放宽流形假设，给出去噪得分匹配的泛化误差界。
Generalization error bound for denoising score matching under relaxed manifold assumption
- 用非参数高斯混合建模数据分布，放松流形约束。
- 收敛速率由内在维度决定，且在高维下仍有效。
- 适合关注理论分析与高维概率模型的研究者。
我们研究去噪得分匹配估计的理论性质。采用非参数高斯混合模型刻画观测数据密度，显著放宽了标准流形假设，允许样本偏离流形。同时仍能利用良好的分布结构。推导出去噪得分匹配估计的逼近误差和泛化误差的非渐近界。收敛速率由内在维度决定。此外，即使环境维数随样本量多项式增长，我们的边界依然成立。
原文摘要 · Abstract (English)
We examine theoretical properties of the denoising score matching estimate. We model the density of observations with a nonparametric Gaussian mixture. We significantly relax the standard manifold assumption allowing the samples step away from the manifold. At the same time, we are still able to leverage a nice distribution structure. We derive non-asymptotic bounds on the approximation and generalization errors of the denoising score matching estimate. The rates of convergence are determined by the intrinsic dimension. Furthermore, our bounds remain valid even if we allow the ambient dimension grow polynomially with the sample size.
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