标题： SILVar：单指标潜在变量模型 显示英文标题

标题： SILVar: Single Index Latent Variable Models

摘要： 一种在存在潜在变量情况下的半参数非线性回归模型被引入。 这些潜在变量可以对应于复杂网络系统中未建模的现象或未测量的代理。 这种新公式允许联合估计系统中的某些非线性、测量变量之间的直接相互作用以及未建模元素对观测系统的影响。 采用的模型的具体形式得到了证明，学习被表述为正则化最大似然估计。 这导致了一类具有“稀疏加低秩”特征的结构化凸优化问题。 提出了所提出的模型与几种常见模型范式之间的关系，例如鲁棒主成分分析（PCA）和向量自回归（VAR）模型。 特别是在VAR设置中，低秩贡献可能来自时间序列中表现出的广泛趋势。 介绍了学习模型的算法细节。 实验展示了模型和估计算法在模拟数据和真实数据上的性能。 显示英文摘要

摘要： A semi-parametric, non-linear regression model in the presence of latent variables is introduced. These latent variables can correspond to unmodeled phenomena or unmeasured agents in a complex networked system. This new formulation allows joint estimation of certain non-linearities in the system, the direct interactions between measured variables, and the effects of unmodeled elements on the observed system. The particular form of the model adopted is justified, and learning is posed as a regularized maximum likelihood estimation. This leads to classes of structured convex optimization problems with a "sparse plus low-rank" flavor. Relations between the proposed model and several common model paradigms, such as those of Robust Principal Component Analysis (PCA) and Vector Autoregression (VAR), are established. Particularly in the VAR setting, the low-rank contributions can come from broad trends exhibited in the time series. Details of the algorithm for learning the model are presented. Experiments demonstrate the performance of the model and the estimation algorithm on simulated and real data.