# Bootstrapping Neural Processes

arXiv: https://arxiv.org/abs/2008.02956 · HTML: https://mlsanity.com/paper/2008.02956/

## Key facts

- Cited by 40 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Aug 2020.

## Built on by (most cited first, 30 of 40)

- [Transformer Neural Processes: Uncertainty-Aware Meta Learning Via Sequence Modeling](https://mlsanity.com/paper/2207.04179/) (2022)
- [Latent Bottlenecked Attentive Neural Processes](https://mlsanity.com/paper/2211.08458/) (2022)
- [NP-Match: When Neural Processes meet Semi-Supervised Learning](https://mlsanity.com/paper/2207.01066/) (2022)
- [The Neural Process Family: Survey, Applications and Perspectives](https://mlsanity.com/paper/2209.00517/) (2022)
- [Affective Processes: stochastic modelling of temporal context for emotion and facial expression recognition](https://mlsanity.com/paper/2103.13372/) (2021)
- [Neural Processes with Stochastic Attention: Paying more attention to the context dataset](https://mlsanity.com/paper/2204.05449/) (2022)
- [Martingale Posterior Neural Processes](https://mlsanity.com/paper/2304.09431/) (2023)
- [Stochastic Optimal Control for Diffusion Bridges in Function Spaces](https://mlsanity.com/paper/2405.20630/) (2024)
- [Versatile Neural Processes for Learning Implicit Neural Representations](https://mlsanity.com/paper/2301.08883/) (2023)
- [Inter-Domain Mixup for Semi-Supervised Domain Adaptation](https://mlsanity.com/paper/2401.11453/) (2024)
- [Memory Efficient Neural Processes via Constant Memory Attention Block](https://mlsanity.com/paper/2305.14567/) (2023)
- [Bridge the Inference Gaps of Neural Processes via Expectation Maximization](https://mlsanity.com/paper/2501.03264/) (2025)
- [Semi-Parametric Inducing Point Networks and Neural Processes](https://mlsanity.com/paper/2205.11718/) (2022)
- [Flow Matching Neural Processes](https://mlsanity.com/paper/2512.23853/) (2025)
- [NP-SemiSeg: When Neural Processes meet Semi-Supervised Semantic Segmentation](https://mlsanity.com/paper/2308.02866/) (2023)
- [Dimension Agnostic Neural Processes](https://mlsanity.com/paper/2502.20661/) (2025)
- [NIERT: Accurate Numerical Interpolation through Unifying Scattered Data Representations using Transformer Encoder](https://mlsanity.com/paper/2209.09078/) (2022)
- [Entity Aware Modelling: A Survey](https://mlsanity.com/paper/2302.08406/) (2023)
- [Theoretical Investigations and Practical Enhancements on Tail Task Risk Minimization in Meta Learning](https://mlsanity.com/paper/2410.22788/) (2024)
- [Compositional Law Parsing with Latent Random Functions](https://mlsanity.com/paper/2209.09115/) (2022)
- [Adaptive Conditional Quantile Neural Processes](https://mlsanity.com/paper/2305.18777/) (2023)
- [Real-time Adaptation for Condition Monitoring Signal Prediction using Label-aware Neural Processes](https://mlsanity.com/paper/2403.16377/) (2024)
- [Distance-informed Neural Processes](https://mlsanity.com/paper/2508.18903/) (2025)
- [Taylorformer: Probabilistic Modelling for Random Processes including Time Series](https://mlsanity.com/paper/2305.19141/) (2023)
- [Exploiting Inferential Structure in Neural Processes](https://mlsanity.com/paper/2306.15169/) (2023)
- [Tree Cross Attention](https://mlsanity.com/paper/2309.17388/) (2023)
- [Probabilistic Interactive 3D Segmentation with Hierarchical Neural Processes](https://mlsanity.com/paper/2505.01726/) (2025)
- [NP-Match: Towards a New Probabilistic Model for Semi-Supervised Learning](https://mlsanity.com/paper/2301.13569/) (2023)
- [Constant Memory Attention Block](https://mlsanity.com/paper/2306.12599/) (2023)
- [R'enyi Neural Processes](https://mlsanity.com/paper/2405.15991/) (2024)

## Abstract (arXiv)

Unlike in the traditional statistical modeling for which a user typically hand-specify a prior, Neural Processes (NPs) implicitly define a broad class of stochastic processes with neural networks. Given a data stream, NP learns a stochastic process that best describes the data. While this "data-driven" way of learning stochastic processes has proven to handle various types of data, NPs still rely on an assumption that uncertainty in stochastic processes is modeled by a single latent variable, which potentially limits the flexibility. To this end, we propose the Boostrapping Neural Process (BNP), a novel extension of the NP family using the bootstrap. The bootstrap is a classical data-driven technique for estimating uncertainty, which allows BNP to learn the stochasticity in NPs without assuming a particular form. We demonstrate the efficacy of BNP on various types of data and its robustness in the presence of model-data mismatch.