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We propose a new method for principal component analysis (PCA) called feature grouping and sparse principal component analysis (FGSPCA). This method is designed to capture both grouping and sparsity structures in factor loadings simultaneously. To achieve this, we use a non‐convex truncated regularization that can adjust for sparsity and grouping effects automatically. This regularization encourages factor loadings with similar values to be either grouped together for feature grouping or be zero for feature selection, helping to reduce model complexity and improve interpretation. While other structured PCA methods often require prior knowledge to construct the regularization term, FGSPCA can capture grouping and sparsity structures without any prior information. We solve the resulting non‐convex optimization problem using an alternating algorithm that combines difference‐of‐convex programming, the augmented Lagrange method, and coordinate descent method. Our experiments show that FGSPCA performs well and efficiently on both synthetic and real‐world datasets. An implementation of FGSPCA is available on GitHub https://github.com/HaiyanJiang/FGSPCA. [ABSTRACT FROM AUTHOR]

We propose a sequential nonparametric test for detecting a change in distribution, based on windowed Kolmogorov–Smirnov statistics. The approach is simple, robust, highly computationally efficient, easy to calibrate, and requires no parametric assumptions about the underlying null and alternative distributions. We show that both the false-alarm rate and the power of our procedure are amenable to rigorous analysis, and that the method outperforms existing sequential testing procedures in practice. We then apply the method to the problem of detecting radiological anomalies, using data collected from measurements of the background gamma-radiation spectrum on a large university campus. In this context, the proposed method leads to substantial improvements in time-to-detection for the kind of radiological anomalies of interest in law-enforcement and border-security applications.Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement. [ABSTRACT FROM AUTHOR]

We study the worst portfolios for a class of law invariant dynamic monetary utility functions with domain in a class of stochastic processes. The concept of comonotonicity is introduced for these processes in order to prove the existence of worst portfolios. Using robust representations of monetary utility function processes in discrete time, a relation between the worst portfolios at different periods of time is presented. Finally, we study conditions to achieve the maximum in the representation theorems for concave monetary utility functions that are continuous for bounded decreasing sequences. [ABSTRACT FROM AUTHOR]