Adaptive Conditional Quantile Neural Processes

TL;DR

This paper introduces Conditional Quantile Neural Processes (CQNPs), a novel probabilistic model that captures complex, multimodal distributions more effectively than Gaussian-based neural processes, enhancing predictive accuracy and flexibility.

Contribution

The paper proposes CQNPs, extending neural processes with quantile regression to better model diverse distribution shapes, including multimodal ones.

Findings

CQNPs outperform baselines in predictive accuracy.

CQNPs better model multimodal and heterogeneous distributions.

Sampling efficiency is improved with the proposed method.

Abstract

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.