# Partially Observed Exchangeable Modeling

arXiv: https://arxiv.org/abs/2102.06083 · HTML: https://mlsanity.com/paper/2102.06083/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 48 references that are in the map.
- First posted on arXiv 11 Feb 2021.

## Builds on (most cited first, 24 of 24)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flows](https://mlsanity.com/paper/1906.12320/) (2019)
- [Conditional Neural Processes](https://mlsanity.com/paper/1807.01613/) (2018)
- [PCN: Point Completion Network](https://mlsanity.com/paper/1808.00671/) (2018)
- [YouTube-VOS: A Large-Scale Video Object Segmentation Benchmark](https://mlsanity.com/paper/1809.03327/) (2018)
- [Neural Processes](https://mlsanity.com/paper/1807.01622/) (2018)
- [Attentive Neural Processes](https://mlsanity.com/paper/1901.05761/) (2019)
- [Order Matters: Sequence to sequence for sets](https://mlsanity.com/paper/1511.06391/) (2015)
- [PU-Net: Point Cloud Upsampling Network](https://mlsanity.com/paper/1801.06761/) (2018)
- [Convolutional Conditional Neural Processes](https://mlsanity.com/paper/1910.13556/) (2019)
- [Towards a Neural Statistician](https://mlsanity.com/paper/1606.02185/) (2016)
- [Causal Structure Learning](https://mlsanity.com/paper/1706.09141/) (2017)
- [Variational Autoencoder with Arbitrary Conditioning](https://mlsanity.com/paper/1806.02382/) (2018)
- [Student-t Processes as Alternatives to Gaussian Processes](https://mlsanity.com/paper/1402.4306/) (2014)
- [Efficient Low Rank Tensor Ring Completion](https://mlsanity.com/paper/1707.08184/) (2017)
- [Flow Models for Arbitrary Conditional Likelihoods](https://mlsanity.com/paper/1909.06319/) (2019)
- [Exchangeable Neural ODE for Set Modeling](https://mlsanity.com/paper/2008.02676/) (2020)
- [Learning about an exponential amount of conditional distributions](https://mlsanity.com/paper/1902.08401/) (2019)
- [BRUNO: A Deep Recurrent Model for Exchangeable Data](https://mlsanity.com/paper/1802.07535/) (2018)
- [Energy-Based Processes for Exchangeable Data](https://mlsanity.com/paper/2003.07521/) (2020)
- [A Universal Marginalizer for Amortized Inference in Generative Models](https://mlsanity.com/paper/1711.00695/) (2017)

## Built on by (most cited first, 3 of 3)

- [Phoneme Hallucinator: One-shot Voice Conversion via Set Expansion](https://mlsanity.com/paper/2308.06382/) (2023)
- [Towards Cost Sensitive Decision Making](https://mlsanity.com/paper/2410.03892/) (2024)
- [IID Relaxation by Logical Expressivity: A Research Agenda for Fitting Logics to Neurosymbolic Requirements](https://mlsanity.com/paper/2404.19485/) (2024)

## Abstract (arXiv)

Modeling dependencies among features is fundamental for many machine learning tasks. Although there are often multiple related instances that may be leveraged to inform conditional dependencies, typical approaches only model conditional dependencies over individual instances. In this work, we propose a novel framework, partially observed exchangeable modeling (POEx) that takes in a set of related partially observed instances and infers the conditional distribution for the unobserved dimensions over multiple elements. Our approach jointly models the intra-instance (among features in a point) and inter-instance (among multiple points in a set) dependencies in data. POEx is a general framework that encompasses many existing tasks such as point cloud expansion and few-shot generation, as well as new tasks like few-shot imputation. Despite its generality, extensive empirical evaluations show that our model achieves state-of-the-art performance across a range of applications.