mlsanityData to 7 Oct 2026

Autoregressive Quantile Flows for Predictive Uncertainty Estimation

arXiv 2112.04643 ↗First posted 9 Dec 2021cs.LGcited by 15

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Abstract (arXiv)

Numerous applications of machine learning involve representing probability distributions over high-dimensional data. We propose autoregressive quantile flows, a flexible class of normalizing flow models trained using a novel objective based on proper scoring rules. Our objective does not require calculating computationally expensive determinants of Jacobians during training and supports new types of neural architectures, such as neural autoregressive flows from which it is easy to sample. We leverage these models in quantile flow regression, an approach that parameterizes predictive conditional distributions with flows, resulting in improved probabilistic predictions on tasks such as time series forecasting and object detection. Our novel objective functions and neural flow parameterizations also yield improvements on popular generation and density estimation tasks, and represent a step beyond maximum likelihood learning of flows.

Key facts. Cited by 15 papers in the map (data through 7 Oct 2026). Builds on 27 of its 47 references that are in the map. First posted on arXiv 9 Dec 2021.

Builds on

27 of 47 references.

References · 27

  1. 2018MobileNetV2: Inverted Residuals and Linear Bottleneckscited by 4,773
  2. 2015Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learningcited by 4,416
  3. 2015Variational Inference with Normalizing Flowscited by 2,161
  4. 2018Glow: Generative Flow with Invertible 1x1 Convolutionscited by 1,539
  5. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,315
  6. 2017DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networkscited by 1,004
  7. 2018Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Modelscited by 748
  8. 2017Masked Autoregressive Flow for Density Estimationcited by 680
  9. 2016Improving Variational Inference with Inverse Autoregressive Flowcited by 636
  10. 2019Neural Spline Flowscited by 590
  11. 2017Distributional Reinforcement Learning with Quantile Regressioncited by 464
  12. 2018Accurate Uncertainties for Deep Learning Using Calibrated Regressioncited by 417
15 more
  1. 2015Autoencoding beyond pixels using a learned similarity metriccited by 407
  2. 2018Implicit Quantile Networks for Distributional Reinforcement Learningcited by 362
  3. 2017A Multi-Horizon Quantile Recurrent Forecastercited by 211
  4. 2018Neural Autoregressive Flowscited by 207
  5. 2018Sample-Efficient Reinforcement Learning with Stochastic Ensemble Value Expansioncited by 167
  6. 2018Neural Importance Samplingcited by 154
  7. 2018Bounding Box Regression with Uncertainty for Accurate Object Detectioncited by 143
  8. 2019Unconstrained Monotonic Neural Networkscited by 91
  9. 2019Block Neural Autoregressive Flowcited by 62
  10. 2019Sum-of-Squares Polynomial Flowcited by 62
  11. 2019Hybrid Models with Deep and Invertible Featurescited by 41
  12. 2020Invertible Generative Modeling using Linear Rational Splinescited by 39
  13. 2019Temporal FiLM: Capturing Long-Range Sequence Dependencies with Feature-Wise Modulationscited by 36
  14. 2015On-the-Job Learning with Bayesian Decision Theorycited by 3
  15. 2018Adversarial Constraint Learning for Structured Predictioncited by 3

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Citing papers per year: 2021: 2; 2022: 2; 2023: 2; 2024: 8; 2025: 1.

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  1. 2024Simple and Effective Masked Diffusion Language Modelscited by 800
  2. 2025Block Diffusion: Interpolating Between Autoregressive and Diffusion Language Modelscited by 385
  3. 2023Diffusion Models With Learned Adaptive Noisecited by 50
  4. 2021Calibrated and Sharp Uncertainties in Deep Learning via Density Estimationcited by 33
  5. 2024DySLIM: Dynamics Stable Learning by Invariant Measure for Chaotic Systemscited by 29
  6. 2024Uncertainty Quantification via Stable Distribution Propagationcited by 10
  7. 2024Quantifying Aleatoric Uncertainty of the Treatment Effect: A Novel Orthogonal Learnercited by 10
  8. 2022Semi-Autoregressive Energy Flows: Exploring Likelihood-Free Training of Normalizing Flowscited by 9
  9. 2022Estimating Regression Predictive Distributions with Sample Networkscited by 4
  10. 2021Dynamic Combination of Heterogeneous Models for Hierarchical Time Seriescited by 3
  11. 2024Denoising Diffusion Variational Inference: Diffusion Models as Expressive Variational Posteriorscited by 2
  12. 2023On Learning the Tail Quantiles of Driving Behavior Distributions via Quantile Regression and Flowscited by 1
3 more
  1. 2024Probabilistic Forecasting of Irregular Time Series via Conditional Flowscited by 1
  2. 2024Model-Free Local Recalibration of Neural Networkscited by 1
  3. 2024Positional Encoder Graph Quantile Neural Networks for Geographic Datacited by 1