Nonstationary Sparse Spectral Permanental Process

TL;DR

This paper introduces a flexible, computationally efficient nonstationary spectral process using sparse spectral representations, with a deep kernel extension for capturing complex data patterns, validated on synthetic and real datasets.

Contribution

It presents a novel nonstationary kernel modeling approach with sparse spectral representation and a deep kernel variant, overcoming limitations of existing permanental processes.

Findings

Effective on synthetic datasets with nonstationarity

Reduces computational complexity to linear scale

Deep kernel enhances modeling of complex patterns

Abstract

Existing permanental processes often impose constraints on kernel types or stationarity, limiting the model's expressiveness. To overcome these limitations, we propose a novel approach utilizing the sparse spectral representation of nonstationary kernels. This technique relaxes the constraints on kernel types and stationarity, allowing for more flexible modeling while reducing computational complexity to the linear level. Additionally, we introduce a deep kernel variant by hierarchically stacking multiple spectral feature mappings, further enhancing the model's expressiveness to capture complex patterns in data. Experimental results on both synthetic and real-world datasets demonstrate the effectiveness of our approach, particularly in scenarios with pronounced data nonstationarity. Additionally, ablation studies are conducted to provide insights into the impact of various hyperparameters on model performance.