This paper proposes Quaternion Collaborative Filtering (QCF), a novel representation learning method for recommendation. Our proposed QCF relies on and exploits computation with Quaternion algebra, benefiting from the expressiveness and rich representation learning capability of Hamilton products. Quaternion representations, based on hypercomplex numbers, enable rich inter-latent dependencies between imaginary components. This encourages intricate relations to be captured when learning user-item interactions, serving as a strong inductive bias as compared with the real-space inner product. All in all, we conduct extensive experiments on six real-world datasets, demonstrating the effectiveness of Quaternion algebra in recommender systems. The results exhibit that QCF outperforms a wide spectrum of strong neural baselines on all datasets. Ablative experiments confirm the effectiveness of Hamilton-based composition over multi-embedding composition in real space.
Firstly, our work is concerned with collaborative filtering, in which matrix factorization @cite_23 remains a competitive baseline. A wide spectrum of variants have been proposed based on it. For example, timeSVD++ @cite_12 takes temporal dynamics and implicit feedback into account and achieves good performance on rating prediction. BPR @cite_25 is a pairwise learning personalized ranking method with matrix factorization. @cite_21 proposed an efficient matrix factorization based recommendation model with a non-uniform weight strategy, just to name a few. Recent years have witnessed a shift from traditional collaborative filtering to neural networks approaches, with exponentially increase in the amount of publications on this topic @cite_35 @cite_24 @cite_17 . The achievements are inspiring and enlightening. Many of the well-established neural networks can be applied to recommender systems. For instance, We can add nonlinear transformations into collaborative filtering with multilayer perceptron @cite_28 @cite_31 @cite_13 @cite_33 @cite_3 , use autoencoder or convolutional neural networks to learn richer feature representations from user item auxiliary information (e.g., profiles, images, video abstract, reviews, etc.) @cite_18 @cite_0 @cite_1 , and utilize recurrent neural networks to model the sequential patterns in user behaviours to make session-aware recommendation @cite_26 @cite_11 .
@cite_35 @cite_18 @cite_26 @cite_11 @cite_33 @cite_28 @cite_21 @cite_1 @cite_3 @cite_24 @cite_0 @cite_23 @cite_31 @cite_13 @cite_25 @cite_12 @cite_17
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We extend variational autoencoders (VAEs) to collaborative filtering for implicit feedback. This non-linear probabilistic model enables us to go beyond the limited modeling capacity of linear factor models which still largely dominate collaborative filtering research. We introduce a generative model with multinomial likelihood and use Bayesian inference to learn this powerful generative model. Despite widespread use in language modeling and economics, the multinomial likelihood receives less attention in the recommender systems literature. We introduce a different regularization parameter for the learning objective, which proves to be crucial for achieving competitive performance. Remarkably, there is an efficient way to tune the parameter using annealing. The resulting model and learning algorithm has information-theoretic connections to maximum entropy discrimination and the information bottleneck principle. Empirically, we show that the proposed approach significantly outperforms several state-of-the-art baselines, including two recently-proposed neural network approaches, on several real-world datasets. We also provide extended experiments comparing the multinomial likelihood with other commonly used likelihood functions in the latent factor collaborative filtering literature and show favorable results. Finally, we identify the pros and cons of employing a principled Bayesian inference approach and characterize settings where it provides the most significant improvements. We extend variational autoencoders (VAEs) to collaborative filtering for implicit feedback. This non-linear probabilistic model enables us to go beyond the limited modeling capacity of linear factor models which still largely dominate collaborative filtering research.We introduce a generative model with multinomial likelihood and use Bayesian inference for parameter estimation. Despite widespread use in language modeling and economics, the multinomial likelihood receives less attention in the recommender systems literature. We introduce a different regularization parameter for the learning objective, which proves to be crucial for achieving competitive performance. Remarkably, there is an efficient way to tune the parameter using annealing. The resulting model and learning algorithm has information-theoretic connections to maximum entropy discrimination and the information bottleneck principle. Empirically, we show that the proposed approach significantly outperforms several state-of-the-art baselines, including two recently-proposed neural network approaches, on several real-world datasets. We also provide extended experiments comparing the multinomial likelihood with other commonly used likelihood functions in the latent factor collaborative filtering literature and show favorable results. Finally, we identify the pros and cons of employing a principled Bayesian inference approach and characterize settings where it provides the most significant improvements. We propose a new method for creating computationally efficient convolutional neural networks (CNNs) by using low-rank representations of convolutional filters. Rather than approximating filters in previously-trained networks with more efficient versions, we learn a set of small basis filters from scratch; during training, the network learns to combine these basis filters into more complex filters that are discriminative for image classification. To train such networks, a novel weight initialization scheme is used. This allows effective initialization of connection weights in convolutional layers composed of groups of differently-shaped filters. We validate our approach by applying it to several existing CNN architectures and training these networks from scratch using the CIFAR, ILSVRC and MIT Places datasets. Our results show similar or higher accuracy than conventional CNNs with much less compute. Applying our method to an improved version of VGG-11 network using global max-pooling, we achieve comparable validation accuracy using 41 less compute and only 24 of the original VGG-11 model parameters; another variant of our method gives a 1 percentage point increase in accuracy over our improved VGG-11 model, giving a top-5 center-crop validation accuracy of 89.7 while reducing computation by 16 relative to the original VGG-11 model. Applying our method to the GoogLeNet architecture for ILSVRC, we achieved comparable accuracy with 26 less compute and 41 fewer model parameters. Applying our method to a near state-of-the-art network for CIFAR, we achieved comparable accuracy with 46 less compute and 55 fewer parameters. In a variety of application domains the content to be recommended to users is associated with text. This includes research papers, movies with associated plot summaries, news articles, blog posts, etc. Recommendation approaches based on latent factor models can be extended naturally to leverage text by employing an explicit mapping from text to factors. This enables recommendations for new, unseen content, and may generalize better, since the factors for all items are produced by a compactly-parametrized model. Previous work has used topic models or averages of word embeddings for this mapping. In this paper we present a method leveraging deep recurrent neural networks to encode the text sequence into a latent vector, specifically gated recurrent units (GRUs) trained end-to-end on the collaborative filtering task. For the task of scientific paper recommendation, this yields models with significantly higher accuracy. In cold-start scenarios, we beat the previous state-of-the-art, all of which ignore word order. Performance is further improved by multi-task learning, where the text encoder network is trained for a combination of content recommendation and item metadata prediction. This regularizes the collaborative filtering model, ameliorating the problem of sparsity of the observed rating matrix.