Temporal prediction is critical for making intelligent and robust decisions in complex dynamic environments. Motion prediction needs to model the inherently uncertain future which often contains multiple potential outcomes, due to multi-agent interactions and the latent goals of others.

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. Summary: This paper studies the Principal Component Analysis (PCA) for large tensors of arbitrary order k under a single-spike model. Solving tensor PCA exactly is in general NP hard. Given a completely observed rank-one symmetric tensor, this paper provides conditions under which one can reliably estimate the unknown unit vector. Specifically, the paper gives conditions on signal-to-noise ratio under several scenarios which allow one to estimate the solution reliably. For the maximum-likelihood estimator (MLE), the authors show that in an ideal case with unbounded computational resources, the MLE is successful with high probability if the signal-to-noise ration is above sqrt(k.log(k))(1+o(1))

Neural Information Processing Systems http://nips.cc/

"NIPS Neural Information Processing Systems 8-11th December 2014, Montreal, Canada",,, "Paper ID:","132" "Title:","Fundamental Limits of Online and Distributed Algorithms for Statistical Learning and Estimation" Current Reviews First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. The paper considers the effect of memory constraints on some classes of online and distributed algorithms. The main goal of the authors is to show that there exist learning problems where imposing a memory constraint provably hurts the performance of any algorithm, in the sense that the best achievable performance guarantees are worse than some known upper bound on an algorithm that operates without memory constraints. The authors also provide a lower bound on the regret of online algorithms that operate under a specific feedback constraint. The results of the paper follow from an elegant information-theoretic argument concerning hide-and-seek problems where a learner has to detect a biased coordinate of i.i.d.

Neural Information Processing Systems http://nips.cc/

Such high-stakes applications require not only point predictions but also accurate quantification of predictive uncertainty, i.e. meaningful confidence values in addition to class predictions.

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. This paper studies a planted partition model for random m-uniform hypergraphs, and proves the consistency of a natural generalization of spectral clustering. The hypergraph adjacency tensor is (mode-1) flattened to a matrix, from which a normalized Laplacian matrix is formed and the standard spectral partitioning is then applied. The striking feature of the analysis is that the rate of convergence improves as m increases, provided that the number of partitions is small. Some experiments on both synthetic and application derived data are reported, and the proposed method is shown to be relatively effective, especially given its simplicity. The model is well-motivated by applications in computer vision and likely elsewhere.