# An efficient manifold density estimator for all recommendation systems

arXiv: https://arxiv.org/abs/2006.01894 · HTML: https://mlsanity.com/paper/2006.01894/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jun 2020.

## Built on by (most cited first, 8 of 8)

- [Does a Technique for Building Multimodal Representation Matter? -- Comparative Analysis](https://mlsanity.com/paper/2206.06367/) (2022)
- [From Variability to Stability: Advancing RecSys Benchmarking Practices](https://mlsanity.com/paper/2402.09766/) (2024)
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- [SINCERE: Sequential Interaction Networks representation learning on Co-Evolving RiEmannian manifolds](https://mlsanity.com/paper/2305.03883/) (2023)
- [Synerise at RecSys 2021: Twitter user engagement prediction with a fast neural model](https://mlsanity.com/paper/2109.12985/) (2021)
- [Modeling Multi-Destination Trips with Sketch-Based Model](https://mlsanity.com/paper/2102.11252/) (2021)
- [Predicting Tweet Engagement with Graph Neural Networks](https://mlsanity.com/paper/2305.10103/) (2023)
- [T-EMDE: Sketching-based global similarity for cross-modal retrieval](https://mlsanity.com/paper/2105.04242/) (2021)

## Abstract (arXiv)

Many unsupervised representation learning methods belong to the class of similarity learning models. While various modality-specific approaches exist for different types of data, a core property of many methods is that representations of similar inputs are close under some similarity function. We propose EMDE (Efficient Manifold Density Estimator) - a framework utilizing arbitrary vector representations with the property of local similarity to succinctly represent smooth probability densities on Riemannian manifolds. Our approximate representation has the desirable properties of being fixed-size and having simple additive compositionality, thus being especially amenable to treatment with neural networks - both as input and output format, producing efficient conditional estimators. We generalize and reformulate the problem of multi-modal recommendations as conditional, weighted density estimation on manifolds. Our approach allows for trivial inclusion of multiple interaction types, modalities of data as well as interaction strengths for any recommendation setting. Applying EMDE to both top-k and session-based recommendation settings, we establish new state-of-the-art results on multiple open datasets in both uni-modal and multi-modal settings.