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

Dynamic Poisson Factorization

Models for recommender systems use latent factors to explain the preferences and behaviors of users with respect to a set of items (e.g., movies, books, academic papers). Typically, the latent factors are assumed to be static and, given these factors, the observed preferences and behaviors of users are assumed to be generated without order. These assumptions limit the explorative and predictive capabilities of such models, since users' interests and item popularity may evolve over time. To address this, we propose dPF, a dynamic matrix factorization model based on the recent Poisson factorization model for recommendations. dPF models the time evolving latent factors with a Kalman filter and the actions with Poisson distributions. We derive a scalable variational inference algorithm to infer the latent factors. Finally, we demonstrate dPF on 10 years of user click data from arXiv.org, one of the largest repository of scientific papers and a formidable source of information about the behavior of scientists. Empirically we show performance improvement over both static and, more recently proposed, dynamic recommendation models. We also provide a thorough exploration of the inferred posteriors over the latent variables.Comment: RecSys 201

Dynamic Machine Learning with Least Square Objectives

As of the writing of this thesis, machine learning has become one of the most active research fields. The interest comes from a variety of disciplines which include computer science, statistics, engineering, and medicine. The main idea behind learning from data is that, when an analytical model explaining the observations is hard to find ---often in contrast to the models in physics such as Newton's laws--- a statistical approach can be taken where one or more candidate models are tuned using data. Since the early 2000's this challenge has grown in two ways: (i) The amount of collected data has seen a massive growth due to the proliferation of digital media, and (ii) the data has become more complex. One example for the latter is the high dimensional datasets, which can for example correspond to dyadic interactions between two large groups (such as customer and product information a retailer collects), or to high resolution image/video recordings. Another important issue is the study of dynamic data, which exhibits dependence on time. Virtually all datasets fall into this category as all data collection is performed over time, however I use the term dynamic to hint at a system with an explicit temporal dependence. A traditional example is target tracking from signal processing literature. Here the position of a target is modeled using Newton's laws of motion, which relates it to time via the target's velocity and acceleration. Dynamic data, as I defined above, poses two important challenges. Firstly, the learning setup is different from the standard theoretical learning setup, also known as Probably Approximately Correct (PAC) learning. To derive PAC learning bounds one assumes a collection of data points sampled independently and identically from a distribution which generates the data. On the other hand, dynamic systems produce correlated outputs. The learning systems we use should accordingly take this difference into consideration. Secondly, as the system is dynamic, it might be necessary to perform the learning online. In this case the learning has to be done in a single pass. Typical applications include target tracking and electricity usage forecasting. In this thesis I investigate several important dynamic and online learning problems, where I develop novel tools to address the shortcomings of the previous solutions in the literature. The work is divided into three parts for convenience. The first part is about matrix factorization for time series analysis which is further divided into two chapters. In the first chapter, matrix factorization is used within a Bayesian framework to model time-varying dyadic interactions, with examples in predicting user-movie ratings and stock prices. In the next chapter, a matrix factorization which uses autoregressive models to forecast future values of multivariate time series is proposed, with applications in predicting electricity usage and traffic conditions. Inspired by the machinery we use in the first part, the second part is about nonlinear Kalman filtering, where a hidden state is estimated over time given observations. The nonlinearity of the system generating the observations is the main challenge here, where a divergence minimization approach is used to unify the seemingly unrelated methods in the literature, and propose new ones. This has applications in target tracking and options pricing. The third and last part is about cost sensitive learning, where a novel method for maximizing area under receiver operating characteristics curve is proposed. Our method has theoretical guarantees and favorable sample complexity. The method is tested on a variety of benchmark datasets, and also has applications in online advertising

Where to next? A dynamic model of user preferences

We consider the problem of predicting users’ preferences on online platforms. We build on recent findings suggesting that users’ preferences change over time, and that helping users expand their horizons is important in ensuring that they stay engaged. Most existing models of user preferences attempt to capture simultaneous preferences: “Users who like A tend to like B as well”. In this paper, we argue that these models fail to anticipate changing preferences. To overcome this issue, we seek to understand the structure that underlies the evolution of user preferences. To this end, we propose the Preference Transition Model (PTM), a dynamic model for user preferences towards classes of items. The model enables the estimation of transition probabilities between classes of items over time, which can be used to estimate how users’ tastes are expected to evolve based on their past history. We test our model’s predictive performance on a number of different prediction tasks on data from three different domains: music streaming, restaurant recommendations and movie recommendations, and find that it outperforms competing approaches. We then focus on a music application, and inspect the structure learned by our model. We find that the PTM uncovers remarkable regularities in users’ preference trajectories over time. We believe that these findings could inform a new generation of dynamic, diversity-enhancing recommender systems

A Dynamic Meta-Learning Model for Time-Sensitive Cold-Start Recommendations

We present a novel dynamic recommendation model that focuses on users who have interactions in the past but turn relatively inactive recently. Making effective recommendations to these time-sensitive cold-start users is critical to maintain the user base of a recommender system. Due to the sparse recent interactions, it is challenging to capture these users' current preferences precisely. Solely relying on their historical interactions may also lead to outdated recommendations misaligned with their recent interests. The proposed model leverages historical and current user-item interactions and dynamically factorizes a user's (latent) preference into time-specific and time-evolving representations that jointly affect user behaviors. These latent factors further interact with an optimized item embedding to achieve accurate and timely recommendations. Experiments over real-world data help demonstrate the effectiveness of the proposed time-sensitive cold-start recommendation model.Comment: 7 pages, conferenc