# Adaptive Conditional Quantile Neural Processes

arXiv: https://arxiv.org/abs/2305.18777 · HTML: https://mlsanity.com/paper/2305.18777/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 53 references that are in the map.
- First posted on arXiv 30 May 2023.

## Builds on (most cited first, 30 of 31)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Conditional Neural Processes](https://mlsanity.com/paper/1807.01613/) (2018)
- [Implicit Quantile Networks for Distributional Reinforcement Learning](https://mlsanity.com/paper/1806.06923/) (2018)
- [Neural Processes](https://mlsanity.com/paper/1807.01622/) (2018)
- [Attentive Neural Processes](https://mlsanity.com/paper/1901.05761/) (2019)
- [Convolutional Conditional Neural Processes](https://mlsanity.com/paper/1910.13556/) (2019)
- [Transformer Neural Processes: Uncertainty-Aware Meta Learning Via Sequence Modeling](https://mlsanity.com/paper/2207.04179/) (2022)
- [Learning in Implicit Generative Models](https://mlsanity.com/paper/1610.03483/) (2016)
- [On Contrastive Learning for Likelihood-free Inference](https://mlsanity.com/paper/2002.03712/) (2020)
- [Meta-Learning Stationary Stochastic Process Prediction with Convolutional Neural Processes](https://mlsanity.com/paper/2007.01332/) (2020)
- [Variational Implicit Processes](https://mlsanity.com/paper/1806.02390/) (2018)
- [Bootstrapping Neural Processes](https://mlsanity.com/paper/2008.02956/) (2020)
- [The Gaussian Neural Process](https://mlsanity.com/paper/2101.03606/) (2021)
- [Doubly Stochastic Variational Inference for Neural Processes with Hierarchical Latent Variables](https://mlsanity.com/paper/2008.09469/) (2020)
- [Equivariant Learning of Stochastic Fields: Gaussian Processes and Steerable Conditional Neural Processes](https://mlsanity.com/paper/2011.12916/) (2020)
- [Latent Bottlenecked Attentive Neural Processes](https://mlsanity.com/paper/2211.08458/) (2022)
- [Practical Conditional Neural Processes Via Tractable Dependent Predictions](https://mlsanity.com/paper/2203.08775/) (2022)
- [Function Contrastive Learning of Transferable Meta-Representations](https://mlsanity.com/paper/2010.07093/) (2020)
- [Neural Processes with Stochastic Attention: Paying more attention to the context dataset](https://mlsanity.com/paper/2204.05449/) (2022)
- [Function-space Inference with Sparse Implicit Processes](https://mlsanity.com/paper/2110.07618/) (2021)
- [On Contrastive Representations of Stochastic Processes](https://mlsanity.com/paper/2106.10052/) (2021)
- [Deep Non-Crossing Quantiles through the Partial Derivative](https://mlsanity.com/paper/2201.12848/) (2022)
- [Fast Nonlinear Vector Quantile Regression](https://mlsanity.com/paper/2205.14977/) (2022)
- [Versatile Neural Processes for Learning Implicit Neural Representations](https://mlsanity.com/paper/2301.08883/) (2023)
- [Energy-Based Processes for Exchangeable Data](https://mlsanity.com/paper/2003.07521/) (2020)
- [Modelling heterogeneous distributions with an Uncountable Mixture of Asymmetric Laplacians](https://mlsanity.com/paper/1910.12288/) (2019)
- [Nonparametric modal regression](https://mlsanity.com/paper/1412.1716/) (2014)

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

- [Spectral Convolutional Conditional Neural Processes](https://mlsanity.com/paper/2404.13182/) (2024)
- [Computational Identifiability](https://mlsanity.com/paper/2606.19361/) (2026)
- [Revisiting Neural Processes via Fourier Transform and Volterra Series](https://mlsanity.com/paper/2606.01172/) (2026)

## Abstract (arXiv)

Neural processes are a family of probabilistic models that inherit the flexibility of neural networks to parameterize stochastic processes. Despite providing well-calibrated predictions, especially in regression problems, and quick adaptation to new tasks, the Gaussian assumption that is commonly used to represent the predictive likelihood fails to capture more complicated distributions such as multimodal ones. To overcome this limitation, we propose Conditional Quantile Neural Processes (CQNPs), a new member of the neural processes family, which exploits the attractive properties of quantile regression in modeling the distributions irrespective of their form. By introducing an extension of quantile regression where the model learns to focus on estimating informative quantiles, we show that the sampling efficiency and prediction accuracy can be further enhanced. Our experiments with real and synthetic datasets demonstrate substantial improvements in predictive performance compared to the baselines, and better modeling of heterogeneous distributions' characteristics such as multimodality.