标题： 可扩展的正则化联合混合模型 显示英文标题

标题： Scalable Regularised Joint Mixture Models

摘要： 在许多应用中，数据在潜在组具有不同底层分布的意义上可能是异构的。当预测模型应用于此类数据时，异构性可能会影响预测性能和可解释性。基于无监督学习和正则化回归交叉领域的进展，我们提出了一种针对异构数据的方法，该方法允许联合学习（i）显式的多变量特征分布，（ii）高维回归模型和（iii）潜在组标签，其中（i）和（ii）特定于潜在组，并且这两个元素共同影响（iii）。这种方法在高维情况下表现出显著效果，通过数据降维实现计算效率的同时，采用重新加权方案保留关键信号，即使特征数量很大时也是如此。我们详细讨论了这些方面及其对建模和计算的影响，包括EM算法的收敛性。该方法模块化，可以结合适合特定应用的数据降维和高维估计器。我们展示了广泛的模拟和真实数据实验的结果，包括高度非高斯的数据。我们的结果显示，在生物医学等领域，这种高效有效的方法适用于需要可解释预测和显式特征空间模型的情况，但隐藏的异质性可能是一个问题。 显示英文摘要

摘要： In many applications, data can be heterogeneous in the sense of spanning latent groups with different underlying distributions. When predictive models are applied to such data the heterogeneity can affect both predictive performance and interpretability. Building on developments at the intersection of unsupervised learning and regularised regression, we propose an approach for heterogeneous data that allows joint learning of (i) explicit multivariate feature distributions, (ii) high-dimensional regression models and (iii) latent group labels, with both (i) and (ii) specific to latent groups and both elements informing (iii). The approach is demonstrably effective in high dimensions, combining data reduction for computational efficiency with a re-weighting scheme that retains key signals even when the number of features is large. We discuss in detail these aspects and their impact on modelling and computation, including EM convergence. The approach is modular and allows incorporation of data reductions and high-dimensional estimators that are suitable for specific applications. We show results from extensive simulations and real data experiments, including highly non-Gaussian data. Our results allow efficient, effective analysis of high-dimensional data in settings, such as biomedicine, where both interpretable prediction and explicit feature space models are needed but hidden heterogeneity may be a concern.