Algorithms are now regularly used to decide whether defendants awaiting trial are too dangerous to be released back into the community. In some cases, black defendants are substantially more likely than white defendants to be incorrectly classi ed as high risk. To mitigate such disparities, several techniques have recently been proposed to achieve algorithmic fairness. Here we reformulate algorithmic fairness as constrained optimization: the objective is to maximize public safety while satisfying formal fairness constraints designed to reduce racial disparities. We show that for several past de nitions of fairness, the optimal algorithms that result require detaining defendants above race-speci c risk thresholds. We further show that the optimal unconstrained algorithm requires applying a single, uniform threshold to all defendants. e unconstrained algorithm thus maximizes public safety while also satisfying one important understanding of equality: that all individuals are held to the same standard, irrespective of race. Because the optimal constrained and unconstrained algorithms generally di er, there is tension between improving public safety and satisfying prevailing notions of algorithmic fairness. By examining data from Broward County, Florida, we show that this trade-o can be large in practice. We focus on algorithms for pretrial release decisions, but the principles we discuss apply to other domains, and also to human decision makers carrying out structured decision rules. ACM Reference format:1 We consider racial disparities because they have been at the center of many recent debates in criminal justice, but the same logic applies across a range of possible a ributes, including gender. arXiv:1701.08230v4 [cs.CY]

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We have cultured Plasmodium falciparum directly from the blood of infected individuals to examine patterns of mature-stage gene expression in patient isolates. Analysis of the transcriptome of P. falciparum is complicated by the highly periodic nature of gene expression because small variations in the stage of parasite development between samples can lead to an apparent difference in gene expression values. To address this issue, we have developed statistical likelihood-based methods to estimate cell cycle progression and commitment to asexual or sexual development lineages in our samples based on microscopy and gene expression patterns. In cases subsequently matched for temporal development, we find that transcriptional patterns in ex vivo culture display little variation across patients with diverse clinical profiles and closely resemble transcriptional profiles that occur in vitro. These statistical methods, available to the research community, assist in the design and interpretation of P. falciparum expression profiling experiments where it is difficult to separate true differential expression from cell-cycle dependent expression. We reanalyze an existing dataset of in vivo patient expression profiles and conclude that previously observed discrete variation is consistent with the commitment of a varying proportion of the parasite population to the sexual development lineage. malaria ͉ microarray

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Many causal questions involve interactions between units, also known as interference, for example between individuals in households, students in schools, or firms in markets. In this paper we formalize the concept of a conditioning mechanism, which provides a framework for constructing valid and powerful randomization tests under general forms of interference. We describe our framework in the context of two-stage randomized designs and apply our approach to a randomized evaluation of an intervention targeting student absenteeism in the School District of Philadelphia. We show improvements over existing methods in terms of computational and statistical power. arXiv:1709.08036v3 [stat.ME]