Rail defects constitute a major cause of derailments in the United States. Derailments are often very fatal and disastrous. While rail defect-caused derailments are becoming an increasing concern, the analysis of rail defects remain relatively unchanged. Weibull analysis has historically been the "go-to" distribution when it comes to analyzing rail defects irrespective of the type, tonnage, size or age. In other words, the analysis is not only defect-based, the defect distribution varies from section to section. "No free-lunch" theorem in statistical learning provides the basis to assert that a single statistical technique is not guaranteed to perform excellently on all defect types because all techniques will perform almost equally if their performances are aggregated on all possible data types. Hence, the use of Weibull distribution is not only ideal for all defect types. It also does not provide a network infrastructure manager the information needed to allocate resources for each defect type. More so, Weibull distribution like most other distributions belong to the beta family which is trained, fitted and tested on the same data-set. In this study, we present an agglomerated machine learning of defects as an alternative to Weibull Analysis of rail infrastructure. This methodology considers different rail defect prediction techniques using Stacking Ensembles in a way that training and testing is done on different data splits. We considered a database of over 20 miles of rail defect and track geometry data spanning approximately 5 years. Our results provide an infrastructure tool developed to assist rail owners and infrastructure managers a decision-making rationale for resource allocation and maintenance rather than the micro-level decision making influenced by the Weibull for limited sections of track.

Sparse graphical modelling/inverse covariance selection is an important problem in machine learning and has seen significant advances in recent years. A major focus has been on methods which perform model selection in high dimensions. To this end, numerous convex $\ell_1$ regularization approaches have been proposed in the literature. It is not however clear which of these methods are optimal in any well-defined sense. A major gap in this regard pertains to the rate of convergence of proposed optimization methods. To address this, an iterative thresholding algorithm for numerically solving the $\ell_1$-penalized maximum likelihood problem for sparse inverse covariance estimation is presented. The proximal gradient method considered in this paper is shown to converge at a linear rate, a result which is the first of its kind for numerically solving the sparse inverse covariance estimation problem. The convergence rate is provided in closed form, and is related to the condition number of the optimal point. Numerical results demonstrating the proven rate of convergence are presented.