# Training Normalizing Flows from Dependent Data

arXiv: https://arxiv.org/abs/2209.14933 · HTML: https://mlsanity.com/paper/2209.14933/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 43 references that are in the map.
- First posted on arXiv 29 Sep 2022.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Assessing Generative Models via Precision and Recall](https://mlsanity.com/paper/1806.00035/) (2018)
- [Deep Structural Causal Models for Tractable Counterfactual Inference](https://mlsanity.com/paper/2006.06485/) (2020)
- [FedGAN: Federated Generative Adversarial Networks for Distributed Data](https://mlsanity.com/paper/2006.07228/) (2020)
- [Generative Models for Effective ML on Private, Decentralized Datasets](https://mlsanity.com/paper/1911.06679/) (2019)
- [Semi-Supervised Learning with Normalizing Flows](https://mlsanity.com/paper/1912.13025/) (2019)
- [SurVAE Flows: Surjections to Bridge the Gap between VAEs and Flows](https://mlsanity.com/paper/2007.02731/) (2020)
- [Understanding Anomaly Detection with Deep Invertible Networks through Hierarchies of Distributions and Features](https://mlsanity.com/paper/2006.10848/) (2020)
- [Normalizing Flows for Knockoff-free Controlled Feature Selection](https://mlsanity.com/paper/2106.01528/) (2021)

## Built on by (most cited first, 1 of 1)

- [Kernelised Normalising Flows](https://mlsanity.com/paper/2307.14839/) (2023)

## Abstract (arXiv)

Normalizing flows are powerful non-parametric statistical models that function as a hybrid between density estimators and generative models. Current learning algorithms for normalizing flows assume that data points are sampled independently, an assumption that is frequently violated in practice, which may lead to erroneous density estimation and data generation. We propose a likelihood objective of normalizing flows incorporating dependencies between the data points, for which we derive a flexible and efficient learning algorithm suitable for different dependency structures. We show that respecting dependencies between observations can improve empirical results on both synthetic and real-world data, and leads to higher statistical power in a downstream application to genome-wide association studies.