Low-Rank Factorization of Determinantal Point Processes for Recommendation

Determinantal point processes (DPPs) have garnered attention as an elegant probabilistic model of set diversity. They are useful for a number of subset selection tasks, including product recommendation. DPPs are parametrized by a positive semi-definite kernel matrix. In this work we present a new method for learning the DPP kernel from observed data using a low-rank factorization of this kernel. We show that this low-rank factorization enables a learning algorithm that is nearly an order of magnitude faster than previous approaches, while also providing for a method for computing product recommendation predictions that is far faster (up to 20x faster or more for large item catalogs) than previous techniques that involve a full-rank DPP kernel. Furthermore, we show that our method provides equivalent or sometimes better predictive performance than prior full-rank DPP approaches, and better performance than several other competing recommendation methods in many cases. We conduct an extensive experimental evaluation using several real-world datasets in the domain of product recommendation to demonstrate the utility of our method, along with its limitations.Comment: 10 pages, 4 figures. Submitted to KDD 201

High-performance sampling of generic Determinantal Point Processes

Determinantal Point Processes (DPPs) were introduced by Macchi as a model for repulsive (fermionic) particle distributions. But their recent popularization is largely due to their usefulness for encouraging diversity in the final stage of a recommender system. The standard sampling scheme for finite DPPs is a spectral decomposition followed by an equivalent of a randomly diagonally-pivoted Cholesky factorization of an orthogonal projection, which is only applicable to Hermitian kernels and has an expensive setup cost. Researchers have begun to connect DPP sampling to $LDL^H$ factorizations as a means of avoiding the initial spectral decomposition, but existing approaches have only outperformed the spectral decomposition approach in special circumstances, where the number of kept modes is a small percentage of the ground set size. This article proves that trivial modifications of $LU$ and $LDL^H$ factorizations yield efficient direct sampling schemes for non-Hermitian and Hermitian DPP kernels, respectively. Further, it is experimentally shown that even dynamically-scheduled, shared-memory parallelizations of high-performance dense and sparse-direct factorizations can be trivially modified to yield DPP sampling schemes with essentially identical performance. The software developed as part of this research, Catamari, https://hodgestar.com/catamari, is released under the Mozilla Public License v2.0. It contains header-only, C++14 plus OpenMP 4.0 implementations of dense and sparse-direct, Hermitian and non-Hermitian DPP samplers.Comment: 25 pages, 11 figures. Submitted to the Royal Society's Philosophical Transactions

Learning Determinantal Point Processes by Corrective Negative Sampling

Determinantal Point Processes (DPPs) have attracted significant interest from the machine-learning community due to their ability to elegantly and tractably model the delicate balance between quality and diversity of sets. DPPs are commonly learned from data using maximum likelihood estimation (MLE). While fitting observed sets well, MLE for DPPs may also assign high likelihoods to unobserved sets that are far from the true generative distribution of the data. To address this issue, which reduces the quality of the learned model, we introduce a novel optimization problem, Contrastive Estimation (CE), which encodes information about "negative" samples into the basic learning model. CE is grounded in the successful use of negative information in machine-vision and language modeling. Depending on the chosen negative distribution (which may be static or evolve during optimization), CE assumes two different forms, which we analyze theoretically and experimentally. We evaluate our new model on real-world datasets; on a challenging dataset, CE learning delivers a considerable improvement in predictive performance over a DPP learned without using contrastive information.Comment: Will appear in AISTATS 201

Learning Nonsymmetric Determinantal Point Processes

Determinantal point processes (DPPs) have attracted substantial attention as an elegant probabilistic model that captures the balance between quality and diversity within sets. DPPs are conventionally parameterized by a positive semi-definite kernel matrix, and this symmetric kernel encodes only repulsive interactions between items. These so-called symmetric DPPs have significant expressive power, and have been successfully applied to a variety of machine learning tasks, including recommendation systems, information retrieval, and automatic summarization, among many others. Efficient algorithms for learning symmetric DPPs and sampling from these models have been reasonably well studied. However, relatively little attention has been given to nonsymmetric DPPs, which relax the symmetric constraint on the kernel. Nonsymmetric DPPs allow for both repulsive and attractive item interactions, which can significantly improve modeling power, resulting in a model that may better fit for some applications. We present a method that enables a tractable algorithm, based on maximum likelihood estimation, for learning nonsymmetric DPPs from data composed of observed subsets. Our method imposes a particular decomposition of the nonsymmetric kernel that enables such tractable learning algorithms, which we analyze both theoretically and experimentally. We evaluate our model on synthetic and real-world datasets, demonstrating improved predictive performance compared to symmetric DPPs, which have previously shown strong performance on modeling tasks associated with these datasets.Comment: NeurIPS 201

Fast Greedy MAP Inference for Determinantal Point Process to Improve Recommendation Diversity

The determinantal point process (DPP) is an elegant probabilistic model of repulsion with applications in various machine learning tasks including summarization and search. However, the maximum a posteriori (MAP) inference for DPP which plays an important role in many applications is NP-hard, and even the popular greedy algorithm can still be too computationally expensive to be used in large-scale real-time scenarios. To overcome the computational challenge, in this paper, we propose a novel algorithm to greatly accelerate the greedy MAP inference for DPP. In addition, our algorithm also adapts to scenarios where the repulsion is only required among nearby few items in the result sequence. We apply the proposed algorithm to generate relevant and diverse recommendations. Experimental results show that our proposed algorithm is significantly faster than state-of-the-art competitors, and provides a better relevance-diversity trade-off on several public datasets, which is also confirmed in an online A/B test

Towards Bursting Filter Bubble via Contextual Risks and Uncertainties

A rising topic in computational journalism is how to enhance the diversity in news served to subscribers to foster exploration behavior in news reading. Despite the success of preference learning in personalized news recommendation, their over-exploitation causes filter bubble that isolates readers from opposing viewpoints and hurts long-term user experiences with lack of serendipity. Since news providers can recommend neither opposite nor diversified opinions if unpopularity of these articles is surely predicted, they can only bet on the articles whose forecasts of click-through rate involve high variability (risks) or high estimation errors (uncertainties). We propose a novel Bayesian model of uncertainty-aware scoring and ranking for news articles. The Bayesian binary classifier models probability of success (defined as a news click) as a Beta-distributed random variable conditional on a vector of the context (user features, article features, and other contextual features). The posterior of the contextual coefficients can be computed efficiently using a low-rank version of Laplace's method via thin Singular Value Decomposition. Efficiencies in personalized targeting of exceptional articles, which are chosen by each subscriber in test period, are evaluated on real-world news datasets. The proposed estimator slightly outperformed existing training and scoring algorithms, in terms of efficiency in identifying successful outliers.Comment: The filter bubble problem; Uncertainty-aware scoring; Empirical-Bayes method; Low-rank Laplace's metho

Recent Advances in Diversified Recommendation

With the rapid development of recommender systems, accuracy is no longer the only golden criterion for evaluating whether the recommendation results are satisfying or not. In recent years, diversity has gained tremendous attention in recommender systems research, which has been recognized to be an important factor for improving user satisfaction. On the one hand, diversified recommendation helps increase the chance of answering ephemeral user needs. On the other hand, diversifying recommendation results can help the business improve product visibility and explore potential user interests. In this paper, we are going to review the recent advances in diversified recommendation. Specifically, we first review the various definitions of diversity and generate a taxonomy to shed light on how diversity have been modeled or measured in recommender systems. After that, we summarize the major optimization approaches to diversified recommendation from a taxonomic view. Last but not the least, we project into the future and point out trending research directions on this topic

Kronecker Determinantal Point Processes

Determinantal Point Processes (DPPs) are probabilistic models over all subsets a ground set of $N$ items. They have recently gained prominence in several applications that rely on "diverse" subsets. However, their applicability to large problems is still limited due to the $\mathcal O(N^3)$ complexity of core tasks such as sampling and learning. We enable efficient sampling and learning for DPPs by introducing KronDPP, a DPP model whose kernel matrix decomposes as a tensor product of multiple smaller kernel matrices. This decomposition immediately enables fast exact sampling. But contrary to what one may expect, leveraging the Kronecker product structure for speeding up DPP learning turns out to be more difficult. We overcome this challenge, and derive batch and stochastic optimization algorithms for efficiently learning the parameters of a KronDPP

Personalized Bundle List Recommendation

Product bundling, offering a combination of items to customers, is one of the marketing strategies commonly used in online e-commerce and offline retailers. A high-quality bundle generalizes frequent items of interest, and diversity across bundles boosts the user-experience and eventually increases transaction volume. In this paper, we formalize the personalized bundle list recommendation as a structured prediction problem and propose a bundle generation network (BGN), which decomposes the problem into quality/diversity parts by the determinantal point processes (DPPs). BGN uses a typical encoder-decoder framework with a proposed feature-aware softmax to alleviate the inadequate representation of traditional softmax, and integrates the masked beam search and DPP selection to produce high-quality and diversified bundle list with an appropriate bundle size. We conduct extensive experiments on three public datasets and one industrial dataset, including two generated from co-purchase records and the other two extracted from real-world online bundle services. BGN significantly outperforms the state-of-the-art methods in terms of quality, diversity and response time over all datasets. In particular, BGN improves the precision of the best competitors by 16\% on average while maintaining the highest diversity on four datasets, and yields a 3.85x improvement of response time over the best competitors in the bundle list recommendation problem.Comment: WWW2019, 11 page

Diverse Landmark Sampling from Determinantal Point Processes for Scalable Manifold Learning

High computational costs of manifold learning prohibit its application for large point sets. A common strategy to overcome this problem is to perform dimensionality reduction on selected landmarks and to successively embed the entire dataset with the Nystr\"om method. The two main challenges that arise are: (i) the landmarks selected in non-Euclidean geometries must result in a low reconstruction error, (ii) the graph constructed from sparsely sampled landmarks must approximate the manifold well. We propose the sampling of landmarks from determinantal distributions on non-Euclidean spaces. Since current determinantal sampling algorithms have the same complexity as those for manifold learning, we present an efficient approximation running in linear time. Further, we recover the local geometry after the sparsification by assigning each landmark a local covariance matrix, estimated from the original point set. The resulting neighborhood selection based on the Bhattacharyya distance improves the embedding of sparsely sampled manifolds. Our experiments show a significant performance improvement compared to state-of-the-art landmark selection techniques