instruction:
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.
question:
We study several questions in the reliable agnostic learning framework of Kalai et al. (2009), which captures learning tasks in which one type of error is costlier than other types. A positive reliable classifier is one that makes no false positive errors. The goal in the positive reliable agnostic framework is to output a hypothesis with the following properties: (i) its false positive error rate is at most ǫ, (ii) its false negative error rate is at most ǫ more than that of the best positive reliable classifier from the class. A closely related notion is fully reliable agnostic learning, which considers partial classifiers that are allowed to predict “unknown” on some inputs. The best fully reliable partial classifier is one that makes no errors and minimizes the probability of predicting “unknown”, and the goal in fully reliable learning is to output a hypothesis that is almost as good as the best fully reliable partial classifier from a class. For distribution-independent learning, the best known algorithms for PAC learning typically utilize polynomial threshold representations, while the state of the art agnostic learning algorithms use pointwise polynomial approximations. We show that one-sided polynomial approximations, an intermediate notion between polynomial threshold representations and point-wise polynomial approximations, suffice for learning in the reliable agnostic settings. We then show that majorities can be fully reliably learned and disjunctions of majorities can be positive reliably learned, through constructions of appropriate onesided polynomial approximations. Our fully reliable algorithm for majorities provides the first evidence that fully reliable learning may be strictly easier than agnostic learning. Our algorithms also satisfy strong attribute-efficiency properties, and in many cases they provide smooth tradeoffs between sample complexity and running time. University of California, Berkeley. Email: vkanade@eecs.berkeley.edu The Simons Institute for the Theory of Computing at UC Berkeley. Email: jthaler@seas.harvard.edu
answer:
Distribution-Independent Reliable Learning


question:
We theoretically analyze and compare the following five popular multiclass classification methods: One vs. All, All Pairs, Tree-based classifiers, Error Correcting Output Codes (ECOC) with randomly generated code matrices, and Multiclass SVM. In the first four methods, the classification is based on a reduction to binary classification. We consider the case where the binary classifier comes from a class of VC dimension d, and in particular from the class of halfspaces over R. We analyze both the estimation error and the approximation error of these methods. Our analysis reveals interesting conclusions of practical relevance, regarding the success of the different approaches under various conditions. Our proof technique employs tools from VC theory to analyze the approximation error of hypothesis classes. This is in sharp contrast to most, if not all, previous uses of VC theory, which only deal with estimation error.
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Multiclass Learning Approaches: A Theoretical Comparison with Implications


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Sentence similarity is considered the basis of many natural language tasks such as information retrieval, question answering and text summarization. The semantic meaning between compared text fragments is based on the words’ semantic features and their relationships. This article reviews a set of word and sentence similarity measures and compares them on benchmark datasets. On the studied datasets, results showed that hybrid semantic measures perform better than both knowledge and corpus based measures. General Terms Semantic Similarity, Natural Language Processing, Computational Linguistics, Text Similarity
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A Comprehensive Comparative Study of Word and Sentence Similarity Measures