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Machine Learning

A Probit Tensor Factorization Model For Relational Learning

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Pages 846-855 | Received 13 Jan 2020, Accepted 21 Oct 2021, Published online: 11 Mar 2022

References

  • Aidini, A., Tsagkatakis, G., and Tsakalides, P. (2018), “1-Bit Tensor Completion,” Electronic Imaging, 2018, 261. DOI: 10.2352/ISSN.2470-1173.2018.13.IPAS-261.
  • Al Hasan, M., Zaki and M. J. (2011), “A Survey of Link Prediction in Social Networks,” in Social Network Data Analytics, pp. 243–275. Springer, Boston, MA.
  • Almansoori, W., Gao, S., Jarada, T. N., Elsheikh, A. M., Murshed, A. N., Jida, J., Alhajj, R., and Rokne, J. (2012), “Link Prediction and Classification in Social Networks and Its Application in Healthcare and Systems Biology,” Network Modeling Analysis in Health Informatics and Bioinformatics, 1, 27–36. DOI: 10.1007/s13721-012-0005-7.
  • Auer, S., Bizer, C., Kobilarov, G., Lehmann, J., Cyganiak, R., and Ives, Z. (2007), “Dbpedia: A Nucleus for a Web of Open Data,” The Semantic Web, 722–735. Springer, Berlin, Heidelberg.
  • Bader, B. W., Harshman, R. A., and Kolda, T. G. (2007), “Temporal Analysis of Semantic Graphs Using Asalsan,” in Seventh IEEE International Conference on Data Mining, 2007. ICDM 2007, pp. 33–42. IEEE.
  • Bordes, A., Glorot, X., Weston, J., and Bengio, Y. (2014), “A Semantic Matching Energy Function for Learning with Multi-Relational Data,” Machine Learning, 94, 233–259. DOI: 10.1007/s10994-013-5363-6.
  • Bordes, A., Usunier, N., Garcia-Duran, A., Weston, J., and Yakhnenko, O. (2013), “Translating Embeddings for Modeling Multi-Relational Data,” in Advances in Neural Information Processing Systems, pp. 2787–2795.
  • Carlson, A., Betteridge, J., Kisiel, B., Settles, B., Hruschka, E. R. Jr., and Mitchell, T. M. (2010), “Toward an Architecture for Never-Ending Language Learning,” in Twenty-Fourth AAAI Conference on Artificial Intelligence, Volume 5, pp. 3.
  • Chang, K.-W., Yih, S. W.-t., Yang, B., and Meek, C. (2014), “Typed Tensor Decomposition of Knowledge Bases for Relation Extraction,” Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing.
  • Cong, F., Lin, Q.-H., Kuang, L.-D., Gong, X.-F., Astikainen, P., and Ristaniemi, T. (2015), “Tensor Decomposition of EEG Signals: A Brief Review,” Journal of Neuroscience Methods, 248, 59–69. DOI: 10.1016/j.jneumeth.2015.03.018.
  • Dempster, A. P., Laird, N. M., and Rubin, D. B. (1977), “Maximum Likelihood from Incomplete Data via the EM Algorithm,” Journal of the Royal Statistical Society, Series B, 39, 1–38.
  • Denham, W. W., McDaniel, C., and Atkins, J. R. (1979), “Aranda and Alyawara Kinship: A Quantitative Argument for a Double Helix Model,” American Ethnologist, 6, 1–24. DOI: 10.1525/ae.1979.6.1.02a00010.
  • Drumond, L., Diaz-Aviles, E., and Schmidt-Thieme, L. (2016), “Multi-Relational Learning at Scale with ADMM,” arXiv preprint arXiv:1604.00647.
  • Durante, D., and Dunson, D. B. (2014), “Nonparametric Bayes Dynamic Modelling of Relational Data,” Biometrika, 101, 883–898. DOI: 10.1093/biomet/asu040.
  • Fan, M., Zhou, Q., Chang, E., and Zheng, T. F. (2014), “Transition-Based Knowledge Graph Embedding with Relational Mapping Properties,” in Proceedings of the 28th Pacific Asia Conference on Language, Information and Computing.
  • Feng, J., Huang, M., Wang, M., Zhou, M., Hao, Y., and Zhu, X. (2016), “Knowledge Graph Embedding by Flexible Translation,” in KR, pp. 557–560.
  • Foulds, J., DuBois, C., Asuncion, A., Butts, C., and Smyth, P. (2011), “A Dynamic Relational Infinite Feature Model for Longitudinal Social Networks,” in Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics, pp. 287–295.
  • Franz, T., Schultz, A., Sizov, S., and Staab, S. (2009), “Triplerank: Ranking Semantic Web Data by Tensor Decomposition,” The Semantic Web-ISWC 2009, 213–228.
  • Garcia-Duran, A., Bordes, A., Usunier, N., and Grandvalet, Y. (2016), “Combining Two and Three-Way Embedding Models for Link Prediction in Knowledge Bases,” Journal of Artificial Intelligence Research, 55, 715–742. DOI: 10.1613/jair.5013.
  • Ghadermarzy, N., Plan, Y., and Yilmaz, O. (2018), “Learning Tensors From Partial Binary Measurements,” IEEE Transactions on Signal Processing, 67, 29–40. DOI: 10.1109/TSP.2018.2879031.
  • Grover, A., and Leskovec, J. (2016), “node2vec: Scalable Feature Learning for Networks,” in Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 855– 864.
  • Harshman, R. A., and Lundy, M. E. (1994), “Parafac: Parallel Factor Analysis,” Computational Statistics & Data Analysis, 18, 39–72.
  • Hitchcock, F. L. (1927), “The Expression of a Tensor or a Polyadic as a Sum of Products,” Journal of Mathematics and Physics, 6, 64–189. DOI: 10.1002/sapm192761164.
  • Hoff, P. D. (2011), “Hierarchical Multilinear Models for Multiway Data,” Computational Statistics & Data Analysis, 55, 530–543.
  • Hoff, P. D. (2015), “Multilinear Tensor Regression for Longitudinal Relational Data,” The Annals of Applied Statistics, 9, 1169.
  • Hoff, P. D. (2016), “Equivariant and Scale-Free Tucker Decomposition Models,” Bayesian Analysis, 11, 627–648.
  • Hu, C., Rai, P., and Carin, L. (2016), “Topic-Based Embeddings for Learning from Large Knowledge Graphs,” in Artificial Intelligence and Statistics, pp. 1133–1141.
  • Jenatton, R., Roux, N. L., Bordes, A., and Obozinski, G. R. (2012), “A Latent Factor Model for Highly Multi-Relational Data,” in Advances in Neural Information Processing Systems, pp. 3167–3175.
  • Ji, G., Liu, K., He, S., and Zhao, J. (2016), “Knowledge Graph Completion With Adaptive Sparse Transfer Matrix,” in AAAI, pp. 985–991.
  • Karami, A., Yazdi, M., and Mercier, G. (2012), “Compression of Hyperspectral Images Using Discerete Wavelet Transform and Tucker Decomposition,” IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 5, 444–450. DOI: 10.1109/JSTARS.2012.2189200.
  • Kemp, C., Tenenbaum, J. B., Griffiths, T. L., Yamada, T., and Ueda, N. (2006), “Learning Systems of Concepts With an infinite Relational Model,” in AAAI, Volume 3, pp. 5.
  • Kok, S., and Domingos, P. (2007), “Statistical Predicate Invention,” in Proceedings of the 24th International Conference on Machine Learning, pp. 433–440. DOI: 10.1145/1273496.1273551.
  • Krivitsky, P. N., and Handcock, M. S. (2008), “Fitting Position Latent Cluster Models for Social Networks With Latentnet,” Journal of Statistical Software, 24, 5. DOI: 10.18637/jss.v024.i05.
  • Krompaß, D., Nickel, M., Jiang, X., and Tresp, V. (2013), “Non-Negative Tensor Factorization with Rescal,” in Tensor Methods for Machine Learning, ECML Workshop.
  • Liben-Nowell, D., and Kleinberg, J. (2007), “The Link-Prediction Problem for Social Networks,” Journal of the American Society for Information Science and Technology, 58, 1019–1031. DOI: 10.1002/asi.20591.
  • Lin, Y., Liu, Z., Sun, M., Liu, Y., and Zhu, X. (2015), “Learning Entity and Relation Embeddings for Knowledge Graph Completion,” in AAAI, pp. 2181–2187.
  • London, B., Rekatsinas, T., Huang, B., and Getoor, L. (2013), “Multi-Relational Learning Using Weighted Tensor Decomposition with Modular Loss,” arXiv preprint arXiv:1303.1733.
  • Mazumder, R., Hastie, T., and Tibshirani, R. (2010), “Spectral Regularization Algorithms for Learning Large Incomplete Matrices,” The Journal of Machine Learning Research, 11, 2287–2322.
  • McCray, A. T., Burgun, A., and Bodenreider, O. (2001), “Aggregating UMLS Semantic Types for Reducing Conceptual Complexity,” Studies in Health Technology and Informatics, 84, 216.
  • Minhas, S., Hoff, P. D., and Ward, M. D. (2016), “A New Approach to Analyzing Coevolving Longitudinal Networks in International Relations,” Journal of Peace Research, 53, 491–505. DOI: 10.1177/0022343316630783.
  • Nguyen, D. Q., Nguyen, T. D., Nguyen, D. Q., and Phung, D. (2017), “A Novel Embedding Model for Knowledge Base Completion Based on Convolutional Neural Network,” arXiv preprint arXiv:1712.02121.
  • Nguyen, D. Q., Sirts, K., Qu, L., and Johnson, M. (2016), “Stranse: A Novel Embedding Model of Entities and Relationships in Knowledge Bases,” arXiv preprint arXiv:1606.08140.
  • Nickel, M., and Tresp, V. (2013), “Logistic Tensor Factorization for Multi-Relational Data,” arXiv preprint arXiv:1306.2084.
  • Nickel, M., Tresp, V., and Kriegel, H.-P. (2011), “A Three-Way Model for Collective Learning on Multi-Relational Data,” in Proceedings of the 28th International Conference on Machine Learning (ICML-11), pp. 809–816.
  • Peng, J., Lu, G., and Shang, X. (2020), “A Survey of Network Representation Learning Methods for Link Prediction in Biological Network,” Current Pharmaceutical Design, 26, 3076–3084. DOI: 10.2174/1381612826666200116145057.
  • Perozzi, B., Al-Rfou, R., and Skiena, S. (2014), “Deepwalk: Online Learning of Social Representations,” in Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 701–710.
  • Rai, P., Wang, Y., Guo, S., Chen, G., Dunson, D., and Carin, L. (2014), “Scalable Bayesian Low-Rank Decomposition of Incomplete Multiway Tensors,” in International Conference on Machine Learning, pp. 1800–1808.
  • Rendle, S., and Schmidt-Thieme, L. (2010), “Pairwise Interaction Tensor Factorization for Personalized Tag Recommendation,” in Proceedings of the Third ACM International Conference on Web Search and Data Mining, pp. 81–90. ACM. DOI: 10.1145/1718487.1718498.
  • Rummel, R. J. (1976), The Dimensionality of Nations Project: Attributes of Nations and Behavior of Nations Dyads, 1950–1965. Number 5409. Inter-University Consortium for Political Research.
  • Sarkar, P., and Moore, A. (2005), “Dynamic Social Network Analysis Using Latent Space Models,” Advances in Neural Information Processing Systems, 18, 1145–1152.
  • Sarkar, P., Siddiqi, S. M., and Gordon, G. J. (2007), “A Latent Space Approach to Dynamic Embedding of Co-occurrence Data,” in Artificial Intelligence and Statistics, pp. 420–427.
  • Schein, A., Paisley, J., Blei, D. M., and Wallach, H. (2015), “Bayesian Poisson Tensor Factorization for Inferring Multilateral Relations from Sparse Dyadic Event Counts,” in Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1045–1054. DOI: 10.1145/2783258.2783414.
  • Schwarz, G. (1978), “Estimating the Dimension of a Model,” The Annals of Statistics, 6, 461–464. DOI: 10.1214/aos/1176344136.
  • Sewell, D. K., and Chen, Y. (2015), “Latent Space Models for Dynamic Networks,” Journal of the American Statistical Association, 110, 1646–1657. DOI: 10.1080/01621459.2014.988214.
  • Shi, C., Lu, W., and Song, R. (2019), “Determining the Number of Latent Factors in Statistical Multi-Relational Learning,” The Journal of Machine Learning Research, 20, 809–846.
  • Singhal, A. (2012), “Introducing the Knowledge Graph: Things, Not Strings,” Official Google Blog.
  • Suchanek, F. M., Kasneci, G., and Weikum, G. (2007), “Yago: A Core of Semantic Knowledge,” in Proceedings of the 16th International Conference on World Wide Web, pp. 697–706. ACM.
  • Sulaimany, S., Khansari, M., and Masoudi-Nejad, A. (2018), “Link Prediction Potentials for Biological Networks,” International Journal of Data Mining and Bioinformatics, 20, 161–184. DOI: 10.1504/IJDMB.2018.093684.
  • Sun, W. W., Lu, J., Liu, H., and Cheng, G. (2017), “Provable Sparse Tensor Decomposition,” Journal of the Royal Statistical Society, Series B, 79, 899–916. DOI: 10.1111/rssb.12190.
  • Trivedi, R., Dai, H., Wang, Y., and Song, L. (2017), “Know-Evolve: Deep Temporal Reasoning for Dynamic Knowledge Graphs,” arXiv preprint arXiv:1705.05742.
  • Tucker, L. R. (1966), “Some Mathematical Notes on Three-Mode Factor Analysis,” Psychometrika, 31, 279–311. DOI: 10.1007/BF02289464.
  • Vervliet, N., Debals, O., and De Lathauwer, L. (2019), “Exploiting Efficient Representations in Large-Scale Tensor Decompositions,” SIAM Journal on Scientific Computing, 41, A789–A815. DOI: 10.1137/17M1152371.
  • Wang, D., Cui, P., and Zhu, W. (2016), “Structural Deep Network Embedding,” in Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1225–1234.
  • Wang, Z., Zhang, J., Feng, J., and Chen, Z. (2014), “Knowledge Graph Embedding by Translating on Hyperplanes,” in AAAI, pp. 1112–1119.
  • Westveld, A. H., and Hoff, P. D. (2011), “A Mixed Effects Model for Longitudinal Relational and Network Data, With Applications to International Trade and Conflict,” The Annals of Applied Statistics, 5, 843– 872. DOI: 10.1214/10-AOAS403.
  • Xiao, H., Huang, M., Hao, Y., and Zhu, X. (2015), “Transa: An Adaptive Approach for Knowledge Graph Embedding,” arXiv preprint arXiv:1509.05490.
  • Xu, K. S., and Hero, A. O. (2014), “Dynamic Stochastic Blockmodels for Time-Evolving Social Networks,” IEEE Journal of Selected Topics in Signal Processing, 8, 552–562. DOI: 10.1109/JSTSP.2014.2310294.
  • Xu, Z., Yan, F., and Qi, Y. (2013), “Bayesian Nonparametric Models for Multiway Data Analysis,” IEEE transactions on pattern analysis and machine intelligence, 37, 475–487. DOI: 10.1109/TPAMI.2013.201.

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