Unsupervised Deep Structure Learning by Recursive Dependency Analysis

Raanan Y. Yehezkel Rohekar, Guy Koren, Shami Nisimov, Gal Novik

Abstract: We introduce an unsupervised structure learning algorithm for deep, feed-forward, neural networks. We propose a new interpretation for depth and inter-layer connectivity where a hierarchy of independencies in the input distribution is encoded in the network structure. This results in structures allowing neurons to connect to neurons in any deeper layer skipping intermediate layers. Moreover, neurons in deeper layers encode low-order (small condition sets) independencies and have a wide scope of the input, whereas neurons in the first layers encode higher-order (larger condition sets) independencies and have a narrower scope. Thus, the depth of the network is automatically determined---equal to the maximal order of independence in the input distribution, which is the recursion-depth of the algorithm. The proposed algorithm constructs two main graphical models: 1) a generative latent graph (a deep belief network) learned from data and 2) a deep discriminative graph constructed from the generative latent graph. We prove that conditional dependencies between the nodes in the learned generative latent graph are preserved in the class-conditional discriminative graph. Finally, a deep neural network structure is constructed based on the discriminative graph. We demonstrate on image classification benchmarks that the algorithm replaces the deepest layers (convolutional and dense layers) of common convolutional networks, achieving high classification accuracy, while constructing significantly smaller structures. The proposed structure learning algorithm requires a small computational cost and runs efficiently on a standard desktop CPU.

TL;DR: A principled approach for structure learning of deep neural networks with a new interpretation for depth and inter-layer connectivity.

Keywords: unsupervised learning, structure learning, deep belief networks, probabilistic graphical models, Bayesian networks

Data: [CIFAR-10](https://paperswithcode.com/dataset/cifar-10), [CIFAR-100](https://paperswithcode.com/dataset/cifar-100), [ImageNet](https://paperswithcode.com/dataset/imagenet), [MNIST](https://paperswithcode.com/dataset/mnist), [SVHN](https://paperswithcode.com/dataset/svhn)