# Probabilistic Residual Learning for Online Recommendations

arXiv: https://arxiv.org/abs/2607.20863 · HTML: https://mlsanity.com/paper/2607.20863/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 50 references that are in the map.
- First posted on arXiv 23 Jul 2026.

## Builds on (most cited first, 28 of 28)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Self-Attentive Sequential Recommendation](https://mlsanity.com/paper/1808.09781/) (2018)
- [LightGCN: Simplifying and Powering Graph Convolution Network for Recommendation](https://mlsanity.com/paper/2002.02126/) (2020)
- [Neural Collaborative Filtering](https://mlsanity.com/paper/1708.05031/) (2017)
- [Deep Learning Recommendation Model for Personalization and Recommendation Systems](https://mlsanity.com/paper/1906.00091/) (2019)
- [Session-based Recommendation with Graph Neural Networks](https://mlsanity.com/paper/1811.00855/) (2018)
- [Bias and Debias in Recommender System: A Survey and Future Directions](https://mlsanity.com/paper/2010.03240/) (2020)
- [Towards Universal Sequence Representation Learning for Recommender Systems](https://mlsanity.com/paper/2206.05941/) (2022)
- [Causal Intervention for Leveraging Popularity Bias in Recommendation](https://mlsanity.com/paper/2105.06067/) (2021)
- [Collaborative Deep Learning for Recommender Systems](https://mlsanity.com/paper/1409.2944/) (2014)
- [CoNet: Collaborative Cross Networks for Cross-Domain Recommendation](https://mlsanity.com/paper/1804.06769/) (2018)
- [Continuously Indexed Domain Adaptation](https://mlsanity.com/paper/2007.01807/) (2020)
- [DDTCDR: Deep Dual Transfer Cross Domain Recommendation](https://mlsanity.com/paper/1910.05189/) (2019)
- [Towards Bayesian Deep Learning: A Framework and Some Existing Methods](https://mlsanity.com/paper/1608.06884/) (2016)
- [CauseRec: Counterfactual User Sequence Synthesis for Sequential Recommendation](https://mlsanity.com/paper/2109.05261/) (2021)
- [A Unified Approach to Domain Incremental Learning with Memory: Theory and Algorithm](https://mlsanity.com/paper/2310.12244/) (2023)
- [From Zero-Shot Learning to Cold-Start Recommendation](https://mlsanity.com/paper/1906.08511/) (2019)
- [Causal Discovery from Incomplete Data: A Deep Learning Approach](https://mlsanity.com/paper/2001.05343/) (2020)
- [Self-Interpretable Time Series Prediction with Counterfactual Explanations](https://mlsanity.com/paper/2306.06024/) (2023)
- [Cross-Market Product Recommendation](https://mlsanity.com/paper/2109.05929/) (2021)
- [Domain-Indexing Variational Bayes: Interpretable Domain Index for Domain Adaptation](https://mlsanity.com/paper/2302.02561/) (2023)
- [Learning to Transfer Graph Embeddings for Inductive Graph based Recommendation](https://mlsanity.com/paper/2005.11724/) (2020)
- [A Heterogeneous Information Network based Cross Domain Insurance Recommendation System for Cold Start Users](https://mlsanity.com/paper/2007.15293/) (2020)
- [Content-aware Neural Hashing for Cold-start Recommendation](https://mlsanity.com/paper/2006.00617/) (2020)
- [Collaborative Recurrent Autoencoder: Recommend while Learning to Fill in the Blanks](https://mlsanity.com/paper/1611.00454/) (2016)
- [Joint Training Capsule Network for Cold Start Recommendation](https://mlsanity.com/paper/2005.11467/) (2020)

## Abstract (arXiv)

Modern recommender systems are typically based on deep learning (DL) models, where a dense encoder learns representations of users and items. As a result, these systems often suffer from the black-box nature and computational complexity of the underlying models, making it difficult to systematically enhance their recommendation capabilities. To address this problem, we propose Probabilistic Residual Learning (PRL), a causal Bayesian recommendation model that models the residual between ground-truth and base predictions, enabling targeted refinement of existing systems. Specifically, PRL (1) probabilistically groups users for localized residual modeling, (2) models domain-level confounders that influence user and item representations, and (3) aggregates cluster-specific residual predictions over the confounders using do-calculus. Experiments demonstrate that our plug-and-play PRL is compatible with various base deep learning recommender systems, improving their performance while automatically discovering meaningful user clusters.