# Neural Conditional Probability for Uncertainty Quantification

arXiv: https://arxiv.org/abs/2407.01171 · HTML: https://mlsanity.com/paper/2407.01171/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 61 references that are in the map.
- First posted on arXiv 1 Jul 2024.

## Builds on (most cited first, 29 of 29)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Provable Guarantees for Self-Supervised Deep Learning with Spectral Contrastive Loss](https://mlsanity.com/paper/2106.04156/) (2021)
- [The Open Catalyst 2020 (OC20) Dataset and Community Challenges](https://mlsanity.com/paper/2010.09990/) (2020)
- [Learning Likelihoods with Conditional Normalizing Flows](https://mlsanity.com/paper/1912.00042/) (2019)
- [Conformal Prediction With Conditional Guarantees](https://mlsanity.com/paper/2305.12616/) (2023)
- [Distributional conformal prediction](https://mlsanity.com/paper/1909.07889/) (2019)
- [Towards Coherent Image Inpainting Using Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2304.03322/) (2023)
- [normflows: A PyTorch Package for Normalizing Flows](https://mlsanity.com/paper/2302.12014/) (2023)
- [Conditional Density Estimation with Neural Networks: Best Practices and Benchmarks](https://mlsanity.com/paper/1903.00954/) (2019)
- [Structured Output Learning with Conditional Generative Flows](https://mlsanity.com/paper/1905.13288/) (2019)
- [Converting High-Dimensional Regression to High-Dimensional Conditional Density Estimation](https://mlsanity.com/paper/1704.08095/) (2017)
- [SchNetPack 2.0: A neural network toolbox for atomistic machine learning](https://mlsanity.com/paper/2212.05517/) (2022)
- [Neural Methods for Point-wise Dependency Estimation](https://mlsanity.com/paper/2006.05553/) (2020)
- [Evading the curse of dimensionality in nonparametric density estimation with simplified vine copulas](https://mlsanity.com/paper/1503.03305/) (2015)
- [Learning invariant representations of time-homogeneous stochastic dynamical systems](https://mlsanity.com/paper/2307.09912/) (2023)
- [The Kernel Mixture Network: A Nonparametric Method for Conditional Density Estimation of Continuous Random Variables](https://mlsanity.com/paper/1705.07111/) (2017)
- [LinCDE: Conditional Density Estimation via Lindsey's Method](https://mlsanity.com/paper/2107.12713/) (2021)
- [Spectral Representation Learning for Conditional Moment Models](https://mlsanity.com/paper/2210.16525/) (2022)
- [RFCDE: Random Forests for Conditional Density Estimation](https://mlsanity.com/paper/1804.05753/) (2018)
- [Fast multivariate empirical cumulative distribution function with connection to kernel density estimation](https://mlsanity.com/paper/2005.03246/) (2020)
- [Regularised Canonical Correlation Analysis: graphical lasso, biplots and beyond](https://mlsanity.com/paper/2403.02979/) (2024)

## Built on by (most cited first, 14 of 14)

- [Self-Supervised Evolution Operator Learning for High-Dimensional Dynamical Systems](https://mlsanity.com/paper/2505.18671/) (2025)
- [Efficient Parametric SVD of Koopman Operator for Stochastic Dynamical Systems](https://mlsanity.com/paper/2507.07222/) (2025)
- [Demystifying Spectral Feature Learning for Instrumental Variable Regression](https://mlsanity.com/paper/2506.10899/) (2025)
- [Outcome-Aware Spectral Feature Learning for Instrumental Variable Regression](https://mlsanity.com/paper/2512.00919/) (2025)
- [CHyLL: Learning Continuous Neural Representations of Hybrid Systems](https://mlsanity.com/paper/2512.10117/) (2025)
- [Toward Scalable and Valid Conditional Independence Testing with Spectral Representations](https://mlsanity.com/paper/2512.19510/) (2025)
- [kooplearn: A Scikit-Learn Compatible Library of Algorithms for Evolution Operator Learning](https://mlsanity.com/paper/2512.21409/) (2025)
- [Revisiting Orbital Minimization Method for Neural Operator Decomposition](https://mlsanity.com/paper/2510.21952/) (2025)
- [Supervised Learning of Random Neural Architectures Structured by Latent Random Fields on Compact Boundaryless Multiply-Connected Manifolds](https://mlsanity.com/paper/2512.10407/) (2025)
- [Geometric Dictionary Learning of Dynamical Systems with Optimal Transport](https://mlsanity.com/paper/2605.18276/) (2026)
- [Score the Algebra, Not the Span: Dimension Reduction for Transfer Operator Models of Dynamical Systems](https://mlsanity.com/paper/2608.18918/) (2026)
- [Multi-Task Learning of Conditional Mean Operators: applications to dynamical systems and uncertainty quantification](https://mlsanity.com/paper/2609.35429/) (2026)
- [Learning Conditional Expectation Operators via Functional Newton Updates](https://mlsanity.com/paper/2609.35598/) (2026)
- [Langevin-Informed Transfer Learning: Replacing Target Samples by Black-Box Feedback](https://mlsanity.com/paper/2610.01522/) (2026)

## Abstract (arXiv)

We introduce Neural Conditional Probability (NCP), an operator-theoretic approach to learning conditional distributions with a focus on statistical inference tasks. NCP can be used to build conditional confidence regions and extract key statistics such as conditional quantiles, mean, and covariance. It offers streamlined learning via a single unconditional training phase, allowing efficient inference without the need for retraining even when conditioning changes. By leveraging the approximation capabilities of neural networks, NCP efficiently handles a wide variety of complex probability distributions. We provide theoretical guarantees that ensure both optimization consistency and statistical accuracy. In experiments, we show that NCP with a 2-hidden-layer network matches or outperforms leading methods. This demonstrates that a a minimalistic architecture with a theoretically grounded loss can achieve competitive results, even in the face of more complex architectures.