Aspects of Statistical Learning in Complex System (English shop)

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This book is concerned with the development of interpretable models for prediction and inferencein complex systems that primarily build on a Stein-type shrinkage approach. To achieve this, new estimators are developed for the variance and the covariance matrix even applicable to large dimensional data sets (e.g., gene expression data). The introduction of dynamical correlation extends the concept of correlation and the corresponding shrinkage estimators consistently to longitudinal data.

Building on the estimation of the covariance matrix, known methods are extended to complex systems and new techniques are developed, including a shrinkage t statistic for high-dimensional case-control analysis, a method to infer networks from longitudinal data, a small sample shrinkage regression, a small sample model selection method for the VAR-process and a new technique of estimating partially causal networks.