Conditional Random Fields (CRFs) are probabilistic models that are frequently used to analyze structured data. We use them to label and segment sequential data in various forms. One thing to note about CRFs is that they are discriminative models. This is in contrast to HMMs, which are generative models.

We can define a conditional probability distribution over a labeled sequence of measurements. We use this framework to build a CRF model. In HMMs, we have to define a joint distribution over the observation sequence and the labels.

One of the main advantages of CRFs is that they are conditional by nature. This is not the case with HMMs. CRFs do not assume any independence between output observations. HMMs assume that the output at any given time is statistically independent of the previous outputs. HMMs need this assumption to ensure that the inference process works in a robust way. But this assumption is not always true! Real...