# A Tri-Role Topic Model for Domain-Specific Question Answering

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4 Figure 2: Tri-Role Topic Model. Note that the voter role of user is modeled implicitly, and the plate model does not show s a q. Contributing answer. An answerer v contributes an answer a A v with probability ekl(v, τ, a), where τ is a scalar. Based on Assumption A3, v prefers to contribute a if the topical similarity between v and a is high. Next, for each word e in a, a topic z is sampled with probability p(z a), and then e is generated with p(e z). The graphical representation of the TRTM model is shown in Figure 2 and the generative process is summarized as follows: For each question q Q u For each answer a A v of question q Asker u composes question q with probability ekl(p(z q), α, p(z u)) For each word w in q Draw a topic z from p(z q) Draw a word w from p(w z) Answerer v selects to answer question q with probability ekl(p(z q), β s a q, p(z v)) Answerer v contributes answer a with probability ekl(p(z a), τ, p(z v)) For each word e in a Draw a topic z from p(z a) Draw a word e from p(e z) The Inference Algorithm of TRTM Given question set Q composed by U and answer set A by answerers from V, we obtain the likelihood of the data in Equation 1. L = u U q Q u ekl u U q Q u w W ekl v V q Q v ekl v V a A v v V a A v e E ( ) p(z q), α, p(z u) [ p(w z)p(z q) z ] n(q,w) ( ) p(z q), β s a q, p(z v) ( ) p(z a), τ, p(z v) [ p(e z)p(z a) z ] n(a,e) The exact inference of Equation 1 is intractable. We propose an Expectation-Maximization (EM) algorithm to appropriately infer TRTM. The EM algorithm has two steps: E-step and M-step. The E-step calculates the expectation of the hidden variables i.e., p(z q, w) and p(z a, e) in TRTM. E-step: p k+1 (z q, w) = p k+1 (z a, e) = p k (w z)p k (z q) z Z pk (w z )p k (z q) p k (e z)p k (z a) z Z pk (e z )p k (z a) The M-step maximizes the log-likelihood (see Equation 1). The following probabilities are calculated: p(w z), p(e z), p(z u), p(z q), p(z a), and p(z v). M-step: p k+1 (w z) = p k+1 (e z) = p k+1 (z u) = w W e E (1) q Q n(q, w)pk+1 (z q, w) q Q n(q, w )p k+1 (z q, w ) a A n(a, e)pk+1 (z a, e) a A n(a, e )p k+1 (z a, e ) [ q Q u p k+1 (z q)] 1/ Qu z Z [ q Q u p k+1 (z q)] 1/ Qu The calculation of the probabilities p(z q), p(z a), and p(z v) are shown in Table 2 for presentation clarity. We iteratively compute probabilities of E-step and M-step until achieving convergent log-likelihood (see Equation 1). k represents the kth iteration of EM algorithm. Note that, in M-step, we first calculate p(z q) and p(z a), then calculate p(z u) and p(z v). Experiment We evaluate the proposed TRTM model on Stack Overflow data 1. Although the model can be used to enable multiple applications, due to page limit, we report one case study for the application of ranking answers for questions. 1

7 References Anderson, A.; Huttenlocher, D.; Kleinberg, J.; and Leskovec, J Discovering value from community activity on focused question answering sites: A case study of stack overflow. In KDD, ACM. Anderson, A.; Huttenlocher, D.; Kleinberg, J.; and Leskovec, J Steering user behavior with badges. In WWW, Blei, D. M.; Ng, A. Y.; and Jordan, M. I Latent dirichlet allocation. J. Mach. Learn. Res. 3: Correa, D., and Sureka, A Chaff from the wheat: Characterization and modeling of deleted questions on stack overflow. In WWW, Dalip, D. H.; Gonçalves, M. A.; Cristo, M.; and Calado, P Exploiting user feedback to learn to rank answers in Q&A forums: A case study with stack overflow. In SIGIR, ACM. Dror, G.; Koren, Y.; Maarek, Y.; and Szpektor, I I want to answer; who has a question?: Yahoo! answers recommender system. In KDD, ACM. Guo, J.; Xu, S.; Bao, S.; and Yu, Y Tapping on the potential of Q&A community by recommending answer providers. In CIKM, ACM. Hofmann, T Probabilistic latent semantic indexing. In SIGIR, ACM. Ji, Z.; Xu, F.; Wang, B.; and He, B Question-answer topic model for question retrieval in community question answering. In CIKM, ACM. Kim, Y.; Park, Y.; and Shim, K DIGTOBI: A recommendation system for digg articles using probabilistic modeling. In WWW, Li, Z.; Shen, H.; and Grant, J. E Collective intelligence in the online social network of Yahoo! answers and its implications. In CIKM, ACM. Page, L.; Brin, S.; Motwani, R.; and Winograd, T The pagerank citation ranking: Bringing order to the web. Technical Report , Stanford InfoLab. Wu, H.; Wang, Y.; and Cheng, X Incremental probabilistic latent semantic analysis for automatic question recommendation. In RecSys, ACM. Xu, F.; Ji, Z.; and Wang, B Dual role model for question recommendation in community question answering. In SIGIR, ACM. Yang, L.; Qiu, M.; Gottipati, S.; Zhu, F.; Jiang, J.; Sun, H.; and Chen, Z CQArank: Jointly model topics and expertise in community question answering. In CIKM, ACM. Zhou, G.; Lai, S.; Liu, K.; and Zhao, J Topic-sensitive probabilistic model for expert finding in question answer communities. In CIKM, ACM.

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