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A Bayesian Nonparametric Approach to Multilevel Regression

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Advances in Knowledge Discovery and Data Mining (PAKDD 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9077))

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Abstract

Regression is at the cornerstone of statistical analysis. Multilevel regression, on the other hand, receives little research attention, though it is prevalent in economics, biostatistics and healthcare to name a few. We present a Bayesian nonparametric framework for multilevel regression where individuals including observations and outcomes are organized into groups. Furthermore, our approach exploits additional group-specific context observations, we use Dirichlet Process with product-space base measure in a nested structure to model group-level context distribution and the regression distribution to accommodate the multilevel structure of the data. The proposed model simultaneously partitions groups into cluster and perform regression. We provide collapsed Gibbs sampler for posterior inference. We perform extensive experiments on econometric panel data and healthcare longitudinal data to demonstrate the effectiveness of the proposed model.

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References

  1. Antoniak, C.E.: Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems. The Annals of Statistics 2(6), 1152–1174 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  2. Argyriou, A., Evgeniou, T., Pontil, M.: Convex multi-task feature learning. Machine Learning 73(3), 243–272 (2008)

    Article  Google Scholar 

  3. Bishop, C.M.: Pattern recognition and machine learning, vol. 1. Springer, New York (2006)

    MATH  Google Scholar 

  4. Caruana, R.: Multitask learning. Machine Learning 28(1), 41–75 (1997)

    Article  MathSciNet  Google Scholar 

  5. Denton, F.T., Spencer, B.G.: Chronic health conditions: changing prevalence in an aging population and some implications for the delivery of health care services. Canadian Journal on Aging 29(1), 11 (2010)

    Article  Google Scholar 

  6. Escobar, M.D., West, M.: Bayesian density estimation and inference using mixtures. Journal of the american statistical association 90(430), 577–588 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  7. Ferguson, T.S.: A Bayesian analysis of some nonparametric problems. The Annals of Statistics 1(2), 209–230 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  8. Gelman, A., Carlin, J.B., Stern, H.S., Rubin, D.B.: Bayesian Data Analysis. Chapman & Hall/CRC (2003)

    Google Scholar 

  9. Goldstein, H.: Multilevel mixed linear model analysis using iterative generalized least squares. Biometrika 73(1), 43–56 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  10. Gupta, S., Phung, D., Venkatesh, S.: Factorial multi-task learning: a bayesian nonparametric approach. In: Proceedings of the 30th International Conference on Machine Learning (ICML-13), pp. 657–665 (2013)

    Google Scholar 

  11. Hox, J.: Multilevel analysis: Techniques and applications. Routledge (2010)

    Google Scholar 

  12. Kang, Z., Grauman, K., Sha, F.: Learning with whom to share in multi-task feature learning. pp. 521–528 (2011)

    Google Scholar 

  13. Kitov, I.O.: Gdp growth rate and population (2008). arXiv preprint arXiv:0811.2125

  14. Leyland, A.H., Goldstein, H.: Multilevel modelling of health statistics. Wiley (2001)

    Google Scholar 

  15. Maddison, A.: Statistics on world population, gdp and per capita gdp, 1–2008 ad. Historical Statistics (2010)

    Google Scholar 

  16. McLean, R.A., Sanders, W.L., Stroup, W.W.: A unified approach to mixed linear models. The American Statistician 45(1), 54–64 (1991)

    Google Scholar 

  17. Munnell, A.H., Cook, L.M.: How does public infrastructure affect regional economic performance? In: Is There a Shortfall in Public Capital Investment? Proceedings of a Conference (1990)

    Google Scholar 

  18. Nguyen, V., Phung, D., Venkatesh, S., Nguyen, X., Bui, H.: Bayesian nonparametric multilevel clustering with group-level contexts. In: Proc. of International Conference on Machine Learning (ICML), pp. 288–296, Beijing, China (2014)

    Google Scholar 

  19. Phung, D., Nguyen, X., Bui, H., Nguyen, T.V., Venkatesh, S.: Conditionally dependent Dirichlet processes for modelling naturally correlated data sources. Technical report, Pattern Recognition and Data Analytics, Deakin University (2012)

    Google Scholar 

  20. Pinheiro, J.C., Bates, D.M.: Mixed-effects models in S and S-PLUS. Springer (2000)

    Google Scholar 

  21. Rodriguez, A., Dunson, D.B., Gelfand, A.E.: The nested Dirichlet process. Journal of the American Statistical Association 103(483), 1131–1154 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  22. Sethuraman, J.: A constructive definition of Dirichlet priors. Statistica Sinica 4(2), 639–650 (1994)

    MATH  MathSciNet  Google Scholar 

  23. Snijders, T.A.B.: Multilevel analysis. Springer (2011)

    Google Scholar 

  24. Teh, Y.W., Jordan, M.I., Beal, M.J., Blei, D.M.: Hierarchical Dirichlet processes. Journal of the American Statistical Association 101(476), 1566–1581 (2006)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Deakin University, Geelong, Australia

    Vu Nguyen, Dinh Phung & Svetha Venkatesh

  2. Adobe Research, San Francisco, USA

    Hung H. Bui

Authors
  1. Vu Nguyen
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  2. Dinh Phung
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  3. Svetha Venkatesh
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  4. Hung H. Bui
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Corresponding author

Correspondence to Vu Nguyen .

Editor information

Editors and Affiliations

  1. Ho Chi Minh City University of Technology, Ho Chi Minh City, Vietnam

    Tru Cao

  2. Singapore Management University, Singapore, Singapore

    Ee-Peng Lim

  3. Nanjing University, Nanjing, China

    Zhi-Hua Zhou

  4. Japan Advanced Institute of Science and Technology, Nomi City, Japan

    Tu-Bao Ho

  5. University of Hong Kong, Hong Kong, Hong Kong SAR

    David Cheung

  6. Osaka University, Osaka, Japan

    Hiroshi Motoda

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© 2015 Springer International Publishing Switzerland

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Nguyen, V., Phung, D., Venkatesh, S., Bui, H.H. (2015). A Bayesian Nonparametric Approach to Multilevel Regression. In: Cao, T., Lim, EP., Zhou, ZH., Ho, TB., Cheung, D., Motoda, H. (eds) Advances in Knowledge Discovery and Data Mining. PAKDD 2015. Lecture Notes in Computer Science(), vol 9077. Springer, Cham. https://doi.org/10.1007/978-3-319-18038-0_26

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  • DOI: https://doi.org/10.1007/978-3-319-18038-0_26

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-18037-3

  • Online ISBN: 978-3-319-18038-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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