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.

Q: In this paper we formulate the framework of recovering a hidden orthonormal basis given access to a<lb>certain "Basis Encoding Function". We describe the class of Basis Encoding Functions (BEF), such that<lb>their local maxima on the unit sphere are in one-to-one correspondence with the basis elements. This<lb>description relies on a certain "hidden convexity" property of these functions. A number of theoretical<lb>and practical problems of recent interest can be interpreted as recovering a hidden basis from potentially<lb>noisy observations. Specifically, we show how our simple and general framework applies to Independent<lb>Component Analysis (ICA), tensor decompositions, spectral clustering and Gaussian mixture learning.<lb>We describe a new algorithm, "gradient iteration", for provable recovery of the hidden basis. We<lb>provide a complete theoretical analysis of Gradient Iteration both for the exact case as well as for the<lb>case when the observed function is a perturbation of the "true" underlying BEF. In both cases we show<lb>convergence and complexity bounds polynomial in dimension and other relevant parameters, such as<lb>perturbation size. Our perturbation results can be considered as a very general non-linear version of<lb>the classical Davis-Kahan theorem for eigenvectors of perturbations of symmetric matrices. In addition<lb>we show that in the exact case the algorithm converges superlinearly and give conditions relating the<lb>degree of convergence to properties of the Basis Encoding Function. Our algorithm can be viewed as a<lb>generalization of the classical power iteration method for eigenanalysis of symmetric matrices as well as<lb>a generalization of power iterations for tensors. Moreover, the Gradient Iteration algorithm can be easily<lb>and efficiently implemented in practice.

A: Learning a Hidden Basis Through Imperfect Measurements: An Algorithmic Primitive
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Q: String Kernel (SK) techniques, especially those using gapped k-mers as features (gk), have obtained great success in classifying sequences like DNA, protein, and text. However, the state-of-the-art gk-SK runs extremely slow when we increase the dictionary size () or allow more number of mismatches (M). This is because current gk-SK uses a trie-based algorithm to calculate co-occurrence of mismatched substrings resulting in a time cost proportional to O( ). We propose a fast algorithm for calculating Gapped k-mer Kernel using Counting (GaKCo). GaKCo uses associative arrays to calculate the co-occurrence of substrings using cumulative counting. This algorithm is fast, scalable to larger and M , and naturally parallelizable. We provide a rigorous asymptotic analysis that compares GaKCo with the state-of-the-art gk-SK. Theoretically, the time cost of GaKCo is independent of the term that slows down the trie-based approach. Experimentally, we observe that GaKCo achieves the same accuracy as the state-of-the-art and outperforms its speed by factors of 2, 100, and 4, on classifying sequences of DNA (5 datasets), protein (12 datasets), and character-based English text (2 datasets), respectively .

A: GaKCo: a Fast Gapped k-mer string Kernel using Counting
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Q: We describe a method to produce a network where current methods such as DeepFool have great difficulty producing adversarial samples. Our construction suggests some insights into how deep networks work. We provide a reasonable analyses that our construction is difficult to defeat, and show experimentally that our method is hard to defeat using several standard networks and datasets. We use our method to produce a system that can reliably detect whether an image is a picture of a real scene or not. Our system applies to images captured with depth maps (RGBD images) and checks if a pair of image and depth map is consistent. It relies on the relative difficulty of producing naturalistic depth maps for images in post processing. We demonstrate that our system is robust to adversarial examples built from currently known attacking approaches.

A:
SafetyNet: Detecting and Rejecting Adversarial Examples Robustly
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