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.

Input: Consider Input: 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.

Output: Learning a Hidden Basis Through Imperfect Measurements: An Algorithmic Primitive


Input: Consider Input: Despite progress in visual perception tasks such as image classification and detection, computers still struggle to understand the interdependency of objects in the scene as a whole, e.g., relations between objects or their attributes. Existing methods often ignore global context cues capturing the interactions among different object instances, and can only recognize a handful of types by exhaustively training individual detectors for all possible relationships. To capture such global interdependency, we propose a deep Variation-structured Reinforcement Learning (VRL) framework to sequentially discover object relationships and attributes in the whole image. First, a directed semantic action graph is built using language priors to provide a rich and compact representation of semantic correlations between object categories, predicates, and attributes. Next, we use a variation-structured traversal over the action graph to construct a small, adaptive action set for each step based on the current state and historical actions. In particular, an ambiguity-aware object mining scheme is used to resolve semantic ambiguity among object categories that the object detector fails to distinguish. We then make sequential predictions using a deep RL framework, incorporating global context cues and semantic embeddings of previously extracted phrases in the state vector. Our experiments on the Visual Relationship Detection (VRD) dataset and the large-scale Visual Genome dataset validate the superiority of VRL, which can achieve significantly better detection results on datasets involving thousands of relationship and attribute types. We also demonstrate that VRL is able to predict unseen types embedded in our action graph by learning correlations on shared graph nodes.

Output: Deep Variation-structured Reinforcement Learning for Visual Relationship and Attribute Detection


Input: Consider Input: We study the problem of learning in the presence of a drifting target concept. Specifically, we provide bounds on the error rate at a given time, given a learner with access to a history of independent samples labeled according to a target concept that can change on each round. One of our main contributions is a refinement of the best previous results for polynomial-time algorithms for the space of linear separators under a uniform distribution. We also provide general results for an algorithm capable of adapting to a variable rate of drift of the target concept. Some of the results also describe an active learning variant of this setting, and provide bounds on the number of queries for the labels of points in the sequence sufficient to obtain the stated bounds on the error rates.


Output: Learning with a Drifting Target Concept