Probit Normal Correlated Topic Model
Affiliation(s)
Center for Quality and Applied Statistics, Rochester Institute of Technology, Rochester, NY, USA.
Center for Quality and Applied Statistics, Rochester Institute of Technology, Rochester, NY, USA.
ABSTRACT
The logistic normal distribution has recently been adapted via the transformation of multivariate Gaussian variables to model the topical distribution of documents in the presence of correlations among topics. In this paper, we propose a probit normal alternative approach to modelling correlated topical structures. Our use of the probit model in the context of topic discovery is novel, as many authors have so far concentrated solely of the logistic model partly due to the formidable inefficiency of the multinomial probit model even in the case of very small topical spaces. We herein circumvent the inefficiency of multinomial probit estimation by using an adaptation of the diagonal orthant multinomial probit in the topic models context, resulting in the ability of our topic modeling scheme to handle corpuses with a large number of latent topics. An additional and very important benefit of our method lies in the fact that unlike with the logistic normal model whose non-conjugacy leads to the need for sophisticated sampling schemes, our approach exploits the natural conjugacy inherent in the auxiliary formulation of the probit model to achieve greater simplicity. The application of our proposed scheme to a well-known Associated Press corpus not only helps discover a large number of meaningful topics but also reveals the capturing of compellingly intuitive correlations among certain topics. Besides, our proposed approach lends itself to even further scalability thanks to various existing high performance algorithms and architectures capable of handling millions of documents.
The logistic normal distribution has recently been adapted via the transformation of multivariate Gaussian variables to model the topical distribution of documents in the presence of correlations among topics. In this paper, we propose a probit normal alternative approach to modelling correlated topical structures. Our use of the probit model in the context of topic discovery is novel, as many authors have so far concentrated solely of the logistic model partly due to the formidable inefficiency of the multinomial probit model even in the case of very small topical spaces. We herein circumvent the inefficiency of multinomial probit estimation by using an adaptation of the diagonal orthant multinomial probit in the topic models context, resulting in the ability of our topic modeling scheme to handle corpuses with a large number of latent topics. An additional and very important benefit of our method lies in the fact that unlike with the logistic normal model whose non-conjugacy leads to the need for sophisticated sampling schemes, our approach exploits the natural conjugacy inherent in the auxiliary formulation of the probit model to achieve greater simplicity. The application of our proposed scheme to a well-known Associated Press corpus not only helps discover a large number of meaningful topics but also reveals the capturing of compellingly intuitive correlations among certain topics. Besides, our proposed approach lends itself to even further scalability thanks to various existing high performance algorithms and architectures capable of handling millions of documents.
KEYWORDS
Topic Model, Bayesian, Gibbs Sampler, Cumulative Distribution Function, Probit, Logit, Diagonal Orthant, Efficient Sampling, Auxiliary Variable, Correlation Structure, Topic, Vocabulary, Conjugate, Dirichlet, Gaussian
Topic Model, Bayesian, Gibbs Sampler, Cumulative Distribution Function, Probit, Logit, Diagonal Orthant, Efficient Sampling, Auxiliary Variable, Correlation Structure, Topic, Vocabulary, Conjugate, Dirichlet, Gaussian
Cite this paper
Yu, X. and Fokoué, E. (2014) Probit Normal Correlated Topic Model. Open Journal of Statistics, 4, 879-888. doi: 10.4236/ojs.2014.411083.
Yu, X. and Fokoué, E. (2014) Probit Normal Correlated Topic Model. Open Journal of Statistics, 4, 879-888. doi: 10.4236/ojs.2014.411083.
References
[1] Blei, D.M. and Ng, A.Y., Jordan, M.I. and Lafferty, J. (2003) Latent Dirichlet Allocation. Journal of Machine Learning Research, 3. [2] Blei, D.M. and Lafferty, J.D. (2006) Correlated Topic Models. Proceedings of the 23rd International Conference on Machine Learning, MIT Press, Cambridge, Massachusetts, 113-120. [3] Mimno, D., Wallach, H.M. and Mccallum, A. (2008) Gibbs Sampling for Logistic Normal Topic Models with Graph-Based Priors. Proceedings of NIPS Workshop on Analyzing Graphs, 2008. [4] Chen, J.F., Zhu, J., Wang, Z., Zheng, X. and Zhang, B. (2013) Scalable Inference for Logistic-Normal Topic Models. In Burges, C.J.C., Bottou, L., Welling, M., Ghahramani, Z. and Weinberger, K.Q., Eds., Advances in Neural Information Processing Systems 26, Curran Associates, Inc., 2445-2453. [5] Johndrow, J., Lum, K. and Dunson, D.B. (2013) Diagonal Orthant Multinomial Probit Models. JMLR Proceedings, Volume 31 of AISTATS, 29-38. [6] Albert, J.H. and Chib, S. (1993) Bayesian Analysis of Binary and Polychotomous Response Data. Journal of the American Statistical Association, 88, 669-679.
http://dx.doi.org/10.1080/01621459.1993.10476321 [7] Grun, B. and Hornik, K. (2011) Topicmodels: An R Package for Fitting Topic Models. Journal of Statistical Software, 40, 1-30. [8] Salomatin, K., Yang, Y.M. and Lad, A. (2009) Multi-Field Correlated Topic Modeling. Proceedings of the SIAM International Conference on Data Mining, SDM 2009, April 30-May 2, 2009, Sparks, 628-637. [9] Yao, L.M., Mimno, D. and McCallum, A. (2009) Efficient Methods for Topic Model Inference on Streaming Document Collections. KDD 2009: Proceedings of 15th ACM SIGKDD int’l Conference on Knowledge Discovery and Data Mining, 937-946. [10] Newman, D., Asuncion, A., Smyth, P. and Welling, M. (2009) Distributed Algorithms for Topic Models. Journal of Machine Learning Research, 10, 1801-1828. [11] Smola, A. and Narayanamurthy, S. (2010) An Architecture for Parallel Topic Models. Proc. VLDB Endow., 3, 703-710. [12] Zhu, J., Chen, N., Perkins, H. and Zhang, B. (2013) Gibbs Max-Margin Topic Models with Data Augmentation. CoRR, abs/1310.2816.
[1] Blei, D.M. and Ng, A.Y., Jordan, M.I. and Lafferty, J. (2003) Latent Dirichlet Allocation. Journal of Machine Learning Research, 3. [2] Blei, D.M. and Lafferty, J.D. (2006) Correlated Topic Models. Proceedings of the 23rd International Conference on Machine Learning, MIT Press, Cambridge, Massachusetts, 113-120. [3] Mimno, D., Wallach, H.M. and Mccallum, A. (2008) Gibbs Sampling for Logistic Normal Topic Models with Graph-Based Priors. Proceedings of NIPS Workshop on Analyzing Graphs, 2008. [4] Chen, J.F., Zhu, J., Wang, Z., Zheng, X. and Zhang, B. (2013) Scalable Inference for Logistic-Normal Topic Models. In Burges, C.J.C., Bottou, L., Welling, M., Ghahramani, Z. and Weinberger, K.Q., Eds., Advances in Neural Information Processing Systems 26, Curran Associates, Inc., 2445-2453. [5] Johndrow, J., Lum, K. and Dunson, D.B. (2013) Diagonal Orthant Multinomial Probit Models. JMLR Proceedings, Volume 31 of AISTATS, 29-38. [6] Albert, J.H. and Chib, S. (1993) Bayesian Analysis of Binary and Polychotomous Response Data. Journal of the American Statistical Association, 88, 669-679.
http://dx.doi.org/10.1080/01621459.1993.10476321 [7] Grun, B. and Hornik, K. (2011) Topicmodels: An R Package for Fitting Topic Models. Journal of Statistical Software, 40, 1-30. [8] Salomatin, K., Yang, Y.M. and Lad, A. (2009) Multi-Field Correlated Topic Modeling. Proceedings of the SIAM International Conference on Data Mining, SDM 2009, April 30-May 2, 2009, Sparks, 628-637. [9] Yao, L.M., Mimno, D. and McCallum, A. (2009) Efficient Methods for Topic Model Inference on Streaming Document Collections. KDD 2009: Proceedings of 15th ACM SIGKDD int’l Conference on Knowledge Discovery and Data Mining, 937-946. [10] Newman, D., Asuncion, A., Smyth, P. and Welling, M. (2009) Distributed Algorithms for Topic Models. Journal of Machine Learning Research, 10, 1801-1828. [11] Smola, A. and Narayanamurthy, S. (2010) An Architecture for Parallel Topic Models. Proc. VLDB Endow., 3, 703-710. [12] Zhu, J., Chen, N., Perkins, H. and Zhang, B. (2013) Gibbs Max-Margin Topic Models with Data Augmentation. CoRR, abs/1310.2816.