Nonstationary Sparse Spectral Permanental Process

• URL: http://arxiv.org/abs/2410.03581v2
• Date: Sat, 12 Oct 2024 03:34:04 GMT
• Title: Nonstationary Sparse Spectral Permanental Process
• Authors: Zicheng Sun, Yixuan Zhang, Zenan Ling, Xuhui Fan, Feng Zhou,
• Abstract summary: 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. Experimental results on both synthetic and real-world datasets demonstrate the effectiveness of our approach.
• Score: 24.10531062895964
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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