Normalising Flows are non-parametric statistical models characterised by their dual capabilities of density estimation and generation. This duality requires an inherently invertible architecture. However, the requirement of invertibility imposes constraints on their expressiveness, necessitating a large number of parameters and innovative architectural designs to achieve good results. Whilst flow-based models predominantly rely on neural-network-based transformations for expressive designs, alternative transformation methods have received limited attention. In this work, we present Ferumal flow, a novel kernelised normalising flow paradigm that integrates kernels into the framework. Our results demonstrate that a kernelised flow can yield competitive or superior results compared to neural network-based flows whilst maintaining parameter efficiency. Kernelised flows excel especially in the low-data regime, enabling flexible non-parametric density estimation in applications with sparse data availability.

翻译：正规化流是一类非参数统计模型，兼具密度估计与数据生成的双重能力。这种二元性要求其架构天然具备可逆性，但可逆性约束限制了模型的表现力，需通过大量参数与创新架构设计才能获得良好效果。尽管基于流的模型主要依赖神经网络变换实现高表现力设计，但替代性变换方法却鲜受关注。本文提出Ferumal流——一种将核方法融入框架的新型核化正规化流范式。实验结果表明，核化流可在保持参数效率的同时，取得与神经网络流相媲美甚至更优的结果。尤其在低数据场景下，核化流表现出卓越性能，能够为数据稀疏的应用提供灵活的非参数密度估计。