Research papers and code for "Anderson Y. Zhang":
The mean field variational Bayes method is becoming increasingly popular in statistics and machine learning. Its iterative Coordinate Ascent Variational Inference algorithm has been widely applied to large scale Bayesian inference. See Blei et al. (2017) for a recent comprehensive review. Despite the popularity of the mean field method there exist remarkably little fundamental theoretical justifications. To the best of our knowledge, the iterative algorithm has never been investigated for any high dimensional and complex model. In this paper, we study the mean field method for community detection under the Stochastic Block Model. For an iterative Batch Coordinate Ascent Variational Inference algorithm, we show that it has a linear convergence rate and converges to the minimax rate within $\log n$ iterations. This complements the results of Bickel et al. (2013) which studied the global minimum of the mean field variational Bayes and obtained asymptotic normal estimation of global model parameters. In addition, we obtain similar optimality results for Gibbs sampling and an iterative procedure to calculate maximum likelihood estimation, which can be of independent interest.

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Community detection is a central problem of network data analysis. Given a network, the goal of community detection is to partition the network nodes into a small number of clusters, which could often help reveal interesting structures. The present paper studies community detection in Degree-Corrected Block Models (DCBMs). We first derive asymptotic minimax risks of the problem for a misclassification proportion loss under appropriate conditions. The minimax risks are shown to depend on degree-correction parameters, community sizes, and average within and between community connectivities in an intuitive and interpretable way. In addition, we propose a polynomial time algorithm to adaptively perform consistent and even asymptotically optimal community detection in DCBMs.

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Community detection is a fundamental statistical problem in network data analysis. Many algorithms have been proposed to tackle this problem. Most of these algorithms are not guaranteed to achieve the statistical optimality of the problem, while procedures that achieve information theoretic limits for general parameter spaces are not computationally tractable. In this paper, we present a computationally feasible two-stage method that achieves optimal statistical performance in misclassification proportion for stochastic block model under weak regularity conditions. Our two-stage procedure consists of a generic refinement step that can take a wide range of weakly consistent community detection procedures as initializer, to which the refinement stage applies and outputs a community assignment achieving optimal misclassification proportion with high probability. The practical effectiveness of the new algorithm is demonstrated by competitive numerical results.

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Top-down visual attention mechanisms have been used extensively in image captioning and visual question answering (VQA) to enable deeper image understanding through fine-grained analysis and even multiple steps of reasoning. In this work, we propose a combined bottom-up and top-down attention mechanism that enables attention to be calculated at the level of objects and other salient image regions. This is the natural basis for attention to be considered. Within our approach, the bottom-up mechanism (based on Faster R-CNN) proposes image regions, each with an associated feature vector, while the top-down mechanism determines feature weightings. Applying this approach to image captioning, our results on the MSCOCO test server establish a new state-of-the-art for the task, achieving CIDEr / SPICE / BLEU-4 scores of 117.9, 21.5 and 36.9, respectively. Demonstrating the broad applicability of the method, applying the same approach to VQA we obtain first place in the 2017 VQA Challenge.

* CVPR 2018 full oral, winner of the 2017 Visual Question Answering challenge
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Performing arts organizations aim to enrich their communities through the arts. To do this, they strive to match their performance offerings to the taste of those communities. Success relies on understanding audience preference and predicting their behavior. Similar to most e-commerce or digital entertainment firms, arts presenters need to recommend the right performance to the right customer at the right time. As part of the Michigan Data Science Team (MDST), we partnered with the University Musical Society (UMS), a non-profit performing arts presenter housed in the University of Michigan, Ann Arbor. We are providing UMS with analysis and business intelligence, utilizing historical individual-level sales data. We built a recommendation system based on collaborative filtering, gaining insights into the artistic preferences of customers, along with the similarities between performances. To better understand audience behavior, we used statistical methods from customer-base analysis. We characterized customer heterogeneity via segmentation, and we modeled customer cohorts to understand and predict ticket purchasing patterns. Finally, we combined statistical modeling with natural language processing (NLP) to explore the impact of wording in program descriptions. These ongoing efforts provide a platform to launch targeted marketing campaigns, helping UMS carry out its mission by allocating its resources more efficiently. Celebrating its 138th season, UMS is a 2014 recipient of the National Medal of Arts, and it continues to enrich communities by connecting world-renowned artists with diverse audiences, especially students in their formative years. We aim to contribute to that mission through data science and customer analytics.

* Presented at the Data For Good Exchange 2016
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In this paper we explore acceleration techniques for large scale nonconvex optimization problems with special focuses on deep neural networks. The extrapolation scheme is a classical approach for accelerating stochastic gradient descent for convex optimization, but it does not work well for nonconvex optimization typically. Alternatively, we propose an interpolation scheme to accelerate nonconvex optimization and call the method Interpolatron. We explain motivation behind Interpolatron and conduct a thorough empirical analysis. Empirical results on DNNs of great depths (e.g., 98-layer ResNet and 200-layer ResNet) on CIFAR-10 and ImageNet show that Interpolatron can converge much faster than the state-of-the-art methods such as the SGD with momentum and Adam. Furthermore, Anderson's acceleration, in which mixing coefficients are computed by least-squares estimation, can also be used to improve the performance. Both Interpolatron and Anderson's acceleration are easy to implement and tune. We also show that Interpolatron has linear convergence rate under certain regularity assumptions.

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