Steffen Rendle

Factorization Machines with libFM

Factorization approaches provide high accuracy in several important prediction problems, for example, recommender systems. However, applying factorization approaches to a new prediction problem is a nontrivial task and requires a lot of expert knowledge. Typically, a new model is developed, a learning algorithm is derived, and the approach has to be implemented. Factorization machines (FM) are a generic approach since they can mimic most factorization models just by feature engineering. This way, factorization machines combine the generality of feature engineering with the superiority of factorization models in estimating interactions between categorical variables of large domain. libFM is a software implementation for factorization machines that features stochastic gradient descent (SGD) and alternating least-squares (ALS) optimization, as well as Bayesian inference using Markov Chain Monto Carlo (MCMC). This article summarizes the recent research on factorization machines both in terms of modeling and learning, provides extensions for the ALS and MCMC algorithms, and describes the software tool libFM.

Factorization Machines

In this paper, we introduce Factorization Machines (FM) which are a new model class that combines the advantages of Support Vector Machines (SVM) with factorization models. Like SVMs, FMs are a general predictor working with any real valued feature vector. In contrast to SVMs, FMs model all interactions between variables using factorized parameters. Thus they are able to estimate interactions even in problems with huge sparsity (like recommender systems) where SVMs fail. We show that the model equation of FMs can be calculated in linear time and thus FMs can be optimized directly. So unlike nonlinear SVMs, a transformation in the dual form is not necessary and the model parameters can be estimated directly without the need of any support vector in the solution. We show the relationship to SVMs and the advantages of FMs for parameter estimation in sparse settings. On the other hand there are many different factorization models like matrix factorization, parallel factor analysis or specialized models like SVD++, PITF or FPMC. The drawback of these models is that they are not applicable for general prediction tasks but work only with special input data. Furthermore their model equations and optimization algorithms are derived individually for each task. We show that FMs can mimic these models just by specifying the input data (i.e. the feature vectors). This makes FMs easily applicable even for users without expert knowledge in factorization models.

Pairwise interaction tensor factorization for personalized tag recommendation

Tagging plays an important role in many recent websites. Recommender systems can help to suggest a user the tags he might want to use for tagging a specific item. Factorization models based on the Tucker Decomposition (TD) model have been shown to provide high quality tag recommendations outperforming other approaches like PageRank, FolkRank, collaborative filtering, etc. The problem with TD models is the cubic core tensor resulting in a cubic runtime in the factorization dimension for prediction and learning. In this paper, we present the factorization model PITF (Pairwise Interaction Tensor Factorization) which is a special case of the TD model with linear runtime both for learning and prediction. PITF explicitly models the pairwise interactions between users, items and tags. The model is learned with an adaption of the Bayesian personalized ranking (BPR) criterion which originally has been introduced for item recommendation. Empirically, we show on real world datasets that this model outperforms TD largely in runtime and even can achieve better prediction quality. Besides our lab experiments, PITF has also won the ECML/PKDD Discovery Challenge 2009 for graph-based tag recommendation.

Factorizing personalized Markov chains for next-basket recommendation

Recommender systems are an important component of many websites. Two of the most popular approaches are based on matrix factorization (MF) and Markov chains (MC). MF methods learn the general taste of a user by factorizing the matrix over observed user-item preferences. On the other hand, MC methods model sequential behavior by learning a transition graph over items that is used to predict the next action based on the recent actions of a user. In this paper, we present a method bringing both approaches together. Our method is based on personalized transition graphs over underlying Markov chains. That means for each user an own transition matrix is learned - thus in total the method uses a transition cube. As the observations for estimating the transitions are usually very limited, our method factorizes the transition cube with a pairwise interaction model which is a special case of the Tucker Decomposition. We show that our factorized personalized MC (FPMC) model subsumes both a common Markov chain and the normal matrix factorization model. For learning the model parameters, we introduce an adaption of the Bayesian Personalized Ranking (BPR) framework for sequential basket data. Empirically, we show that our FPMC model outperforms both the common matrix factorization and the unpersonalized MC model both learned with and without factorization.

MyMediaLite: a free recommender system library

MyMediaLite is a fast and scalable, multi-purpose library of recommender system algorithms, aimed both at recommender system researchers and practitioners. It addresses two common scenarios in collaborative filtering: rating prediction (e.g. on a scale of 1 to 5 stars) and item prediction from positive-only implicit feedback (e.g. from clicks or purchase actions). The library offers state-of-the-art algorithms for those two tasks. Programs that expose most of the librarys functionality, plus a GUI demo, are included in the package. Efficient data structures and a common API are used by the implemented algorithms, and may be used to implement further algorithms. The API also contains methods for real-time updates and loading/storing of already trained recommender models. MyMediaLite is free/open source software, distributed under the terms of the GNU General Public License (GPL). Its methods have been used in four different industrial field trials of the MyMedia project, including one trial involving over 50,000 households.

Fast context-aware recommendations with factorization machines

The situation in which a choice is made is an important information for recommender systems. Context-aware recommenders take this information into account to make predictions. So far, the best performing method for context-aware rating prediction in terms of predictive accuracy is Multiverse Recommendation based on the Tucker tensor factorization model. However this method has two drawbacks: (1) its model complexity is exponential in the number of context variables and polynomial in the size of the factorization and (2) it only works for categorical context variables. On the other hand there is a large variety of fast but specialized recommender methods which lack the generality of context-aware methods. We propose to apply Factorization Machines (FMs) to model contextual information and to provide context-aware rating predictions. This approach results in fast context-aware recommendations because the model equation of FMs can be computed in linear time both in the number of context variables and the factorization size. For learning FMs, we develop an iterative optimization method that analytically finds the least-square solution for one parameter given the other ones. Finally, we show empirically that our approach outperforms Multiverse Recommendation in prediction quality and runtime.

Learning Attribute-to-Feature Mappings for Cold-Start Recommendations

Cold-start scenarios in recommender systems are situations in which no prior events, like ratings or clicks, are known for certain users or items. To compute predictions in such cases, additional information about users (user attributes, e.g. gender, age, geographical location, occupation) and items (item attributes, e.g. genres, product categories, keywords) must be used. We describe a method that maps such entity (e.g. user or item) attributes to the latent features of a matrix (or higher-dimensional) factorization model. With such mappings, the factors of a MF model trained by standard techniques can be applied to the new-user and the new-item problem, while retaining its advantages, in particular speed and predictive accuracy. We use the mapping concept to construct an attribute-aware matrix factorization model for item recommendation from implicit, positive-only feedback. Experiments on the new-item problem show that this approach provides good predictive accuracy, while the prediction time only grows by a constant factor.

Online-updating regularized kernel matrix factorization models for large-scale recommender systems

Regularized matrix factorization models are known to generate high quality rating predictions for recommender systems. One of the major drawbacks of matrix factorization is that once computed, the model is static. For real-world applications dynamic updating a model is one of the most important tasks. Especially when ratings on new users or new items come in, updating the feature matrices is crucial. In this paper, we generalize regularized matrix factorization (RMF) to regularized kernel matrix factorization (RKMF). Kernels provide a flexible method for deriving new matrix factorization methods. Furthermore with kernels nonlinear interactions between feature vectors are possible. We propose a generic method for learning RKMF models. From this method we derive an online-update algorithm for RKMF models that allows to solve the new-user/new-item problem. Our evaluation indicates that our proposed online-update methods are accurate in approximating a full retrain of a RKMF model while the runtime of online-updating is in the range of milliseconds even for huge datasets like Netflix.

Improving pairwise learning for item recommendation from implicit feedback

Pairwise algorithms are popular for learning recommender systems from implicit feedback. For each user, or more generally context, they try to discriminate between a small set of selected items and the large set of remaining (irrelevant) items. Learning is typically based on stochastic gradient descent (SGD) with uniformly drawn pairs. In this work, we show that convergence of such SGD learning algorithms slows down considerably if the item popularity has a tailed distribution. We propose a non-uniform item sampler to overcome this problem. The proposed sampler is context-dependent and oversamples informative pairs to speed up convergence. An efficient implementation with constant amortized runtime costs is developed. Furthermore, it is shown how the proposed learning algorithm can be applied to a large class of recommender models. The properties of the new learning algorithm are studied empirically on two real-world recommender system problems. The experiments indicate that the proposed adaptive sampler improves the state-of-the art learning algorithm largely in convergence without negative effects on prediction quality or iteration runtime.

Scaling factorization machines to relational data

The most common approach in predictive modeling is to describe cases with feature vectors (aka design matrix). Many machine learning methods such as linear regression or support vector machines rely on this representation. However, when the underlying data has strong relational patterns, especially relations with high cardinality, the design matrix can get very large which can make learning and prediction slow or even infeasible. This work solves this issue by making use of repeating patterns in the design matrix which stem from the underlying relational structure of the data. It is shown how coordinate descent learning and Bayesian Markov Chain Monte Carlo inference can be scaled for linear regression and factorization machine models. Empirically, it is shown on two large scale and very competitive datasets (Netflix prize, KDDCup 2012), that (1) standard learning algorithms based on the design matrix representation cannot scale to relational predictor variables, (2) the proposed new algorithms scale and (3) the predictive quality of the proposed generic feature-based approach is as good as the best specialized models that have been tailored to the respective tasks.