论文标题
使用正则条件可能性学习具有潜在变量的指数式家庭图形模型
Learning Exponential Family Graphical Models with Latent Variables using Regularized Conditional Likelihood
论文作者
论文摘要
如果观察到的变量受到潜在变量的影响，则将图形模型拟合到给定样品观察的随机变量集合中，这是一项具有挑战性的任务，该变量可能会引起观察到的变量之间的显着混淆统计依赖性。我们提出了一个新的凸松弛框架，基于潜在可变量图形建模的正则条件可能性，其中指数族的图形模型给出了在潜在变量上的有条件分布的条件分布。与以前提出的可访问方法相比，通过表征观察到的变量的边际分布进行进行的，我们的方法适用于更广泛的设置范围，因为它不需要了解潜在变量的特定分布形式，并且可以专业化以使观察到的数据不良好地模仿试态度。我们通过一系列关于合成和实际数据的数值实验来证明我们的框架的效用和灵活性。
Fitting a graphical model to a collection of random variables given sample observations is a challenging task if the observed variables are influenced by latent variables, which can induce significant confounding statistical dependencies among the observed variables. We present a new convex relaxation framework based on regularized conditional likelihood for latent-variable graphical modeling in which the conditional distribution of the observed variables conditioned on the latent variables is given by an exponential family graphical model. In comparison to previously proposed tractable methods that proceed by characterizing the marginal distribution of the observed variables, our approach is applicable in a broader range of settings as it does not require knowledge about the specific form of distribution of the latent variables and it can be specialized to yield tractable approaches to problems in which the observed data are not well-modeled as Gaussian. We demonstrate the utility and flexibility of our framework via a series of numerical experiments on synthetic as well as real data.
