AI 中文总结
该研究提出一种基于通路级共享尺度混合构造的鲁棒深度混合模型，采用随机期望最大化算法估计参数，在重尾及污染场景下聚类性能优于深度高斯混合模型，可识别异质潜在结构并降低异常观测影响。
AI 中文摘要
我们提出了一种基于通路级共享尺度混合构造的鲁棒深度混合模型。层特定的成分指标根据各自对应的混合比例独立分布，共同定义了一条贯穿潜在层次结构的完整通路。在选定通路的条件下，单个服从伽马分布的潜在精度变量会在最深层潜在分布、所有中间潜在转换以及观测模型之间共享。对该共享精度进行积分后，每条完整通路会得到精确的多元学生t分布，这使得鲁棒性能够在整个潜在层次结构中连贯传播，而非在各个潜在层中单独引入。模型参数通过随机期望最大化算法进行估计：完整通路的责任度可通过解析方式计算，而共享潜在精度变量和潜在高斯变量则从其条件分布中采样生成，之后再更新模型参数；通路特定的自由度参数则通过一维数值优化进行估计。模拟研究表明，在重尾分布和存在污染的设定下，与深度高斯混合模型相比，该模型能准确恢复通路特定的自由度参数，同时聚类性能持续提升。真实数据应用进一步说明，该模型能够识别异质潜在结构，同时降低异常观测的影响。该框架保留了深度高斯混合模型的层次表示和简约参数共享结构，同时提供了连贯的通路级鲁棒性。
英文摘要
We propose a robust deep mixture model based on a pathway-wise shared scale-mixture construction. Layer-specific component indicators are independently distributed according to their corresponding mixing proportions and jointly define a complete pathway through the latent hierarchy. Conditional on the selected pathway, a single gamma-distributed latent precision variable is shared across the deepest latent distribution, every intermediate latent transition, and the observation model. Integrating out this shared precision yields an exact multivariate Student-$t$ distribution for each complete pathway, allowing robustness to propagate coherently throughout the entire latent hierarchy rather than being introduced separately within individual latent layers. Model parameters are estimated using a stochastic expectation--maximisation algorithm. Complete-pathway responsibilities are evaluated analytically, whereas the shared latent precision variables and latent Gaussian variables are generated from their conditional distributions before updating the model parameters. The pathway-specific degrees-of-freedom parameters are estimated by one-dimensional numerical optimisation. Simulation studies demonstrate accurate recovery of the pathway-specific degrees-of-freedom parameters together with consistently improved clustering performance relative to the deep Gaussian mixture model under heavy-tailed and contaminated settings. Real-data applications further illustrate the ability of the proposed model to identify heterogeneous latent structures while reducing the influence of atypical observations. The proposed framework retains the hierarchical representation and parsimonious parameter-sharing structure of the deep Gaussian mixture model while providing coherent pathway-wise robustness.
Comments20 pages, 2 figures
