Dynamic Matrix Factorization with Priors on Unknown Values

Abstract

Advanced and effective collaborative filtering methods based on explicit feedback assume that unknown ratings do not follow the same model as the observed ones (not missing at random). In this work, we build on this assumption, and introduce a novel dynamic matrix factorization framework that allows to set an explicit prior on unknown values. When new ratings, users, or items enter the system, we can update the factorization in time independent of the size of data (number of users, items and ratings). Hence, we can quickly recommend items even to very recent users. We test our methods on three large datasets, including two very sparse ones, in static and dynamic conditions. In each case, we outrank state-of-the-art matrix factorization methods that do not use a prior on unknown ratings.

Fast Matrix Factorization for Online Recommendation with Implicit Feedback

“…To resolve this, [23] describes an approximate solution to ALS. Recently, [4] employs the Randomized block Coordinate Descent (RCD) learner [28], reducing the complexity and applying it to a dynamic scenario. Similarly, [31] enriches the implicit feedback matrix with neighbor-based similarly, followed by applying unweighted SVD.…”

“…In this work, we concern the above two challenging problems of the MF method -implicit feedback and online learning. We note that we are not the first to consider both aspects for MF, as a recent work by Devooght et al [4] has proposed an efficient implicit MF method for learning with dynamic data. However, we argue that Devooght's method [4] models missing data in an unrealistic, suboptimal way.…”

“…We note that we are not the first to consider both aspects for MF, as a recent work by Devooght et al [4] has proposed an efficient implicit MF method for learning with dynamic data. However, we argue that Devooght's method [4] models missing data in an unrealistic, suboptimal way. Specifically, it assigns a uniform weight to the missing data, assuming that the missing entries are equally likely to be negative feedback.…”

“…In particular, we assign the weight of missing data based on the popularity of items, which is arguably more effective than the previous methods [4,12,23,30,31] that are limited by the uniformity assumption. Our eALS algorithm is fast in accounting for missing data -analytically K times faster than ALS [12] where K denotes number of latent factors -the same time complexity with the recent dynamic MF solution [4]. This level of efficiency makes eALS suitable for learning online, for which we develop an incremental update strategy that instantly refreshes model parameters given new incoming data.…”

“…This level of efficiency makes eALS suitable for learning online, for which we develop an incremental update strategy that instantly refreshes model parameters given new incoming data. Another key advantage of eALS is that it works without learning rate, bypassing the wellknown difficulty for tuning gradient descent methods such as [4] and Stochastic Gradient Descent (SGD) [25].…”