Approximate Message Passing with Restricted Boltzmann Machine Priors

Approximate Message Passing (AMP) has been shown to be an excellent statistical approach to signal inference and compressed sensing problem. The AMP framework provides modularity in the choice of signal prior; here we propose a hierarchical form of the Gauss-Bernouilli prior which utilizes a Restricted Boltzmann Machine (RBM) trained on the signal support to push reconstruction performance beyond that of simple iid priors for signals whose support can be well represented by a trained binary RBM. We present and analyze two methods of RBM factorization and demonstrate how these affect signal reconstruction performance within our proposed algorithm. Finally, using the MNIST handwritten digit dataset, we show experimentally that using an RBM allows AMP to approach oracle-support performance

Unsupervised Learning of Visual Structure using Predictive Generative Networks

The ability to predict future states of the environment is a central pillar of intelligence. At its core, effective prediction requires an internal model of the world and an understanding of the rules by which the world changes. Here, we explore the internal models developed by deep neural networks trained using a loss based on predicting future frames in synthetic video sequences, using a CNN-LSTM-deCNN framework. We first show that this architecture can achieve excellent performance in visual sequence prediction tasks, including state-of-the-art performance in a standard 'bouncing balls' dataset (Sutskever et al., 2009). Using a weighted mean-squared error and adversarial loss (Goodfellow et al., 2014), the same architecture successfully extrapolates out-of-the-plane rotations of computer-generated faces. Furthermore, despite being trained end-to-end to predict only pixel-level information, our Predictive Generative Networks learn a representation of the latent structure of the underlying three-dimensional objects themselves. Importantly, we find that this representation is naturally tolerant to object transformations, and generalizes well to new tasks, such as classification of static images. Similar models trained solely with a reconstruction loss fail to generalize as effectively. We argue that prediction can serve as a powerful unsupervised loss for learning rich internal representations of high-level object features.Comment: under review as conference paper at ICLR 201