also relatively simple , It is often used in text categorization
5. Good for small-scale data , Be able to handle multi category tasks , For incremental training
   shortcoming ：

• Theoretically , Compared with other classification methods, naive Bayesian model has the smallest error rate . But it's not always the case , This is because the naive Bayesian model assumes Properties are independent of each other , This assumption is often not true in practical application , When the number of attributes is large or the correlation between attributes is large , The classification effect is not good .
• Need to know Prior probability , And a priori probability is often based on assumptions or existing training data , In some cases, there may be errors in classification decision-making due to the assumption of a priori probability .

Naive Bayes

Naive Bayes It's based on Independent hypothesis of characteristic conditions and Bayesian principle It's a new classification algorithm . Naive Bayes Obtained through training data X And y Of Joint distribution ; Then for what to predict X, according to Bayes' formula , Output Posterior probability maximal y.
Naive Bayes It's a kind of Generative Learning algorithms , Its generation method is through learning X,Y The joint distribution of . Assume that each feature is given y Are independent of each other .

Bayes' formula

$P(B\mid A)=\frac{P(B)P(A\mid B)}{P(A)}$
In the formula , event B The probability of is P（B）, event B A conditional event has occurred A The probability of is P（A|B）, event A The occurrence of a conditional event B The probability of is P（B|A）

Naive Bayes “ simple ” How to understand

Naive Bayes The simplicity in can be understood as “ Simple , naive ” It means , because “ simple ” It's a hypothesis Features are equally important , Are independent of each other , Not affecting each other , But in our real society , Attributes are not always independent of each other .

What is Laplace smoothing

Laplace smoothing yes Naive Bayes In dealing with Zero probability A way to correct the problem . When it comes to classification , There may be a case where an attribute does not appear at the same time with a class in the training set , If the calculation is directly based on the expression of naive Bayesian classifier, there will be Zero probability The phenomenon . In order to prevent the information carried by other attributes from being used by attribute values that have not appeared in the training set “ erase ”, That's why Laplace estimator Amendment . The way to do it is ： Add... To the molecule 1, For a priori probability , Add the number of possible categories in the training set to the denominator ; For conditional probability , Add... To the denominator i Possible values of attributes

The application of naive Bayes

Naive Bayes The most widely used should be Document classification , Spam text filtering , Sentiment analysis , Recommendation system , Spelling correction etc. .

Naive Bayes is not sensitive to outliers

Naive Bayes Yes outliers Insensitivity . So in data processing , We can not remove outliers , Because preserving outliers can maintain the overall accuracy of naive Bayesian algorithm , Removing outliers may lead to the decline of generalization ability of the model due to the loss of some outliers in the process of prediction

A priori probability and a posteriori probability

Prior probability ： It's directly the probability of something happening
Posterior probability ： Know that something has happened , The probability of this happening