Rating model with latent parameters based on the softmax function

The relevance of the work is due to the widespread use of recommendation systems using rating assessments. Based on the results of the review of recommendation methods, it is concluded that it is possible and expedient to build a probabilistic rating model similar to the Item Response Theory models. It is proposed to use latent interest parameters for each subject, characterizing its tendency to set a certain rating, and latent agreeability parameters for each object, characterizing the frequency of obtaining a certain rating. The probabilities of the estimates are determined by a softmax function with interest and matching parameters. The equations connecting observations and latent parameters are obtained using the maximum likelihood method. An iterative procedure for calculating parameters based on rating estimates has been developed and its convergence has been substantiated. The model was tested using the well-known Nexflix set with movie ratings and statistical characteristics of the ratings predictions were presented. The accuracy of predicting ratings turned out to be comparable with the accuracy of predictions of other models. The advantage of the proposed model is a compact description of the assessment probabilities in the form of sets of latent parameters of subjects and objects, which makes it possible to predict rating estimates. The disadvantages include the computational complexity of estimating the parameters and the need to recalculate the parameters when new data becomes available. The proposed model can be used to study and predict ratings.

1. Su X., Khoshgoftaar T.M. A Survey of Collaborative Filtering Techniques. Advances in Artificial Intelligence. 2009. https://doi.org/10.1155/2009/421425

2. Alieva O.A., Gangan E.S., Ilyushin E.A., Kachalin A.I. Automatic Evaluation of Recommendation Models. Modern Information Technologies and IT-Education. 2020;16(2):398–406. https://doi.org/10.25559/SITITO.16.202002.398-406

3. Koren Y., Bell R., Volinsky Ch. Matrix Factorization Techniques for Recommender Systems. Computer. 2009;42(8):30–37. https://doi.org/10.1109/MC.2009.263

4. Salakhutdinov R., Mnih A. Probabilistic Matrix Factorization. In: Advances in Neural Information Processing Systems 20: Proceedings of the Twenty-First Annual Conference on Neural Information Processing Systems, 03–06 December 2007, Vancouver, British Columbia, Canada. Curran Associates, Inc.; 2008. Р. 1257–1264.

5. Silva M.G., Madeira S.C., Henriques R. A Comprehensive Survey on Biclustering-based Collaborative Filtering. ACM Computing Surveys. 2024;56(12). https://doi.org/10.1145/3674723

6. Zhang Sh., Yao L., Sun A., Tay Y. Deep Learning Based Recommender System: A Survey and New Perspectives. ACM Computing Surveys. 2019;52(1). https://doi.org/10.1145/3285029

7. Cheng H.-T., Koc L., Harmsen J., et al. Wide & deep learning for recommender systems. In: DLRS 2016: Proceedings of the 1st Workshop on Deep Learning for Recommender Systems, 15 September 2016, Boston, MA, USA. New York: ACM; 2016. P. 7–10. https://doi.org/10.1145/2988450.2988454

8. Wright B.D., Masters G.N. Rating scale analysis: Rasch measurement. Chicago: MESA Press; 1982. 206 p.

9. Hu B., Zhou Y., Wang J., Li L., Shen L. Application of Item Response Theory to Collaborative Filtering. In: Advances in Neural Networks – ISNN 2009: Proceedings: Part I: 6th International Symposium on Neural Networks, ISNN 2009, 26–29 May 2009, Wuhan, China. Berlin, Heidelberg: Springer; 2009. P. 766–773. https://doi.org/10.1007/978-3-642-01507-6_86

10. Bergner Y., Halpin P., Vie J.-J. Multidimensional Item Response Theory in the Style of Collaborative Filtering. Psychometrika. 2022;87(1):266–288. https://doi.org/10.1007/s11336-021-09788-9

11. Bratischenko V.V. Model with latent parameters for analysis of ratings. Modern high technologies. 2023;(2):23–29. (In Russ.). https://doi.org/10.17513/snt.39519