A Collaborative Kalman Filter for Time-Evolving Dyadic Processes
This work addresses the challenge of incorporating temporal dynamics into collaborative filtering for applications like recommendation systems, representing an incremental improvement over existing factorization models.
The authors tackled the problem of modeling time-evolving dyadic processes in collaborative filtering by introducing the collaborative Kalman filter (CKF), which models latent embeddings as Brownian motions and includes a method for learning evolving drift parameters, achieving quantitative evaluation on large datasets like 10 million Movielens and 100 million Netflix.
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.