Conditional Neural Processes~(CNPs) formulate distributions over functions and generate function observations with exact conditional likelihoods. CNPs, however, have limited expressivity for high-dimensional observations, since their predictive distribution is factorized into a product of unconstrained (typically) Gaussian outputs. Previously, this could be handled using latent variables or autoregressive likelihood, but at the expense of intractable training and quadratically increased complexity. Instead, we propose calibrating CNPs with an adversarial training scheme besides regular maximum likelihood estimates. Specifically, we train an energy-based model (EBM) with noise contrastive estimation, which enforces EBM to identify true observations from the generations of CNP. In this way, CNP must generate predictions closer to the ground-truth to fool EBM, instead of merely optimizing with respect to the fixed-form likelihood. From generative function reconstruction to downstream regression and classification tasks, we demonstrate that our method fits mainstream CNP members, showing effectiveness when unconstrained Gaussian likelihood is defined, requiring minimal computation overhead while preserving foundation properties of CNPs.

翻译：条件神经过程（CNPs）将函数上的分布形式化，并利用精确的条件似然生成函数观测值。然而，CNPs 在高维观测上的表达能力有限，因为其预测分布被分解为无约束（通常为高斯分布）输出的乘积。以往可以通过潜在变量或自回归似然来处理这一问题，但代价是训练复杂度和计算复杂度呈二次增长。为此，我们提出在常规最大似然估计之外，采用对抗训练方案校准 CNPs。具体而言，我们使用噪声对比估计训练基于能量的模型（EBM），迫使 EBM 从 CNP 生成的结果中识别真实观测值。这样，CNP 必须生成更接近真实值的预测以欺骗 EBM，而非仅仅优化固定形式的似然。从生成函数重构到下游回归与分类任务，我们证明该方法适用于主流 CNP 架构：在定义无约束高斯似然时表现出有效性，仅需极少的计算开销，同时保留 CNPs 的基础特性。