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：归一化流是一种以密度估计与生成双重能力为特征的非参数统计模型。这种双重性要求其架构本质可逆。然而，可逆性要求对其表达能力施加了约束，需要大量参数与创新的架构设计才能取得良好效果。尽管基于流的模型主要依赖基于神经网络的变换来实现表达能力强的设计，但其他变换方法受到的关注有限。在本工作中，我们提出Ferumal流，这是一种将核函数集成到框架中的新型核化归一化流范式。我们的结果表明，与基于神经网络的流相比，核化流在保持参数效率的同时，能够产生具有竞争力或更优的结果。核化流尤其在低数据量场景中表现优异，使得在数据稀疏的应用中能够实现灵活的非参数密度估计。