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.

Q: This paper presents generalized probabilistic models for high-order projective dependency parsing and an algorithmic framework for learning these statistical models involving dependency trees. Partition functions and marginals for high-order dependency trees can be computed efficiently, by adapting our algorithms which extend the inside-outside algorithm to higher-order cases. To show the effectiveness of our algorithms, we perform experiments on three languages English, Chinese and Czech, using maximum conditional likelihood estimation for model training and L-BFGS for parameter estimation. Our methods achieve competitive performance for English, and outperform all previously reported dependency parsers for Chinese and Czech.

A: Probabilistic Models for High-Order Projective Dependency Parsing
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Q: The success of semi-supervised learning crucially relies on the scalability to a huge amount of unlabelled data that are needed to capture the underlying manifold structure for better classification. Since computing the pairwise similarity between the training data is prohibitively expensive in most kinds of input data, currently, there is no general readyto-use semi-supervised learning method/tool available for learning with tens of millions or more data points. In this paper, we adopted the idea of two low-rank label propagation algorithms, GLNP (Global Linear Neighborhood Propagation) and Kernel Nystrom Approximation, and implemented the parallelized version of the two algorithms accelerated with Nesterov's accelerated projected gradient descent for Big-data Label Propagation (BigLP). The parallel algorithms are tested on five real datasets ranging from 7000 to 10,000,000 in size and a simulation dataset of 100,000,000 samples. In the experiments, the implementation can scale up to datasets with 100,000,000 samples and hundreds of features and the algorithms also significantly improved the prediction accuracy when only a very small percentage of the data is labeled. The results demonstrate that the BigLP implementation is highly scalable to big data and effective in utilizing the unlabeled data for semi-supervised learning.

A: Low-rank Label Propagation for Semi-supervised Learning with 100 Millions Samples
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Q: We develop a general duality between neural networks and compositional kernels, striving towards a better understanding of deep learning. We show that initial representations generated by common random initializations are sufficiently rich to express all functions in the dual kernel space. Hence, though the training objective is hard to optimize in the worst case, the initial weights form a good starting point for optimization. Our dual view also reveals a pragmatic and aesthetic perspective of neural networks and underscores their expressive power. Email: amitdaniely@google.com Email: rf@cs.stanford.edu. Work performed at Google. Email: singer@google.com ar X iv :1 60 2. 05 89 7v 1 [ cs .L G ] 1 8 Fe b 20 16

A:
Toward Deeper Understanding of Neural Networks: The Power of Initialization and a Dual View on Expressivity
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