判别式模型与生成式模型的区别

产生式模型(Generative Model)与判别式模型(Discrimitive Model)是分类器常遇到的概念，它们的区别在于：

对于输入x，类别标签y：
产生式模型估计它们的联合概率分布P(x,y)
判别式模型估计条件概率分布P(y|x)

产生式模型可以根据贝叶斯公式得到判别式模型，但反过来不行。

Andrew Ng在NIPS2001年有一篇专门比较判别模型和产生式模型的文章：
On Discrimitive vs. Generative classifiers: A comparision of logistic regression and naive Bayes

( http://robotics.stanford.edu/~ang/papers/nips01-discriminativegenerative.pdf )

判别式模型常见的主要有：

　　　　Logistic Regression

　　　　SVM

　　　　Traditional Neural Networks

　　　　Nearest Neighbor

　　　　CRF

　　　　Linear Discriminant Analysis

　　　　Boosting

　　　　Linear Regression

产生式模型常见的主要有：

Gaussians

Naive Bayes

Mixtures of Multinomials

Mixtures of Gaussians

Mixtures of Experts

HMMs

　　　　Sigmoidal Belief Networks, Bayesian Networks

　　　　Markov Random Fields

　　　　Latent Dirichlet Allocation

一个通俗易懂的解释

　　Let's say you have input data x and you want to classify the data into labels y. A generative model learns the joint probability distribution p(x,y) and a discriminative model learns the conditional probability distribution p(y|x) – which you should read as 'the probability of y given x'.

　　Here's a really simple example. Suppose you have the following data in the form (x,y):

(1,0), (1,0), (2,0), (2, 1)

　　p(x,y) is

	y=0	y=1
x=1	1/2	0
x=2	1/4	1/4

　　p(y|x) is

	y=0	y=1
x=1	1	0
x=2	1/2	1/2

　　If you take a few minutes to stare at those two matrices, you will understand the difference between the two probability distributions.

　　The distribution p(y|x) is the natural distribution for classifying a given example x into a class y, which is why algorithms that model this directly are called discriminative algorithms. Generative algorithms model p(x,y), which can be tranformed into p(y|x) by applying Bayes rule and then used for classification. However, the distribution p(x,y) can also be used for other purposes. For example you could use p(x,y) to generate likely ( x,y) pairs.

　　From the description above you might be thinking that generative models are more generally useful and therefore better, but it's not as simple as that. This paper is a very popular reference on the subject of discriminative vs. generative classifiers, but it's pretty heavy going. The overall gist is that discriminative models generally outperform generative models in classification tasks.