提出非平稳核的稀疏谱表示，提升模型表达力并降低计算开销。
Nonstationary Sparse Spectral Permanental Process
- 用稀疏谱表示突破核函数类型和平稳性限制。
- 计算复杂度降至线性级别，实测在非平稳数据上表现更优。
- 适合处理具有明显非平稳特性的复杂数据，如时序或空间数据。
现有永续过程常对核函数类型或平稳性施加约束，限制了模型表达能力。为克服此问题，我们提出一种新型方法，利用非平稳核的稀疏谱表示，放宽核函数类型与平稳性约束，实现更灵活建模，同时将计算复杂度降至线性水平。此外，通过分层堆叠多个谱特征映射，引入深度核变体，进一步增强模型捕捉复杂数据模式的能力。在合成与真实数据集上的实验结果表明，该方法在显著非平稳场景下表现优异。消融研究还揭示了不同超参数对模型性能的影响。
原文摘要 · Abstract (English)
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.
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