标题： 可观察的字典学习用于高维统计推断 显示英文标题

标题： Observable dictionary learning for high-dimensional statistical inference

摘要： 本文介绍了一种从少量观测中高效推断高维分布式量的方法。 感兴趣的量（QoI）在从训练集中学习到的基（字典）中进行近似。 在基中与QoI近似相关的系数是通过最小化与观测的不匹配来确定的。 为了获得感兴趣的量的概率估计，采用了一种贝叶斯方法。 将QoI视为具有分层先验分布的随机场，以便得到后验分布的显式表达式。 本工作的主要贡献在于推导出用于推断相关系数的\emph{与观测链一致的表示基}。 然后对所得的字典进行调整，使其既能被传感器观测，又能准确地近似后验均值。 提出了一种生成此类可观测字典的算法。 该方法通过从少量壁挂点传感器中估计开放腔流的速度场进行了说明。 并与依赖于主成分分析和K-SVD字典的标准估计方法进行了比较，结果展示了本方法的优越性能。 显示英文摘要

摘要： This paper introduces a method for efficiently inferring a high-dimensional distributed quantity from a few observations. The quantity of interest (QoI) is approximated in a basis (dictionary) learned from a training set. The coefficients associated with the approximation of the QoI in the basis are determined by minimizing the misfit with the observations. To obtain a probabilistic estimate of the quantity of interest, a Bayesian approach is employed. The QoI is treated as a random field endowed with a hierarchical prior distribution so that closed-form expressions can be obtained for the posterior distribution. The main contribution of the present work lies in the derivation of \emph{a representation basis consistent with the observation chain} used to infer the associated coefficients. The resulting dictionary is then tailored to be both observable by the sensors and accurate in approximating the posterior mean. An algorithm for deriving such an observable dictionary is presented. The method is illustrated with the estimation of the velocity field of an open cavity flow from a handful of wall-mounted point sensors. Comparison with standard estimation approaches relying on Principal Component Analysis and K-SVD dictionaries is provided and illustrates the superior performance of the present approach.