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.
On the neural networks side, people have tried to use a neural network to approximate intractable posterior distributions for a long time, especially for learning sigmoid belief networks, see for example @cite_8 and recent paper @cite_0 and citations therein. As far as we know, no previous work on the neural network side have discussed the connection with mean field or belief propagation type methods used for variational inference in graphical models.
@cite_0 @cite_8
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Highly expressive directed latent variable models, such as sigmoid belief networks, are difficult to train on large datasets because exact inference in them is intractable and none of the approximate inference methods that have been applied to them scale well. We propose a fast non-iterative approximate inference method that uses a feedforward network to implement efficient exact sampling from the variational posterior. The model and this inference network are trained jointly by maximizing a variational lower bound on the log-likelihood. Although the naive estimator of the inference network gradient is too high-variance to be useful, we make it practical by applying several straightforward model-independent variance reduction techniques. Applying our approach to training sigmoid belief networks and deep autoregressive networks, we show that it outperforms the wake-sleep algorithm on MNIST and achieves state-of-the-art results on the Reuters RCV1 document dataset. Convolutional neural networks (CNNs) work well on large datasets. But labelled data is hard to collect, and in some applications larger amounts of data are not available. The problem then is how to use CNNs with small data -- as CNNs overfit quickly. We present an efficient Bayesian CNN, offering better robustness to over-fitting on small data than traditional approaches. This is by placing a probability distribution over the CNN's kernels. We approximate our model's intractable posterior with Bernoulli variational distributions, requiring no additional model parameters. On the theoretical side, we cast dropout network training as approximate inference in Bayesian neural networks. This allows us to implement our model using existing tools in deep learning with no increase in time complexity, while highlighting a negative result in the field. We show a considerable improvement in classification accuracy compared to standard techniques and improve on published state-of-the-art results for CIFAR-10. Highly expressive directed latent variable models, such as sigmoid belief networks, are difficult to train on large datasets because exact inference in them is intractable and none of the approximate inference methods that have been applied to them scale well. We propose a fast non-iterative approximate inference method that uses a feedforward network to implement efficient exact sampling from the variational posterior. The model and this inference network are trained jointly by maximizing a variational lower bound on the log-likelihood. Although the naive estimator of the inference model gradient is too high-variance to be useful, we make it practical by applying several straightforward model-independent variance reduction techniques. Applying our approach to training sigmoid belief networks and deep autoregressive networks, we show that it outperforms the wake-sleep algorithm on MNIST and achieves state-of-the-art results on the Reuters RCV1 document dataset. For the past decade, convolutional networks have been used for 3D reconstruction of neurons from electron microscopic (EM) brain images. Recent years have seen great improvements in accuracy, as evidenced by submissions to the SNEMI3D benchmark challenge. Here we report the first submission to surpass the estimate of human accuracy provided by the SNEMI3D leaderboard. A variant of 3D U-Net is trained on a primary task of predicting affinities between nearest neighbor voxels, and an auxiliary task of predicting long-range affinities. The training data is augmented by simulated image defects. The nearest neighbor affinities are used to create an oversegmentation, and then supervoxels are greedily agglomerated based on mean affinity. The resulting SNEMI3D score exceeds the estimate of human accuracy by a large margin. While one should be cautious about extrapolating from the SNEMI3D benchmark to real-world accuracy of large-scale neural circuit reconstruction, our result inspires optimism that the goal of full automation may be realizable in the future.