AI 中文总结
研究提出去噪从属概率模型（DSPM），其混合向量由特定波动率过程驱动成平稳 AR(1)链，证明相关界定结果，通过实验验证模型效果，耦合链与数据恢复控制、学习先验记忆，解决噪声机制及模型相关问题。
AI 中文摘要
重尾扩散模型用高斯方差混合替代高斯噪声：去噪列维概率模型（DLPM）在坐标间使混合变量独立同分布，而学生 t 分布的 EDM 每个样本共享一个混合变量。二者都没有动力学，但噪声幅度的时间依赖性——波动率聚类——是金融回报的典型特征事实。我们引入去噪从属概率模型（DSPM），其混合向量是由沿数据轴的 tempered - 稳定从属增量（离散的 Barndorff - Nielsen - Shephard 波动率过程）驱动的平稳 AR(1)链。在该链的条件下，DDPM 机制完全适用；峰度和平方噪声自相关在链参数中具有封闭形式，给出了精确识别、解析可逆的校准；DDPM、DLPM 和学生 t 噪声是一个记忆参数的边界情况。然后我们证明了一个界定结果：当去噪器以混合变量为条件时，它们的分布是一个干扰因素——在精确去噪器极限下，生成的分布对其不变，对链的干预无效。实验证实了两方面：条件模型无论混合律如何都能匹配数据的聚类，设计的 x8 波动率冲击使包络移动不到 13%，而盲模型能准确传递校准后的机制。最后，通过变分波动率编码器将链与数据耦合——用随机波动率似然训练，简化的去噪损失的对数行列式可证明会下降——恢复了控制（冲击响应 3.07 对比朴素的 2.83），恢复了潜在波动率（相关性 0.76），并学习到接近真实持续性的先验记忆。
英文摘要
Heavy-tailed diffusion models replace Gaussian noise by a Gaussian variance mixture: denoising Levy probabilistic models (DLPM) take the mixing variables i.i.d. across coordinates, while Student-t EDM shares one mixing variable per sample. Neither has dynamics, yet temporal dependence of the noise amplitude - volatility clustering - is the defining stylized fact of financial returns. We introduce the Denoising Subordinated Probabilistic Model (DSPM), whose mixing vector is a stationary AR(1) chain driven by tempered-stable subordinator increments (the discrete Barndorff-Nielsen-Shephard volatility process) along the data axis. Conditionally on the chain the DDPM machinery survives verbatim; kurtosis and squared-noise autocorrelation are closed-form in the chain parameters, giving an exactly identified, analytically invertible calibration; DDPM, DLPM and Student-t noise are boundary cases of one memory parameter. We then prove a delimiting result: when the denoiser is conditioned on the mixing variables, their law is a nuisance - in the exact-denoiser limit the generated distribution is invariant to it and interventions on the chain do nothing. Experiments confirm both halves: conditioned models match the data's clustering whatever the mixing law, a designed x8 volatility shock moves the envelope by under 13%, while blind models transmit the mechanism exactly as calibrated. Finally, coupling the chain to the data by a variational volatility encoder - trained with the stochastic-volatility likelihood whose log-determinant the simplified denoising loss provably drops - restores control (shock response 3.07 vs. naive 2.83), recovers latent volatility (correlation 0.76), and learns the prior memory toward the true persistence.
Comments14 pages, 5 figures; working draft, code available from the author
