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: 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 Nyström 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: In this study, we introduce an ensemble-based approach for online machine learning. The ensemble of base classifiers in our approach is obtained by learning Naïve Bayes classifiers on different training sets which are generated by projecting the original training set to lower dimensional space. We propose a mechanism to learn sequences of data using data chunks paradigm. The experiments conducted on a number of UCI datasets and one synthetic dataset demonstrate that the proposed approach performs significantly better than some well-known online learning algorithms.

A: An ensemble-based online learning algorithm for streaming data
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Q: Deep neural nets have caused a revolution in many classification tasks. A related ongoing revolution—also theoretically not understood—concerns their ability to serve as generative models for complicated types of data such as images and texts. These models are trained using ideas like variational autoencoders and Generative Adversarial Networks. We take a first cut at explaining the expressivity of multilayer nets by giving a sufficient criterion for a function to be approximable by a neural network with n hidden layers. A key ingredient is Barron’s Theorem [Bar93], which gives a Fourier criterion for approximability of a function by a neural network with 1 hidden layer. We show that a composition of n functions which satisfy certain Fourier conditions (“Barron functions”) can be approximated by a n+ 1layer neural network. For probability distributions, this translates into a criterion for a probability distribution to be approximable in Wasserstein distance—a natural metric on probability distributions—by a neural network applied to a fixed base distribution (e.g., multivariate gaussian). Building up recent lower bound work, we also give an example function that shows that composition of Barron functions is more expressive than Barron functions alone.

A:
On the ability of neural nets to express distributions
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