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]: We first consider the problem of learning k-parities in the on-line mistake-bound model: given a hidden vector x ∈ {0, 1} with |x| = k and a sequence of “questions” a1, a2, · · · ∈ {0, 1} , where the algorithm must reply to each question with 〈ai, x〉 (mod 2), what is the best tradeoff between the number of mistakes made by the algorithm and its time complexity? We improve the previous best result of Buhrman et. al. [BGM10] by an exp(k) factor in the time complexity. Second, we consider the problem of learning k-parities in the presence of classification noise of rate η ∈ (0, 1/2). A polynomial time algorithm for this problem (when η > 0 and k = ω(1)) is a longstanding challenge in learning theory. Grigorescu et al. [GRV11] showed an algorithm running in time ( n k/2 )1+4η+o(1) . Note that this algorithm inherently requires time ( n k/2 ) even when the noise rate η is polynomially small. We observe that for sufficiently small noise rate, it is possible to break the ( n k/2 ) barrier. In particular, if for some function f(n) = ω(1) and α ∈ [1/2, 1), k = n/f(n) and η = o(f(n)/ log n), then there is an algorithm for the problem with running time poly(n) · ( n k )1−α · e.
[EX A]: On learning k-parities with and without noise

[EX Q]: In this article, how word embeddings can be used as features in Chinese sentiment classification is presented. Firstly, a Chinese opinion corpus is built with a million comments from hotel review websites. Then the word embeddings which represent each comment are used as input in different machine learning methods for sentiment classification, including SVM, Logistic Regression, Convolutional Neural Network (CNN) and ensemble methods. These methods get better performance compared with N-gram models using Naive Bayes (NB) and Maximum Entropy (ME). Finally, a combination of machine learning methods is proposed which presents an outstanding performance in precision, recall and F1 score. After selecting the most useful methods to construct the combinational model and testing over the corpus, the final F1 score is 0.920.
[EX A]: An Empirical Study on Sentiment Classification of Chinese Review using Word Embedding

[EX Q]: We consider the problem of principal component analysis (PCA) in a streaming stochastic setting, where our goal is to find a direction of approximate maximal variance, based on a stream of i.i.d. data points in R. A simple and computationally cheap algorithm for this is stochastic gradient descent (SGD), which incrementally updates its estimate based on each new data point. However, due to the non-convex nature of the problem, analyzing its performance has been a challenge. In particular, existing guarantees rely on a non-trivial eigengap assumption on the covariance matrix, which is intuitively unnecessary. In this paper, we provide (to the best of our knowledge) the first eigengap-free convergence guarantees for SGD in the context of PCA. This also partially resolves an open problem posed in [10]. Moreover, under an eigengap assumption, we show that the same techniques lead to new SGD convergence guarantees with better dependence on the eigengap.
[EX A]:
Convergence of Stochastic Gradient Descent for PCA