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.

[EX 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.
[EX A]: Learning a Hidden Basis Through Imperfect Measurements: An Algorithmic Primitive

[EX Q]: This paper deals with the problem of esti mating the probability that one event was a cause of another in a given scenario. Us ing structural-semantical definitions of the probabilities of necessary or sufficient cau sation (or both), we show how to optimally bound these quantities from data obtained in experimental and observational studies, making minimal assumptions concerning the data-generating process. In particular, we strengthen the results of Pearl (1999) by weakening the data-generation assumptions and deriving theoretically sharp bounds on the probabilities of causation. These results delineate precisely how empirical data can be used both in settling questions of attribution and in solving attribution-related problems of decision making.
[EX A]: Probabilities of Causation: Bounds and Identification

[EX Q]: The impact of culture in visual emotion perception has recently captured the attention of multimedia research. In this study, we provide powerful computational linguistics tools to explore, retrieve and browse a dataset of 16K multilingual affective visual concepts and 7.3M Flickr images. First, we design an effective crowdsourcing experiment to collect human judgements of sentiment connected to the visual concepts. We then use word embeddings to represent these concepts in a low dimensional vector space, allowing us to expand the meaning around concepts, and thus enabling insight about commonalities and differences among different languages. We compare a variety of concept representations through a novel evaluation task based on the notion of visual semantic relatedness. Based on these representations, we design clustering schemes to group multilingual visual concepts, and evaluate them with novel metrics based on the crowdsourced sentiment annotations as well as visual semantic relatedness. The proposed clustering framework enables us to analyze the full multilingual dataset in-depth and also show an application on a facial data subset, exploring cultural insights of portrait-related affective visual concepts.
[EX A]:
Multilingual Visual Sentiment Concept Matching