text: Recommendation for e-commerce with a mix of durable and nondurable goods has characteristics that distinguish it from the well-studied media recommendation problem. The demand for items is a combined effect of form utility and time utility, i.e., a product must both be intrinsically appealing to a consumer and the time must be right for purchase. In particular for durable goods, time utility is a function of inter-purchase duration within product category because consumers are unlikely to purchase two items in the same category in close temporal succession. Moreover, purchase data, in contrast to ratings data, is implicit with non-purchases not necessarily indicating dislike. Together, these issues give rise to the positive-unlabeled demand-aware recommendation problem that we pose via joint low-rank tensor completion and product category inter-purchase duration vector estimation. We further relax this problem and propose a highly scalable alternating minimization approach with which we can solve problems with millions of users and millions of items in a single thread. We also show superior prediction accuracies on multiple real-world data sets.
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  @cite_4: In this paper, we consider the matrix completion problem when the observations are one-bit measurements of some underlying matrix M, and in particular the observed samples consist only of ones and no zeros. This problem is motivated by modern applications such as recommender systems and social networks where only "likes" or "friendships" are observed. The problem of learning from only positive and unlabeled examples, called PU (positive-unlabeled) learning, has been studied in the context of binary classification. We consider the PU matrix completion problem, where an underlying real-valued matrix M is first quantized to generate one-bit observations and then a subset of positive entries is revealed. Under the assumption that M has bounded nuclear norm, we provide recovery guarantees for two different observation models: 1) M parameterizes a distribution that generates a binary matrix, 2) M is thresholded to obtain a binary matrix. For the first case, we propose a "shifted matrix completion" method that recovers M using only a subset of indices corresponding to ones, while for the second case, we propose a "biased matrix completion" method that recovers the (thresholded) binary matrix. Both methods yield strong error bounds --- if M is n by n, the Frobenius error is bounded as O(1 ((1-rho)n), where 1-rho denotes the fraction of ones observed. This implies a sample complexity of O(n n) ones to achieve a small error, when M is dense and n is large. We extend our methods and guarantees to the inductive matrix completion problem, where rows and columns of M have associated features. We provide efficient and scalable optimization procedures for both the methods and demonstrate the effectiveness of the proposed methods for link prediction (on real-world networks consisting of over 2 million nodes and 90 million links) and semi-supervised clustering tasks.
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  @cite_19: Item recommendation is the task of predicting a personalized ranking on a set of items (e.g. websites, movies, products). In this paper, we investigate the most common scenario with implicit feedback (e.g. clicks, purchases). There are many methods for item recommendation from implicit feedback like matrix factorization (MF) or adaptive knearest-neighbor (kNN). Even though these methods are designed for the item prediction task of personalized ranking, none of them is directly optimized for ranking. In this paper we present a generic optimization criterion BPR-Opt for personalized ranking that is the maximum posterior estimator derived from a Bayesian analysis of the problem. We also provide a generic learning algorithm for optimizing models with respect to BPR-Opt. The learning method is based on stochastic gradient descent with bootstrap sampling. We show how to apply our method to two state-of-the-art recommender models: matrix factorization and adaptive kNN. Our experiments indicate that for the task of personalized ranking our optimization method outperforms the standard learning techniques for MF and kNN. The results show the importance of optimizing models for the right criterion.
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  @cite_20: Inferring user preferences over a set of items is an important problem that has found numerous applications. This work focuses on the scenario where the explicit feature representation of items is unavailable, a setup that is similar to collaborative filtering. In order to learn a user's preferences from his her response to only a small number of pairwise comparisons, we propose to leverage the pairwise comparisons made by many crowd users, a problem we refer to as crowdranking. The proposed crowdranking framework is based on the theory of matrix completion, and we present efficient algorithms for solving the related optimization problem. Our theoretical analysis shows that, on average, only O ( r log m ) pairwise queries are needed to accurately recover the ranking list of m items for the target user, where r is the rank of the unknown rating matrix, r << m . Our empirical study with two real-world benchmark datasets for collaborative filtering and one crowdranking dataset we collected via Amazon Mechanical Turk shows the promising performance of the proposed algorithm compared to the state-of-the-art approaches.
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  @cite_12: Abstract The gamma-Poisson form of the negative binomial distribution (NBD) model generally gives a good fit to many aspects of repeat-buying behavior for a wide range of frequently bought branded consumer goods. Nonetheless, empirical evidence suggests that purchasing a particular brand-size in successive equal time-periods tends to be more regular than Poisson. An alternative model is therefore examined in which inter-purchase times for a given consumer are described by an Erlang distribution rather than by the negative exponential distribution implicit in the Poisson assumption of the NBD model. But it is found that the NBD model is robust to this kind of departure. Because of its greater simplicity, the NBD model therefore seems preferable for practical use.
  @cite_17: Context-aware recommender systems (CARS) aim at improving users’ satisfaction by tailoring recommendations to each particular context. In this work we propose a contextual pre-ltering technique based on implicit user feedback. We introduce a new context-aware recommendation approach called user micro-proling . We split each single user prole into several possibly overlapping sub-proles, each representing users in particular contexts. The predictions are done using these micro-proles instead of a single user model. The users’ taste can depend on the exact partition of the contextual variable. The identication of a meaningful partition of the users’ prole and its evaluation is a non-trivial task, especially when using implicit feedback and a continuous contextual domain. We propose an o-line evaluation procedure for CARS in these conditions and evaluate our approach on a time-aware music recommendation sytem.
summary: Our contributions herein relate to three different areas of prior work: consumer modeling from a microeconomics and marketing perspective @cite_12 , time-aware recommender systems @cite_13 @cite_15 @cite_5 @cite_14 , and PU learning @cite_2 @cite_9 @cite_4 @cite_0 @cite_19 @cite_17 . The extensive consumer modeling literature is concerned with descriptive and analytical models of choice rather than prediction or recommendation, but nonetheless forms the basis for our modeling approach. A variety of time-aware recommender systems have been proposed to exploit time information, but none of them explicitly consider the notion of time utility derived from inter-purchase durations in item categories. Much of the PU learning literature is focused on the binary classification problem, e.g. @cite_2 @cite_9 , whereas we are in the collaborative filtering setting. For the papers that do examine collaborative filtering with PU learning or learning with implicit feedback @cite_0 @cite_19 @cite_17 @cite_20 , they mainly focus on media recommendation and overlook users' demands, thus are not suitable for durable goods recommendation.