Aaron Schein
David M. Blei
ABSTRACT
We present a Bayesian tensor factorization model for inferring latent group structures from dynamic pairwise interaction patterns. For decades, political scientists have collected and analyzed records of the form "country i took action a toward country j at time t" - known as dyadic events - in order to form and test theories of international relations. We represent these event data as a tensor of counts and develop Bayesian Poisson tensor factorization to infer a low-dimensional, interpretable representation of their salient patterns. We demonstrate that our model's predictive performance is better than that of standard non-negative tensor factorization methods. We also provide a comparison of our variational updates to their maximum likelihood counterparts. In doing so, we identify a better way to form point estimates of the latent factors than that typically used in Bayesian Poisson matrix factorization. Finally, we showcase our model as an exploratory analysis tool for political scientists. We show that the inferred latent factor matrices capture interpretable multilateral relations that both conform to and inform our knowledge of international a airs.
Supplemental Material
- A. Cemgil. Bayesian inference for nonnegative matrix factorisation models. Computational Intelligence and Neuroscience, 2009. Google Scholar
Digital Library
- E. Chi and T. Kolda. On tensors, sparsity, and nonnegative factorizations. SIAM Journal on Matrix Analysis and Applications, 33(4):1272--1299, 2012.Google ScholarDigital Library
- R. Dorfman. A formula for the Gini coefficient. The Review of Economics and Statistics, pages 146--149, 1979.Google ScholarCross Ref
- R. Erikson, P. Pinto, and K. Rader. Dyadic analysis in international relations: A cautionary tale. Political Analysis, 22(4):457--463.Google ScholarCross Ref
- B. Ermis and A. Cemgil. A Bayesian tensor factorization model via variational inference for link prediction. arXiv:1409.8276, 2014.Google Scholar
- D. Gerner, P. Schrodt, R. Abu-Jabr, and Ö. Yilmaz. Conflict and mediation event observations (CAMEO): A new event data framework for the analysis of foreign policy interactions. Working paper.Google Scholar
- N. Gillis and F. Glineur. Nonnegative factorization and the maximum edge biclique problem. arXiv:0810.4225, 2008.Google Scholar
- E. Gonzalez and Y. Zhang. Accelerating the Lee-Seung algorithm for non-negative matrix factorization. Technical Report TR-05-02, Department of Computational and Applied Mathematics, Rice University, 2005.Google Scholar
- P. Gopalan and D. Blei. Efficient discovery of overlapping communities in massive networks. Proceedings of the National Academy of Sciences, 2013.Google ScholarCross Ref
- P. Gopalan, S. Gerrish, M. Freedman, D. Blei, and D. Mimno. Scalable inference of overlapping communities. In Advances in Neural Information Processing Systems Twenty-Five, 2012.Google Scholar
- P. Gopalan, J. Hofman, and D. Blei. Scalable recommendation with Poisson factorization. In Proceedings of the Thirty-First Conference on Uncertainty in Artificial Intelligence, 2015.Google ScholarDigital Library
- D. Green, S. Kim, and D. Yoon. Dirty pool. International Organization, 55(2):441--468, 2001.Google ScholarCross Ref
- R. Harshman. Foundations of the PARAFAC procedure: Models and conditions for an "explanatory" multimodal factor analysis. UCLA Working Papers in Phonetics, 16:1--84, 1970.Google Scholar
- P. Hoff. Equivariant and scale-free Tucker decomposition models. arXiv:1312.6397, 2013.Google Scholar
- P. Hoff. Multilinear tensor regression for longitudinal relational data. arXiv:1412.0048, 2014.Google Scholar
- P. Hoff and M. Ward. Modeling dependencies in international relations networks. Political Analysis, 12(2):160--175, 2004.Google ScholarCross Ref
- G. King. Proper nouns and methodological propriety: Pooling dyads in international relations data. International Organization, 55(2):497--507, 2001.Google ScholarCross Ref
- T. Kolda and J. Sun. Scalable tensor decompositions for multi-aspect data mining. In Proceedings of the Eighth IEEE International Conference on Data Mining, pages 363--372, 2008. Google ScholarDigital Library
- D. Lee and S. Seung. Learning the parts of objects by non-negative matrix factorization. Nature, 401:788--791, 1999.Google ScholarCross Ref
- K. Leetaru and P. Schrodt. GDELT: Global data on events, location, and tone, 1979--2012. Working paper, 2013.Google Scholar
- D. Liang, J. Paisley, and D. Ellis. Codebook-based scalable music tagging with Poisson matrix factorization. In Proceedings of the Fifteenth International Society for Music Information Retrieval Conference, 2015.Google Scholar
- C. Lin. On the convergence of multiplicative update algorithms for nonnegative matrix factorization. IEEE Transactions on Neural Networks, 18(6):1589--1596, 2007. Google ScholarDigital Library
- B. Marlin. Collaborative filtering: A machine learning perspective. Master's thesis, University of Toronto, 2004.Google Scholar
- S. O'Brien. Crisis early warning and decision support: Contemporary approaches and thoughts on future research. International Studies Review, 12(1):87--104, 2010.Google ScholarCross Ref
- J. Paisley, D. Blei, and M. Jordan. Bayesian nonnegative matrix factorization with stochastic variational inference. In Handbook of Mixed Membership Models and Their Applications. Chapman and Hall/CRC, 2014.Google Scholar
- P. Poast. (Mis)using dyadic data to analyze multilateral events. Political Analysis, 2010.Google Scholar
- A. Schein, J. Paisley, D. Blei, and H. Wallach. Inferring polyadic events with Poisson tensor factorization. In Proceedings of the NIPS 2014 Workshop on "Networks: From Graphs to Rich Data", 2014.Google Scholar
- D. Singer and M. S. (producers). Correlates of war project: International and civil war data, 1816-1992 (computer file). Inter-University Consortium for Political and Social Research (distributor), 1994.Google Scholar
- B. Stewart. Latent factor regressions for the social sciences. Working paper, 2014.Google Scholar
- L. Tucker. Some mathematical notes on three-mode factor analysis. Psychometrika, 31(3):279--311, 1966.Google ScholarCross Ref
- M. Ward, A. Beger, J. Cutler, M. Dickenson, C. Doorff, and B. Radford. Comparing GDELT and ICEWS event data. Working paper, 2013.Google Scholar
- M. Welling and M. Weber. Positive tensor factorization. Pattern Recognition Letters, 22(12):1255--1261, 2001. Google ScholarDigital Library
- Wikipedia. Cruise missile strikes on Afghanistan and Sudan (August 1998). Accessed June 8, 2015.Google Scholar
- Wikipedia. Embassy of Ecuador, London. Accessed October 30, 2014.Google Scholar
- Wikipedia. Japanese Iraq reconstruction and support group. Accessed June 8, 2015.Google Scholar
- Wikipedia. Jyllands-Posten Muhammad cartoons controversy. Accessed June 8, 2015.Google Scholar
- Wikipedia. Six-party talks. Accessed June 8, 2015.Google Scholar
- M. Zhou and L. Carin. Negative binomial process count and mixture modeling. IEEE Transactions on Pattern Analysis and Machine Intelligence, 37(2):307--320, 2015.Google ScholarDigital Library
- M. Zhou, L. Hannah, D. Dunson, and L. Carin. Beta-negative binomial process and Poisson factor analysis. arXiv:1112.3605, 2011.Google Scholar
Index Terms
- Bayesian Poisson Tensor Factorization for Inferring Multilateral Relations from Sparse Dyadic Event Counts
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