Non-convex Global Minimization and False Discovery Rate Control for the TREX

The TREX is a recently introduced method for performing sparse high-dimensional regression. Despite its statistical promise as an alternative to the lasso, square-root lasso, and scaled lasso, the TREX is computationally challenging in that it requires solving a non-convex optimization problem. This paper shows a remarkable result: despite the non-convexity of the TREX problem, there exists a polynomial-time algorithm that is guaranteed to find the global minimum. This result adds the TREX to a very short list of non-convex optimization problems that can be globally optimized (principal components analysis being a famous example). After deriving and developing this new approach, we demonstrate that (i) the ability of the preexisting TREX heuristic to reach the global minimum is strongly dependent on the difficulty of the underlying statistical problem, (ii) the new polynomial-time algorithm for TREX permits a novel variable ranking and selection scheme, (iii) this scheme can be incorporated into a rule that controls the false discovery rate (FDR) of included features in the model. To achieve this last aim, we provide an extension of the results of Barber & Candes (2015) to establish that the knockoff filter framework can be applied to the TREX. This investigation thus provides both a rare case study of a heuristic for non-convex optimization and a novel way of exploiting non-convexity for statistical inference

Removal of zinc from a base-metal solution using ion exchange at Rustenburg Base Metal Refiners.

Includes abstract.Includes bibliographical references.Anglo American Platinum’s expansion project, which aimed at increasing platinum production to 3.5 million oz per annum, necessitated an expansion in the Rustenburg Base Metal Refinery (RBMR) to accommodate the associated increase in the production of base metals (Cu, Ni, and Co). RBMR’s name plate capacity increased from 21 000 to 33 000 tonnes of nickel per annum. The expansion project involved various brownfield and greenfield installations and was completed in 2011. The new circuit and various process additions posed a significant risk to the nickel cathode quality with regard to zinc contamination. Mass balancing of the pre-expansion circuit showed that as much as 50% of the zinc entering the plant would exit through the nickel cathode, thus making it the major bleed for zinc from the circuit. The expansion circuit mass balance showed that although a portion of the zinc would exit through the pressure iron removal residue, this small bleed stream would not be sufficient to ensure that the nickel cathode does not exceed 50 ppm (LME specification). Another factor contributing to the zinc problem was the fact that more Platreef ore, with higher zinc levels, was being mined. These factors indicated that a dedicated zinc removal section was required to ensure a sustainable nickel cathode production containing less than 50 ppm zinc

Fairness in Credit Scoring: Assessment, Implementation and Profit Implications

The rise of algorithmic decision-making has spawned much research on fair machine learning (ML). Financial institutions use ML for building risk scorecards that support a range of credit-related decisions. Yet, the literature on fair ML in credit scoring is scarce. The paper makes two contributions. First, we provide a systematic overview of algorithmic options for incorporating fairness goals in the ML model development pipeline. In this scope, we also consolidate the space of statistical fairness criteria and examine their adequacy for credit scoring. Second, we perform an empirical study of different fairness processors in a profit-oriented credit scoring setup using seven real-world data sets. The empirical results substantiate the evaluation of fairness measures, identify more and less suitable options to implement fair credit scoring, and clarify the profit-fairness trade-off in lending decisions. Specifically, we find that multiple fairness criteria can be approximately satisfied at once and identify separation as a proper criterion for measuring the fairness of a scorecard. We also find fair in-processors to deliver a good balance between profit and fairness. More generally, we show that algorithmic discrimination can be reduced to a reasonable level at a relatively low cost.Comment: Preprint submitted to European Journal of Operational Researc

Construction and validation of the SON-R 5 1/2-17, the Snijders-Oomen non-verbal intelligence test

In this thesis the construction and validation of the SON-R 5,5-17 is described, the recent revision of the Snijders-Oomen non-verbal intelligence test. The SON-R is an individual test of (non-verbal) intelligence for children in the ages of 51/2 to 17 years. The test was published in 1989 with an extensive 'Manual and researchr eport' in English, German and Dutch. The thesis is for the greater part a reprint of the 'Manual and research report' with the omission of norm tablesa nd instructionsf or practical use of the test and with the addition of some new parts. ... Zie: Summar