Putting MAP back on the map

Conditional Random Fields (CRFs) are popular models in

computer vision for solving labeling problems such as image denoising.

This paper tackles the rarely addressed but important problem of learn-

ing the full form of the potential functions of pairwise CRFs. We ex-

amine two popular learning techniques, maximum likelihood estimation

and maximum margin training. The main focus of the paper is on models

such as pairwise CRFs, that are simplistic (misspecified) and do not fit

the data well. We empirically demonstrate that for misspecified models

maximum-margin training with MAP prediction is superior to maximum

likelihood estimation with any other prediction method. Additionally we

examine the common belief that MLE is better at producing predictions

matching image statistics.

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