Gaussian Process Framework for Deep Neural Networks

For course ORIE 6741 Bayesian Machine Learning taught by Prof. Andrew Wilson

Recent work (Garriga-Alonso et al., 2018) has shown deep convolutional neural networks(DNNs) can be approximated by a shallow Gaus-sian processes (GP) with much fewer parameters.A lot of features in modern convolutional neuralnetwork (CNN) have not been considered in thiswork. In this paper, to extend the flexibility ofthe transformation from modern neural networkarchitecture to shallow Gaussian process, a frame-work for DNNs is introduced. An average poolingoperation and a concatenation operation are de-rived to support densely-connection structures tofit in Garriga-Alonso et al.’s architecture by trans-forming them into simple matrix multiplication.The newly derived DenseNet-GP significantly re-duce the time for calculating the kernel matrixfor the GP while having comparable accuracy inclassifying images in CIFAR10.

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Modeling and Analysis of Tagging Networks in Stack Exchange Communities

With Prof. Austin R. Benson

Large Question-and-Answer (Q&A) platforms support diverse knowledge curation on the Web. While researchers have studied user behaviour on such platforms in a variety of contexts, there is relatively little insight into important by-products of user behaviour that also encode knowledge. Here, we analyse and model the macroscopic structure of tags applied by users to annotate and catalogue questions, using a collection of 168 Stack Exchange websites that span a diversity of sizes and topics. We study the distribution of tag frequencies and also the structure of ‘co-tagging’ networks where nodes are tags and links connect tags that have been applied to the same question. We find striking similarity in tagging structure across Stack Exchange communities, even though each community evolves independently (albeit under similar guidelines). Our findings thus provide evidence that social tagging behaviour is largely driven by the Stack Exchange platform itself and not by the individual Stack Exchange communities. We also develop a simple generative model that creates random bipartite graphs of tags and questions. Our model accounts for the tag frequency distribution but does not explicitly account for co-tagging correlations. Even under these constraints, we demonstrate empirically and theoretically that our model can reproduce a number of the statistical properties that characterize co-tagging networks.

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Analysis of Probabilistic Temporal Networks

For course CS 6850 The Structure of Information Networks taught by Prof. Jon Kleinberg

We propose the probabilistic temporal network that we can encode this uncertainty into the network by giving each edge a probability of being ”available” during each time slot. Interesting questions include routing and cascading in such network. Our idea of this probabilistic networks is inspired by the temporal network models, in which edges have some kind of time-relevant labeling. In this paper we focus on the routing problem in a simple probabilistic temporal network where each edge have uniform independent probability of being ”available” in each time slot.

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