A Neural Process (NP) estimates a stochastic process implicitly defined with neural networks given a stream of data, rather than pre-specifying priors already known, such as Gaussian processes. An ideal NP would learn everything from data without any inductive biases, but in practice, we often restrict the class of stochastic processes for the ease of estimation. One such restriction is the use of a finite-dimensional latent variable accounting for the uncertainty in the functions drawn from NPs. Some recent works show that this can be improved with more "data-driven" source of uncertainty such as bootstrapping. In this work, we take a different approach based on the martingale posterior, a recently developed alternative to Bayesian inference. For the martingale posterior, instead of specifying prior-likelihood pairs, a predictive distribution for future data is specified. Under specific conditions on the predictive distribution, it can be shown that the uncertainty in the generated future data actually corresponds to the uncertainty of the implicitly defined Bayesian posteriors. Based on this result, instead of assuming any form of the latent variables, we equip a NP with a predictive distribution implicitly defined with neural networks and use the corresponding martingale posteriors as the source of uncertainty. The resulting model, which we name as Martingale Posterior Neural Process (MPNP), is demonstrated to outperform baselines on various tasks.

翻译：神经过程（NP）利用神经网络隐式定义随机过程，从数据流中估计而非预先指定已知的先验（如高斯过程）。理想NP应能无归纳偏置地从数据中学习一切，但实践中常因简化估计而限制随机过程类别。此类限制包括使用有限维潜变量来刻画NP生成函数的不确定性。近期研究表明，通过自助法等更"数据驱动"的不确定性来源可改进这一方法。本文基于鞅后验（贝叶斯推断的新近替代方案）另辟蹊径：鞅后验无需指定先验-似然对，而是定义未来数据的预测分布。在预测分布的特定条件下，可证明生成未来数据的不确定性恰好对应隐式定义贝叶斯后验的不确定性。基于此结论，我们摒弃任何形式的潜变量假设，为NP配备由神经网络隐式定义的预测分布，并将相应鞅后验作为不确定性来源。由此产生的模型——鞅后验神经过程（MPNP）——在多项任务中超越基线方法。