A Collaborative Kalman Filter for Time-Evolving Dyadic Processes

We present the collaborative Kalman filter (CKF), a dynamic model for collaborative filtering and related factorization models. Using the matrix factorization approach to collaborative filtering, the CKF accounts for time evolution by modeling each low-dimensional latent embedding as a multidimensional Brownian motion. Each observation is a random variable whose distribution is parameterized by the dot product of the relevant Brownian motions at that moment in time. This is naturally interpreted as a Kalman filter with multiple interacting state space vectors. We also present a method for learning a dynamically evolving drift parameter for each location by modeling it as a geometric Brownian motion. We handle posterior intractability via a mean-field variational approximation, which also preserves tractability for downstream calculations in a manner similar to the Kalman filter. We evaluate the model on several large datasets, providing quantitative evaluation on the 10 million Movielens and 100 million Netflix datasets and qualitative evaluation on a set of 39 million stock returns divided across roughly 6,500 companies from the years 1962-2014.Comment: Appeared at 2014 IEEE International Conference on Data Mining (ICDM

TSCMF: Temporal and social collective matrix factorization model for recommender systems

In real-world recommender systems, user preferences are dynamic and typically change over time. Capturing the temporal dynamics of user preferences is essential to design an efficient personalized recommender system and has recently attracted significant attention. In this paper, we consider user preferences change individually over time. Moreover, based on the intuition that social influence can affect the users’ preferences in a recommender system, we propose a Temporal and Social CollectiveMatrix Factorization model called TSCMF for recommendation.We jointly factorize the users’ rating information and social trust information in a collective matrix factorization framework by introducing a joint objective function. We model user dynamics into this framework by learning a transition matrix of user preferences between two successive time periods for each individual user. We present an efficient optimization algorithm based on stochastic gradient descent for solving the objective function. The experiments on a real-world dataset illustrate that the proposed model outperforms the competitive methods.Moreover, the complexity analysis demonstrates that the proposed model can be scaled up to large datasets

Modeling user preference dynamics with coupled tensor factorization for social media recommendation

An essential problem in real-world recommender systems is that user preferences are not static and users are likely to change their preferences over time. Recent studies have shown that the modelling and capturing the dynamics of user preferences lead to significant improvements on recommendation accuracy and, consequently, user satisfaction. In this paper, we develop a framework to capture user preference dynamics in a personalized manner based on the fact that changes in user preferences can vary individually. We also consider the plausible assumption that older user activities should have less influence on a user’s current preferences. We introduce an individual time decay factor for each user according to the rate of his preference dynamics to weigh the past user preferences and decrease their importance gradually. We exploit users’ demographics as well as the extracted similarities among users over time, aiming to enhance the prior knowledge about user preference dynamics, in addition to the past weighted user preferences in a developed coupled tensor factorization technique to provide top-K recommendations. The experimental results on the two real social media datasets—Last.fm and Movielens—indicate that our proposed model is better and more robust than other competitive methods in terms of recommendation accuracy and is more capable of coping with problems such as cold-start and data sparsity

Bayesian Temporal Factorization for Multidimensional Time Series Prediction

Large-scale and multidimensional spatiotemporal data sets are becoming ubiquitous in many real-world applications such as monitoring urban traffic and air quality. Making predictions on these time series has become a critical challenge due to not only the large-scale and high-dimensional nature but also the considerable amount of missing data. In this paper, we propose a Bayesian temporal factorization (BTF) framework for modeling multidimensional time series -- in particular spatiotemporal data -- in the presence of missing values. By integrating low-rank matrix/tensor factorization and vector autoregressive (VAR) process into a single probabilistic graphical model, this framework can characterize both global and local consistencies in large-scale time series data. The graphical model allows us to effectively perform probabilistic predictions and produce uncertainty estimates without imputing those missing values. We develop efficient Gibbs sampling algorithms for model inference and model updating for real-time prediction and test the proposed BTF framework on several real-world spatiotemporal data sets for both missing data imputation and multi-step rolling prediction tasks. The numerical experiments demonstrate the superiority of the proposed BTF approaches over existing state-of-the-art methods.Comment: 15 pages, 9 figures, 3 table