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 Input:
Independent Component Analysis (ICA) is the problem of learning a square matrix A, given samples of X = AS, where S is a random vector with independent coordinates. Most existing algorithms are provably efficient only when each Si has finite and moderately valued fourth moment. However, there are practical applications where this assumption need not be true, such as speech and finance. Algorithms have been proposed for heavy-tailed ICA, but they are not practical, using random walks and the full power of the ellipsoid algorithm multiple times. The main contributions of this paper are: (1) A practical algorithm for heavy-tailed ICA that we call HTICA. We provide theoretical guarantees and show that it outperforms other algorithms in some heavy-tailed regimes, both on real and synthetic data. Like the current state-of-the-art, the new algorithm is based on the centroid body (a first moment analogue of the covariance matrix). Unlike the state-of-the-art, our algorithm is practically efficient. To achieve this, we use explicit analytic representations of the centroid body, which bypasses the use of the ellipsoid method and random walks. (2) We study how heavy tails affect different ICA algorithms, including HTICA. Somewhat surprisingly, we show that some algorithms that use the covariance matrix or higher moments can successfully solve a range of ICA instances with infinite second moment. We study this theoretically and experimentally, with both synthetic and real-world heavy-tailed data.

Ex Output:
Heavy-Tailed Analogues of the Covariance Matrix for ICA


Ex Input:
This paper proposes a novel approach for relation extraction from free text which is trained to jointly use information from the text and from existing knowledge. Our model is based on two scoring functions that operate by learning low-dimensional embeddings of words and of entities and relationships from a knowledge base. We empirically show on New York Times articles aligned with Freebase relations that our approach is able to efficiently use the extra information provided by a large subset of Freebase data (4M entities, 23k relationships) to improve over existing methods that rely on text features alone.

Ex Output:
Connecting Language and Knowledge Bases with Embedding Models for Relation Extraction


Ex Input:
Semantic segmentation requires a detailed labeling of image pixels by object category. Information derived from local image patches is necessary to describe the detailed shape of individual objects. However, this information is ambiguous and can result in noisy labels. Global inference of image content can instead capture the general semantic concepts present. We advocate that holistic inference of image concepts provides valuable information for detailed pixel labeling. We propose a generic framework to leverage holistic information in the form of a LabelBank for pixellevel segmentation. We show the ability of our framework to improve semantic segmentation performance in a variety of settings. We learn models for extracting a holistic LabelBank from visual cues, attributes, and/or textual descriptions. We demonstrate improvements in semantic segmentation accuracy on standard datasets across a range of state-of-the-art segmentation architectures and holistic inference approaches.

Ex Output:

LabelBank: Revisiting Global Perspectives for Semantic Segmentation