# Learning Exceptional Subgroups by End-to-End Maximizing KL-divergence

arXiv: https://arxiv.org/abs/2402.12930 · HTML: https://mlsanity.com/paper/2402.12930/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 44 references that are in the map.
- First posted on arXiv 20 Feb 2024.

## Builds on (most cited first, 15 of 15)

- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Domino: Discovering Systematic Errors with Cross-Modal Embeddings](https://mlsanity.com/paper/2203.14960/) (2022)
- [Deep Neural Decision Trees](https://mlsanity.com/paper/1806.06988/) (2018)
- [Automated Data Slicing for Model Validation:A Big data - AI Integration Approach](https://mlsanity.com/paper/1807.06068/) (2018)
- [The Spotlight: A General Method for Discovering Systematic Errors in Deep Learning Models](https://mlsanity.com/paper/2107.00758/) (2021)
- [Scalable Rule-Based Representation Learning for Interpretable Classification](https://mlsanity.com/paper/2109.15103/) (2021)
- [Learning Accurate and Interpretable Decision Rule Sets from Neural Networks](https://mlsanity.com/paper/2103.02826/) (2021)
- [Transparent Classification with Multilayer Logical Perceptrons and Random Binarization](https://mlsanity.com/paper/1912.04695/) (2019)
- [Learning Neural Set Functions Under the Optimal Subset Oracle](https://mlsanity.com/paper/2203.01693/) (2022)
- [Identifying Consistent Statements about Numerical Data with Dispersion-Corrected Subgroup Discovery](https://mlsanity.com/paper/1701.07696/) (2017)
- [Data-Driven Subgroup Identification for Linear Regression](https://mlsanity.com/paper/2305.00195/) (2023)
- [Finding Interpretable Class-Specific Patterns through Efficient Neural Search](https://mlsanity.com/paper/2312.04311/) (2023)

## Built on by (most cited first, 5 of 5)

- [Compact Rule-Based Classifier Learning via Gradient Descent](https://mlsanity.com/paper/2502.01375/) (2025)
- [Neuro-Symbolic Rule Lists](https://mlsanity.com/paper/2411.06428/) (2024)
- [Subgroup Discovery with the Cox Model](https://mlsanity.com/paper/2512.20762/) (2025)
- [Discovering Subgroups with Exceptional Survival Characteristics](https://mlsanity.com/paper/2602.22179/) (2026)
- [Differential Subgroup Discovery: Characterizing Where Two Populations Differ, and Why](https://mlsanity.com/paper/2604.27741/) (2026)

## Abstract (arXiv)

Finding and describing sub-populations that are exceptional regarding a target property has important applications in many scientific disciplines, from identifying disadvantaged demographic groups in census data to finding conductive molecules within gold nanoparticles. Current approaches to finding such subgroups require pre-discretized predictive variables, do not permit non-trivial target distributions, do not scale to large datasets, and struggle to find diverse results. To address these limitations, we propose Syflow, an end-to-end optimizable approach in which we leverage normalizing flows to model arbitrary target distributions, and introduce a novel neural layer that results in easily interpretable subgroup descriptions. We demonstrate on synthetic and real-world data, including a case study, that Syflow reliably finds highly exceptional subgroups accompanied by insightful descriptions.