TASK DEFINITION: In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
PROBLEM: We use some of the largest order statistics of the random projections of a reference signal to construct a binary embedding that is adapted to signals correlated with such signal. The embedding is characterized from the analytical standpoint and shown to provide improved performance on tasks such as classification in a reduced-dimensionality space. KeywordsBinary Embeddings, Random projections

SOLUTION: Binary adaptive embeddings from order statistics of random projections

PROBLEM: The Support Vector Machine using Privileged Information (SVM+) has been proposed to train a classifier to utilize the additional privileged information that is only available in the training phase but not available in the test phase. In this work, we propose an efficient solution for SVM+ by simply utilizing the squared hinge loss instead of the hinge loss as in the existing SVM+ formulation, which interestingly leads to a dual form with less variables and in the same form with the dual of the standard SVM. The proposed algorithm is utilized to leverage the additional web knowledge that is only available during training for the image categorization tasks. The extensive experimental results on both Caltech101 and WebQueries datasets show that our proposed method can achieve a factor of up to hundred times speedup with the comparable accuracy when compared with the existing SVM+ method.

SOLUTION: Simple and Efficient Learning using Privileged Information

PROBLEM: Approximations of Laplace-Beltrami operators on manifolds through graph Laplacians have become popular tools in data analysis and machine learning. These discretized operators usually depend on bandwidth parameters whose tuning remains a theoretical and practical problem. In this paper, we address this problem for the unnormalized graph Laplacian by establishing an oracle inequality that opens the door to a well-founded data-driven procedure for the bandwidth selection. Our approach relies on recent results by Lacour and Massart [LM15] on the so-called Lepski's method.

SOLUTION:
Data driven estimation of Laplace-Beltrami operator