Discriminative Model and Generative Model

本文探讨了生成模型与判别模型的区别。通过一个简单例子展示了两种模型如何学习不同的概率分布,并讨论了它们各自的优势及应用场景。对于分类任务而言,通常判别模型表现更优。

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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 adiscriminative 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 calleddiscriminative 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.


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