# Practical Conditional Neural Processes Via Tractable Dependent Predictions

arXiv: https://arxiv.org/abs/2203.08775 · HTML: https://mlsanity.com/paper/2203.08775/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 51 references that are in the map.
- First posted on arXiv 16 Mar 2022.

## Builds on (most cited first, 21 of 21)

- [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)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Xception: Deep Learning with Depthwise Separable Convolutions](https://mlsanity.com/paper/1610.02357/) (2016)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Conditional Neural Processes](https://mlsanity.com/paper/1807.01613/) (2018)
- [Meta-Dataset: A Dataset of Datasets for Learning to Learn from Few Examples](https://mlsanity.com/paper/1903.03096/) (2019)
- [Attentive Neural Processes](https://mlsanity.com/paper/1901.05761/) (2019)
- [Convolutional Conditional Neural Processes](https://mlsanity.com/paper/1910.13556/) (2019)
- [DeepSD: Generating High Resolution Climate Change Projections through Single Image Super-Resolution](https://mlsanity.com/paper/1703.03126/) (2017)
- [Meta-Learning Stationary Stochastic Process Prediction with Convolutional Neural Processes](https://mlsanity.com/paper/2007.01332/) (2020)
- [Equivariant Learning of Stochastic Fields: Gaussian Processes and Steerable Conditional Neural Processes](https://mlsanity.com/paper/2011.12916/) (2020)
- [Convolutional conditional neural processes for local climate downscaling](https://mlsanity.com/paper/2101.07950/) (2021)
- [Scalable Exact Inference in Multi-Output Gaussian Processes](https://mlsanity.com/paper/1911.06287/) (2019)
- [Intercomparison of Machine Learning Methods for Statistical Downscaling: The Case of Daily and Extreme Precipitation](https://mlsanity.com/paper/1702.04018/) (2017)
- [Group Equivariant Conditional Neural Processes](https://mlsanity.com/paper/2102.08759/) (2021)
- [Quantifying Uncertainty in Discrete-Continuous and Skewed Data with Bayesian Deep Learning](https://mlsanity.com/paper/1802.04742/) (2018)
- [Bayesian Meta-Learning for the Few-Shot Setting via Deep Kernels](https://mlsanity.com/paper/1910.05199/) (2019)
- [GP-ConvCNP: Better Generalization for Convolutional Conditional Neural Processes on Time Series Data](https://mlsanity.com/paper/2106.04967/) (2021)

## Built on by (most cited first, 25 of 25)

- [ClimaX: A foundation model for weather and climate](https://mlsanity.com/paper/2301.10343/) (2023)
- [Autoregressive Conditional Neural Processes](https://mlsanity.com/paper/2303.14468/) (2023)
- [Spectral Diffusion Processes](https://mlsanity.com/paper/2209.14125/) (2022)
- [The Neural Process Family: Survey, Applications and Perspectives](https://mlsanity.com/paper/2209.00517/) (2022)
- [Amortized Probabilistic Conditioning for Optimization, Simulation and Inference](https://mlsanity.com/paper/2410.15320/) (2024)
- [Amortized Bayesian Experimental Design for Decision-Making](https://mlsanity.com/paper/2411.02064/) (2024)
- [Environmental Sensor Placement with Convolutional Gaussian Neural Processes](https://mlsanity.com/paper/2211.10381/) (2022)
- [Practical Equivariances via Relational Conditional Neural Processes](https://mlsanity.com/paper/2306.10915/) (2023)
- [Translation Equivariant Transformer Neural Processes](https://mlsanity.com/paper/2406.12409/) (2024)
- [Random Grid Neural Processes for Parametric Partial Differential Equations](https://mlsanity.com/paper/2301.11040/) (2023)
- [Episodic Multi-Task Learning with Heterogeneous Neural Processes](https://mlsanity.com/paper/2310.18713/) (2023)
- [PABBO: Preferential Amortized Black-Box Optimization](https://mlsanity.com/paper/2503.00924/) (2025)
- [Dimension Agnostic Neural Processes](https://mlsanity.com/paper/2502.20661/) (2025)
- [Convolutional Neural Processes for Inpainting Satellite Images](https://mlsanity.com/paper/2205.12407/) (2022)
- [Spectral Convolutional Conditional Neural Processes](https://mlsanity.com/paper/2404.13182/) (2024)
- [Efficient Autoregressive Inference for Transformer Probabilistic Models](https://mlsanity.com/paper/2510.09477/) (2025)
- [Adaptive Conditional Quantile Neural Processes](https://mlsanity.com/paper/2305.18777/) (2023)
- [Meta-Statistical Learning: Supervised Learning of Statistical Estimators](https://mlsanity.com/paper/2502.12088/) (2025)
- [Noise-Aware Differentially Private Regression via Meta-Learning](https://mlsanity.com/paper/2406.08569/) (2024)
- [Sparse Gaussian Neural Processes](https://mlsanity.com/paper/2504.01650/) (2025)
- [Adversarially Contrastive Estimation of Conditional Neural Processes](https://mlsanity.com/paper/2303.13004/) (2023)
- [R'enyi Neural Processes](https://mlsanity.com/paper/2405.15991/) (2024)
- [MIST: Mutual Information Estimation Via Supervised Training](https://mlsanity.com/paper/2511.18945/) (2025)
- [Gaussian Mixture Copula Processes for Irregular Time Series](https://mlsanity.com/paper/2605.23632/) (2026)
- [Revisiting Neural Processes via Fourier Transform and Volterra Series](https://mlsanity.com/paper/2606.01172/) (2026)

## Abstract (arXiv)

Conditional Neural Processes (CNPs; Garnelo et al., 2018a) are meta-learning models which leverage the flexibility of deep learning to produce well-calibrated predictions and naturally handle off-the-grid and missing data. CNPs scale to large datasets and train with ease. Due to these features, CNPs appear well-suited to tasks from environmental sciences or healthcare. Unfortunately, CNPs do not produce correlated predictions, making them fundamentally inappropriate for many estimation and decision making tasks. Predicting heat waves or floods, for example, requires modelling dependencies in temperature or precipitation over time and space. Existing approaches which model output dependencies, such as Neural Processes (NPs; Garnelo et al., 2018b) or the FullConvGNP (Bruinsma et al., 2021), are either complicated to train or prohibitively expensive. What is needed is an approach which provides dependent predictions, but is simple to train and computationally tractable. In this work, we present a new class of Neural Process models that make correlated predictions and support exact maximum likelihood training that is simple and scalable. We extend the proposed models by using invertible output transformations, to capture non-Gaussian output distributions. Our models can be used in downstream estimation tasks which require dependent function samples. By accounting for output dependencies, our models show improved predictive performance on a range of experiments with synthetic and real data.