Recent work has shown that optical flow estimation can be formulated as a supervised learning problem. Moreover, convolutional networks have been successfully applied to this task. However, supervised flow learning is obfuscated by the shortage of labeled training data. As a consequence, existing methods have to turn to large synthetic datasets for easily computer generated ground truth. In this work, we explore if a deep network for flow estimation can be trained without supervision. Using image warping by the estimated flow, we devise a simple yet effective unsupervised method for learning optical flow, by directly minimizing photometric consistency. We demonstrate that a flow network can be trained from end-to-end using our unsupervised scheme. In some cases, our results come tantalizingly close to the performance of methods trained with full supervision.

Tensor decomposition is an important technique for capturing the high-order interactions among multiway data. Multi-linear tensor composition methods, such as the Tucker decomposition and the CANDECOMP/PARAFAC (CP), assume that the complex interactions among objects are multi-linear, and are thus insufficient to represent nonlinear relationships in data. Another assumption of these methods is that a predefined rank should be known. However, the rank of tensors is hard to estimate, especially for cases with missing values. To address these issues, we design a Bayesian generative model for tensor decomposition. Different from the traditional Bayesian methods, the high-order interactions of tensor entries are modeled with variational auto-encoder. The proposed model takes advantages of Neural Networks and nonparametric Bayesian models, by replacing the multi-linear product in traditional Bayesian tensor decomposition with a complex nonlinear function (via Neural Networks) whose parameters can be learned from data. Experimental results on synthetic data and real-world chemometrics tensor data have demonstrated that our new model can achieve significantly higher prediction performance than the state-of-the-art tensor decomposition approaches.