Structured predictions¶
It is an example of MAP inference on PGM over a conditional random field
\[
\arg \max_y \log p(y|x) = \arg \max_y \sum_{c}\theta_c(y_c,x_c)
\]
\(\theta_c(y_c, x_c) = \log \phi_c(y_c, x_c)\) are clique potentials
An example to structured prediction is handwriting recognition, where we given images \(x_i \in [0,1]^{d \times d}\) of characters in the form of pixel matrices. MAP inference is finding most likely word \((y_i)_{i=1}^n\) encoded by the image.