The mean field algorithm is a widely used approximate inference algorithm for graphical models whose exact inference is intractable. In each iteration of mean field, the approximate marginals for each variable are updated by getting information from the neighbors. This process can be equivalently converted into a feedforward network, with each layer representing one iteration of mean field and with tied weights on all layers. This conversion enables a few natural extensions, e.g. untying the weights in the network. In this paper, we study these mean field networks (MFNs), and use them as inference tools as well as discriminative models. Preliminary experiment results show that MFNs can learn to do inference very efficiently and perform significantly better than mean field as discriminative models.
Another work by @cite_3 briefly draws a connection between mean field inference of a specific binary MRF with neural networks, but did not explore further variations.
@cite_3
2129981175
Convolutional networks have achieved a great deal of success in high-level vision problems such as object recognition. Here we show that they can also be used as a general method for low-level image processing. As an example of our approach, convolutional networks are trained using gradient learning to solve the problem of restoring noisy or degraded images. For our training data, we have used electron microscopic images of neural circuitry with ground truth restorations provided by human experts. On this dataset, Markov random field (MRF), conditional random field (CRF), and anisotropic diffusion algorithms perform about the same as simple thresholding, but superior performance is obtained with a convolutional network containing over 34,000 adjustable parameters. When restored by this convolutional network, the images are clean enough to be used for segmentation, whereas the other approaches fail in this respect. We do not believe that convolutional networks are fundamentally superior to MRFs as a representation for image processing algorithms. On the contrary, the two approaches are closely related. But in practice, it is possible to train complex convolutional networks, while even simple MRF models are hindered by problems with Bayesian learning and inference procedures. Our results suggest that high model complexity is the single most important factor for good performance, and this is possible with convolutional networks.