# Transformation Autoregressive Networks

arXiv: https://arxiv.org/abs/1801.09819 · HTML: https://mlsanity.com/paper/1801.09819/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jan 2018.

## Built on by (most cited first, 27 of 27)

- [Diffusion Normalizing Flow](https://mlsanity.com/paper/2110.07579/) (2021)
- [Copula Flows for Synthetic Data Generation](https://mlsanity.com/paper/2101.00598/) (2021)
- [Invertible Tabular GANs: Killing Two Birds with OneStone for Tabular Data Synthesis](https://mlsanity.com/paper/2202.03636/) (2022)
- [Arbitrary Conditional Distributions with Energy](https://mlsanity.com/paper/2102.04426/) (2021)
- [Multi-scale Attention Flow for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2205.07493/) (2022)
- [Acquisition Conditioned Oracle for Nongreedy Active Feature Acquisition](https://mlsanity.com/paper/2302.13960/) (2023)
- [PU-Flow: a Point Cloud Upsampling Network with Normalizing Flows](https://mlsanity.com/paper/2107.05893/) (2021)
- [Sparse Flows: Pruning Continuous-depth Models](https://mlsanity.com/paper/2106.12718/) (2021)
- [Marginal Tail-Adaptive Normalizing Flows](https://mlsanity.com/paper/2206.10311/) (2022)
- [Flexible Tails for Normalizing Flows](https://mlsanity.com/paper/2406.16971/) (2024)
- [Differentially Private Normalizing Flows for Privacy-Preserving Density Estimation](https://mlsanity.com/paper/2103.14068/) (2021)
- [Transformer Neural Autoregressive Flows](https://mlsanity.com/paper/2401.01855/) (2024)
- [Marginalizable Density Models](https://mlsanity.com/paper/2106.04741/) (2021)
- [Funnels: Exact maximum likelihood with dimensionality reduction](https://mlsanity.com/paper/2112.08069/) (2021)
- [Flow-based Spatio-Temporal Structured Prediction of Motion Dynamics](https://mlsanity.com/paper/2104.04391/) (2021)
- [AdaCat: Adaptive Categorical Discretization for Autoregressive Models](https://mlsanity.com/paper/2208.02246/) (2022)
- [Generative Models for 3D Point Clouds](https://mlsanity.com/paper/2302.13408/) (2023)
- [Distribution Guided Active Feature Acquisition](https://mlsanity.com/paper/2410.03915/) (2024)
- [Robotic Manipulation via Imitation Learning: Taxonomy, Evolution, Benchmark, and Challenges](https://mlsanity.com/paper/2508.17449/) (2025)
- [Neural Inverse Transform Sampler](https://mlsanity.com/paper/2206.11172/) (2022)
- [Flexible Tails for Normalising Flows, with Application to the Modelling of Financial Return Data](https://mlsanity.com/paper/2311.00580/) (2023)
- [TERM Model: Tensor Ring Mixture Model for Density Estimation](https://mlsanity.com/paper/2312.08075/) (2023)
- [ELF: Exact-Lipschitz Based Universal Density Approximator Flow](https://mlsanity.com/paper/2112.06997/) (2021)
- [Normalizing Flow with Variational Latent Representation](https://mlsanity.com/paper/2211.11638/) (2022)
- [Sinusoidal Flow: A Fast Invertible Autoregressive Flow](https://mlsanity.com/paper/2110.13344/) (2021)
- [Are Deep Sequence Classifiers Good at Non-Trivial Generalization?](https://mlsanity.com/paper/2210.13082/) (2022)
- [Variational Polya Tree](https://mlsanity.com/paper/2510.22651/) (2025)

## Abstract (arXiv)

The fundamental task of general density estimation p(x) has been of keen interest to machine learning. In this work, we attempt to systematically characterize methods for density estimation. Broadly speaking, most of the existing methods can be categorized into either using: textita) autoregressive models to estimate the conditional factors of the chain rule, p(xi, |, xi-1, ldots); or textitb) non-linear transformations of variables of a simple base distribution. Based on the study of the characteristics of these categories, we propose multiple novel methods for each category. For example we proposed RNN based transformations to model non-Markovian dependencies. Further, through a comprehensive study over both real world and synthetic data, we show for that jointly leveraging transformations of variables and autoregressive conditional models, results in a considerable improvement in performance. We illustrate the use of our models in outlier detection and image modeling. Finally we introduce a novel data driven framework for learning a family of distributions.