Optimizing 0/1 Loss for Perceptrons by Random Coordinate Descent

The 0/1 loss is an important cost function for perceptrons. Nevertheless it cannot be easily minimized by most existing perceptron learning algorithms. In this paper, we propose a family of random coordinate descent algorithms to directly minimize the 0/1 loss for perceptrons, and prove their convergence. Our algorithms are computationally efficient, and usually achieve the lowest 0/1 loss compared with other algorithms. Such advantages make them favorable for nonseparable real-world problems. Experiments show that our algorithms are especially useful for ensemble learning, and could achieve the lowest test error for many complex data sets when coupled with AdaBoost

OPE of the stress tensors and surface operators

We demonstrate that the divergent terms in the OPE of a stress tensor and a surface operator of general shape cannot be constructed only from local geometric data depending only on the shape of the surface. We verify this holographically at d=3 for Wilson line operators or equivalently the twist operator corresponding to computing the entanglement entropy using the Ryu-Takayanagi formula. We discuss possible implications of this result.Comment: 20 pages, no figur

Ordinal Regression by Extended Binary Classification

We present a reduction framework from ordinal regression to binary classification based on extended examples. The framework consists of three steps: extracting extended examples from the original examples, learning a binary classifier on the extended examples with any binary classification algorithm, and constructing a ranking rule from the binary classifier. A weighted 0/1 loss of the binary classifier would then bound the mislabeling cost of the ranking rule. Our framework allows not only to design good ordinal regression algorithms based on well-tuned binary classification approaches, but also to derive new generalization bounds for ordinal regression from known bounds for binary classification. In addition, our framework unifies many existing ordinal regression algorithms, such as perceptron ranking and support vector ordinal regression. When compared empirically on benchmark data sets, some of our newly designed algorithms enjoy advantages in terms of both training speed and generalization performance over existing algorithms, which demonstrates the usefulness of our framework

Assisted optimal state discrimination without entanglement

A fundamental problem in quantum information is to explore the roles of different quantum correlations in a quantum information procedure. Recent work [Phys. Rev. Lett., 107 (2011) 080401] shows that the protocol for assisted optimal state discrimination (AOSD) may be implemented successfully without entanglement, but with another correlation, quantum dissonance. However, both the original work and the extension to discrimination of $d$ states [Phys. Rev. A, 85 (2012) 022328] have only proved that entanglement can be absent in the case with equal a \emph{priori} probabilities. By improving the protocol in [Sci. Rep., 3 (2013) 2134], we investigate this topic in a simple case to discriminate three nonorthogonal states of a qutrit, with positive real overlaps. In our procedure, the entanglement between the qutrit and an auxiliary qubit is found to be completely unnecessary. This result shows that the quantum dissonance may play as a key role in optimal state discrimination assisted by a qubit for more general cases.Comment: 6 pages, 3 figures. Accepted by EPL. We extended the protocol for assisted optimal state discrimination to the case with positive real overlaps, and presented a proof for the absence of entanglemen

Scene Graph Generation with External Knowledge and Image Reconstruction

Scene graph generation has received growing attention with the advancements in image understanding tasks such as object detection, attributes and relationship prediction,~\etc. However, existing datasets are biased in terms of object and relationship labels, or often come with noisy and missing annotations, which makes the development of a reliable scene graph prediction model very challenging. In this paper, we propose a novel scene graph generation algorithm with external knowledge and image reconstruction loss to overcome these dataset issues. In particular, we extract commonsense knowledge from the external knowledge base to refine object and phrase features for improving generalizability in scene graph generation. To address the bias of noisy object annotations, we introduce an auxiliary image reconstruction path to regularize the scene graph generation network. Extensive experiments show that our framework can generate better scene graphs, achieving the state-of-the-art performance on two benchmark datasets: Visual Relationship Detection and Visual Genome datasets.Comment: 10 pages, 5 figures, Accepted in CVPR 201