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Multi-label classification using stacked hierarchical Dirichlet processes with reduced sampling complexity

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Abstract

Nonparametric topic models based on hierarchical Dirichlet processes (HDPs) allow for the number of topics to be automatically discovered from the data. The computational complexity of standard Gibbs sampling techniques for model training is linear in the number of topics. Recently, it was reduced to be linear in the number of topics per word using a technique called alias sampling combined with Metropolis Hastings (MH) sampling. We propose a different proposal distribution for the MH step based on the observation that distributions on the upper hierarchy level change slower than the document-specific distributions at the lower level. This reduces the sampling complexity, making it linear in the number of topics per document by using an approximation based on Metropolis–Hastings sampling. By utilizing a single global distribution, we are able to further improve the test set log-likelihood of this approximation. Furthermore, we propose a novel model of stacked HDPs utilizing this sampling method. An extensive analysis reveals the importance of the correct setting of hyperparameters for classification and shows the convergence properties of our method. Experiments demonstrate the effectiveness of the proposed approach in the context of multi-label classification as compared to previous Dependency-LDA models.

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Notes

  1. See Buntine and Hutter [3] for an efficient way to compute ratios of these numbers. They can be precomputed once and subsequently retrieved in O(1). Note that it may be necessary to store large values sparsely if the number of tokens in a restaurant becomes very large.

  2. This improved method can also be applied if \(a>0\), i.e., we are dealing with a hierarchical Poisson–Dirichlet topic model. In this case, we need to divide q by \((b_1+M_d)\) and remultiply this factor when subtracting q from p.

  3. see Papanikolaou et al. [15] for a formal justification of this approach.

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Acknowledgements

We thank the anonymous reviewers for useful comments and suggestions, Jinseok Nam for providing the source code of the neural network classifier and Andrey Tyukin for helpful discussions on Stirling numbers. The first author was supported by a scholarship from PRIME Research, Mainz.

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  1. Institute of Computer Science, Johannes Gutenberg-University of Mainz, Staudingerweg 9, 55128, Mainz, Germany

    Sophie Burkhardt & Stefan Kramer

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  1. Sophie Burkhardt
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  2. Stefan Kramer
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Correspondence to Sophie Burkhardt.

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This paper is an extended version of an ICBK 2017 conference paper [5]

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Burkhardt, S., Kramer, S. Multi-label classification using stacked hierarchical Dirichlet processes with reduced sampling complexity. Knowl Inf Syst 59, 93–115 (2019). https://doi.org/10.1007/s10115-018-1204-z

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