<p>I encountered a modified CRF named <a href="https://arxiv.org/pdf/1809.03599.pdf" rel="nofollow noreferrer">fuzzy CRF</a> as shown below. </p>

<p><a href="https://i.stack.imgur.com/JcAfW.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/JcAfW.png" alt="enter image description here"></a></p>

<p>Its mathematics is quite simple as we can see from equation 2 in the paper: </p>

<p><a href="https://i.stack.imgur.com/fttY8.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/fttY8.png" alt="enter image description here"></a></p>

<p>We just sum all the energies of the paths in the numerator, and the denominator remains the same. For inference, we can apply Viterbi or beam search.   </p>
MultiLabel Classification using Conditional Random Field
<p>Is it possible to use Conditional Random Field for MultiLabel Classification? I saw a python CRF implementation at <a href="https://pystruct.github.io/user_guide.html" rel="noreferrer">https://pystruct.github.io/user_guide.html</a>, but couldn't figure a way to do multilabel classification.</p>