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I'm trying to use PyStruct's CRF implementation. In its user guide, it says the following:

I call these models Conditional Random Fields (CRFs), but this a slight abuse of notation, as PyStruct actually implements perceptron and max-margin learning, not maximum likelihood learning. So these models might better be called Maximum Margin Random Fields.

How are max margin and max likelihood related? Will they give similar answers?

It seems like max-margin learning is discriminative, while max-likelihood is generative, but I'd like to know more than that.

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All these methods are discriminative. They do exactly the same computation at prediction time. The difference is at training time: optimization objective is different. For the same training data these models can assign different values to model parameters after training. Max-margin methods are generalization of SVMs to structured prediction; CRF is a generalization of Logistic Regression for structured prediction. In practice they should give similar results.

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