We observe that the technique of Markov contraction can be used to establish measure concentration for a broad class of non-contracting chains. In particular, geometric ergodicity provides a simple and versatile framework. This leads to a short, elementary proof of a general concentration inequality for Markov and hidden Markov chains (HMM), which supercedes some of the known results and easily extends to other processes such as Markov trees. As applications, we give a Dvoretzky-Kiefer-Wolfowitz-type inequality and a uniform Chernoff bound. All of our bounds are dimension-free and hold for countably infinite state spaces.

Real eigenpairs of symmetric tensors play an important role in multiple applications. In this paper we propose and analyze a fast iterative Newton-based method to compute real eigenpairs of symmetric tensors. We derive sufficient conditions for a real eigenpair to be a stable fixed point for our method, and prove that given a sufficiently close initial guess, the convergence rate is quadratic. Empirically, our method converges to a significantly larger number of eigenpairs compared to previously proposed iterative methods, and with enough random initializations typically finds all real eigenpairs. In particular, for a generic symmetric tensor, the sufficient conditions for local convergence of our Newton-based method hold simultaneously for all its real eigenpairs.

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We show that a recently proposed 1-nearest-neighbor-based multiclass learning algorithm is universally strongly Bayes consistent in all metric spaces where such Bayes consistency is possible, making it an "optimistically universal" Bayes-consistent learner. This is the first learning algorithm known to enjoy this property; by comparison, k-NN and its variants are not generally universally Bayes consistent, except under additional structural assumptions, such as an inner product, a norm, finite doubling dimension, or a Besicovitch-type property.The metric spaces in which universal Bayes consistency is possible are the "essentially separable" ones -a new notion that we define, which is more general than standard separability. The existence of metric spaces that are not essentially separable is independent of the ZFC axioms of set theory. We prove that essential separability exactly characterizes the existence of a universal Bayes-consistent learner for the given metric space. In particular, this yields the first impossibility result for universal Bayes consistency.Taken together, these positive and negative results resolve the open problems posed in Kontorovich, Sabato, Weiss (2017).

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Sighted individuals draw a significant amount of information from signs but this information is denied to the visually impaired. VIDI is an evolving system for detecting and recognizing signs in the environment and voice synthesizing their textual contents. The wide variety of signs commonly encountered and the uncontrolled nature of the real world add significant complexity to the problem. VIDI treats the recognition problem as one of matching an unknown sign image, obtained from the detection component as a hypothesized sign, to a database of known signs. A color based support vector machine classifier coarsely picks a group of sign classes that are the most likely matches to the query. A finer retrieval technique employing corners and shape contexts ranks the hypothesized sign classes and verifies whether or not the top ranked class is the true class of the query. The database includes a set of real images with a wide variety of sign classes, each containing multiple signs exhibiting not only illumination differences, but also rotational variations. Tested on over 1,200 images, our system correctly recognizes and identifies the sign class of a query, achieving a 94.75% accuracy.

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