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Variational Autoencoders for Collaborative Filtering
Dawen Liang, Rahul G. Krishnan, Matthew D. Hoffman, Tony Jebara
TL;DR
Collaborative filtering needs models that overcome the limited capacity of dominant linear latent-factor approaches while handling sparse implicit-feedback data. The paper extends VAEs with a multinomial generative likelihood, Bayesian inference, and partial regularization tuned by annealing. The resulting methods significantly outperform state-of-the-art baselines, including recent neural-network approaches, across several real-world datasets.
Problem
Linear latent-factor models dominate collaborative filtering but have limited modeling capacity, while sparse user interactions make preference inference challenging.
Method
The paper extends VAEs with a multinomial likelihood, Bayesian inference, and a partially regularized objective whose additional parameter is tuned using KL annealing.
Results
The proposed methods significantly outperform state-of-the-art baselines, including two recently proposed neural-network approaches, on several real-world datasets.
Takeaways & Limitations
Mult-vaepr and Mult-dae provide competitive performance, while principled Bayesian inference is reported to be more robust and its benefits vary across settings.
Takeaways & Limitations
Likelihood choice remains data-dependent, and multinomial normalization can become computationally expensive when item sets are very large.
Abstract
from arXiv · showhide
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.
1 INTRODUCTION
Collaborative filtering remains dominated by linear latent-factor models despite their limited modeling capacity. This paper extends VAEs with a multinomial likelihood and Bayesian inference, reporting competitive performance and strong results against established and neural baselines.
- Latent factor models dominate collaborative filtering because of their simplicity and effectiveness, but their linearity limits modeling capacity.
- The paper extends VAEs to implicit-feedback collaborative filtering, enabling nonlinear probabilistic latent-variable models powered by neural networks.
- A multinomial likelihood is proposed for implicit feedback because it is well-suited to the data and closer to ranking loss than Gaussian or logistic likelihoods.
- Sparse user interactions make recommendation a small-data inference problem requiring shared statistical strength to avoid overfitting.
- The standard VAE objective is adjusted because it is considered over-regularized, with connections to information bottleneck and maximum-entropy discrimination.
- Empirically, the resulting methods significantly outperform state-of-the-art baselines, including two recently proposed neural-network approaches, on several real-world datasets.
2 METHOD
The paper extends variational autoencoders to implicit-feedback collaborative filtering with a multinomial generative model and variational inference. It modifies VAE regularization through β, tunes it by annealing, and introduces Mult-vaepr while analyzing related autoencoder variants and computational tradeoffs.
- 2.1 Model: The model represents each user's click history as multinomial samples from a softmax distribution generated from a nonlinear latent representation.A multilayer perceptron maps a Gaussian latent vector to probabilities over all items.
- 2.1 Model: The multinomial likelihood focuses probability mass on clicked items while forcing items to compete within a normalized probability budget.The paper compares this likelihood with Gaussian and logistic alternatives used in latent-factor collaborative filtering.
- 2.2 Variational inference: Variational inference approximates each intractable posterior with a diagonal Gaussian whose parameters are produced from the observed user vector by an inference network.This amortized inference architecture combines qϕ(zu | xu) with the generative model to form a variational autoencoder.
- 2.2.2 Alternative interpretation of elbo: The method treats β as a free regularization parameter, weakening the prior constraint when β < 1 rather than strictly optimizing the marginal-likelihood lower bound.This sacrifices some ability to generate novel user histories by ancestral sampling but is motivated by recommendation performance.
- 2.2.2 Alternative interpretation of elbo: Annealing β from 0 toward 1 identifies the peak validation ranking metric, after which training can stop increasing β to obtain the partially regularized Mult-vaepr.The procedure is more efficient than training multiple models for a grid search, though it may be sub-optimal relative to thorough grid search.
- 2.2.3 Computational Burden: For very large item sets, multinomial normalization can become computationally expensive because predictions for all items are required.The paper reports no bottleneck on evaluated datasets with fewer than 50K items.
- 2.3 A taxonomy of autoencoders: Mult-dae uses input dropout to reduce the overfitting observed when an autoencoder places all probability mass on a user's nonzero entries.Unlike the VAE, the autoencoder uses a delta variational distribution and does not regularize toward a prior.
3 RELATED WORK
The paper situates its VAE approach among work on VAEs for sparse data, information-theoretic objectives, and neural collaborative filtering. It emphasizes both the model’s connections to prior methods and a trade-off introduced by its regularization choice.
- VAEs on sparse data: VAEs can underfit large, sparse, high-dimensional data without annealing, motivating the paper’s modified training approach.The paper reports similar issues without annealing or when annealing to β = 1.
- Information-theoretic connection with VAE: The β-weighted objective connects the method to maximum-entropy discrimination by balancing discriminative and generative aspects.
- Information-theoretic connection with VAE: The objective also connects to the deep variational information bottleneck, where β < 1 has been associated with more robust supervised classification.
- Information-theoretic connection with VAE: Unlike β-VAE, which uses β ≫1 to encourage disentangled representations, this work explores β ≤1 for collaborative filtering.
- Neural networks for collaborative filtering: Compared with collaborative denoising autoencoders, VAEs use parameters that grow linearly with items rather than both users and items, reducing overfitting exposure.The cited comparison also notes that CDAE requires additional optimization for unseen users, although the supplied passage truncates that point.
- Neural networks for collaborative filtering: Neural-network methods using side information to address cold-start problems are complementary to this approach.
4 EMPIRICAL STUDY
The empirical study evaluates Mult-vaepr and Mult-dae across multiple implicit-feedback datasets, ranking metrics, baselines, likelihoods, and user-activity levels. Both proposed models perform strongly, with Mult-vaepr showing advantages over Mult-dae and the multinomial likelihood outperforming alternatives.
- The study uses MovieLens-20M, Netflix Prize, and Million Song Dataset after binarizing ratings or play counts into implicit feedback.
- Mult-vaepr achieves state-of-the-art results on three real-world datasets against linear, nonlinear, and neural-network baselines.
- Both Mult-vaepr and Mult-dae significantly outperform baselines across datasets and ranking metrics.The evaluation uses Recall@R and NDCG@R under strong generalization, with held-out users providing fold-in histories for representation learning.
- Mult-dae significantly outperforms ncf without pre-training on ML-1M and Pinterest, and improves over pre-trained ncf on Pinterest.
- The multinomial likelihood performs better than Gaussian and logistic likelihoods for Mult-vaepr and Mult-dae on ML-20M, with similar results on the other datasets.The likelihood choice is tuned separately for each model and likelihood.
- Mult-vaepr consistently improves recommendation performance for users with few clicks, while Mult-dae can outperform it among the most active users.The stronger prior assumption in Mult-vaepr may help when interactions are scarce but potentially hurt when users provide more data.
5 CONCLUSION
The paper extends VAEs to implicit-feedback collaborative filtering with a neural multinomial generative model and partial regularization. Mult-VAEpr and Mult-DAE perform competitively, while Mult-VAEpr significantly outperforms state-of-the-art baselines; the regularization trade-off and theoretical understanding remain open directions.
- The proposed VAE variant goes beyond the limited modeling capacity of linear factor models for implicit-feedback collaborative filtering.
- A neural generative model with multinomial likelihood is introduced and shown to be well suited to user-item implicit feedback.
- Mult-VAEpr partially regularizes the VAE using an additional parameter, with KL annealing providing an efficient tuning procedure.
- Mult-VAEpr and Mult-DAE provide competitive performance, with Mult-VAEpr significantly outperforming state-of-the-art baselines across several real-world datasets, including two neural-network approaches.
- Future work includes studying the trade-off controlled by β, developing theoretical insight into its effectiveness, and incorporating side information.