arXiv subjects

Ravi Shroff

Publications and source records attributed to Ravi Shroff.

9 recordsLinked to original sources

arXiv2023

Differences in academic preparedness do not fully explain Black-White enrollment disparities in advanced high school coursework

Whether racial disparities in enrollment in advanced high school coursework can be attributed to differences in prior academic preparation is a central question in sociological research and education policy. However, previous investigations face methodological limitations, for they compare race-specific enrollment rates of students after adjusting for characteristics only partially related to their academic preparedness for advanced coursework. Informed by a recently-developed statistical technique, we propose and estimate a novel measure of students' academic preparedness and use administrative data from the New York City Department of Education to measure differences in AP mathematics enrollment rates among similarly prepared students of different races. We find that preexisting differences in academic preparation do not fully explain the under-representation of Black students relative to White students in AP mathematics. Our results imply that achieving equal opportunities for AP enrollment not only requires equalizing earlier academic experiences, but also addressing inequities that emerge from coursework placement processes.

stat.ME↗

arXiv2022

Causal Conceptions of Fairness and their Consequences

Recent work highlights the role of causality in designing equitable decision-making algorithms. It is not immediately clear, however, how existing causal conceptions of fairness relate to one another, or what the consequences are of using these definitions as design principles. Here, we first assemble and categorize popular causal definitions of algorithmic fairness into two broad families: (1) those that constrain the effects of decisions on counterfactual disparities; and (2) those that constrain the effects of legally protected characteristics, like race and gender, on decisions. We then show, analytically and empirically, that both families of definitions \emph{almost always} -- in a measure theoretic sense -- result in strongly Pareto dominated decision policies, meaning there is an alternative, unconstrained policy favored by every stakeholder with preferences drawn from a large, natural class. For example, in the case of college admissions decisions, policies constrained to satisfy causal fairness definitions would be disfavored by every stakeholder with neutral or positive preferences for both academic preparedness and diversity. Indeed, under a prominent definition of causal fairness, we prove the resulting policies require admitting all students with the same probability, regardless of academic qualifications or group membership. Our results highlight formal limitations and potential adverse consequences of common mathematical notions of causal fairness.

cs.LG↗

arXiv2020

A Causal Framework for Observational Studies of Discrimination

In studies of discrimination, researchers often seek to estimate a causal effect of race or gender on outcomes. For example, in the criminal justice context, one might ask whether arrested individuals would have been subsequently charged or convicted had they been a different race. It has long been known that such counterfactual questions face measurement challenges related to omitted-variable bias, and conceptual challenges related to the definition of causal estimands for largely immutable characteristics. Another concern, which has been the subject of recent debates, is post-treatment bias: many studies of discrimination condition on apparently intermediate outcomes, like being arrested, that themselves may be the product of discrimination, potentially corrupting statistical estimates. There is, however, reason to be optimistic. By carefully defining the estimand -- and by considering the precise timing of events -- we show that a primary causal quantity of interest in discrimination studies can be estimated under an ignorability condition that may hold approximately in some observational settings. We illustrate these ideas by analyzing both simulated data and the charging decisions of a prosecutor's office in a large county in the United States.

stat.ME↗

arXiv2018

Mitigating Included- and Omitted-Variable Bias in Estimates of Disparate Impact

Managers, employers, policymakers, and others often seek to understand whether decisions are biased against certain groups. One popular analytic strategy is to estimate disparities after adjusting for observed covariates, typically with a regression model. This approach, however, suffers from two key statistical challenges. First, omitted-variable bias can skew results if the model does not adjust for all relevant factors; second, and conversely, included-variable bias -- a lesser-known phenomenon -- can skew results if the set of covariates includes irrelevant factors. Here we introduce a new, three-step statistical method, which we call risk-adjusted regression, to address both concerns in settings where decision makers have clearly measurable objectives. In the first step, we use all available covariates to estimate the value, or inversely, the risk, of taking a certain action, such as approving a loan application or hiring a job candidate. Second, we measure disparities in decisions after adjusting for these risk estimates alone, mitigating the problem of included-variable bias. Finally, in the third step, we assess the sensitivity of results to potential mismeasurement of risk, addressing concerns about omitted-variable bias. To do so, we develop a novel, non-parametric sensitivity analysis that yields tight bounds on the true disparity in terms of the average gap between true and estimated risk -- a single interpretable parameter that facilitates credible estimates. We demonstrate this approach on a detailed dataset of 2.2 million police stops of pedestrians in New York City, and show that traditional statistical tests of discrimination can substantially underestimate the magnitude of disparities.

stat.AP↗

arXiv2018

The Measure and Mismeasure of Fairness

The field of fair machine learning aims to ensure that decisions guided by algorithms are equitable. Over the last decade, several formal, mathematical definitions of fairness have gained prominence. Here we first assemble and categorize these definitions into two broad families: (1) those that constrain the effects of decisions on disparities; and (2) those that constrain the effects of legally protected characteristics, like race and gender, on decisions. We then show, analytically and empirically, that both families of definitions typically result in strongly Pareto dominated decision policies. For example, in the case of college admissions, adhering to popular formal conceptions of fairness would simultaneously result in lower student-body diversity and a less academically prepared class, relative to what one could achieve by explicitly tailoring admissions policies to achieve desired outcomes. In this sense, requiring that these fairness definitions hold can, perversely, harm the very groups they were designed to protect. In contrast to axiomatic notions of fairness, we argue that the equitable design of algorithms requires grappling with their context-specific consequences, akin to the equitable design of policy. We conclude by listing several open challenges in fair machine learning and offering strategies to ensure algorithms are better aligned with policy goals.

cs.CY↗

arXiv2018

Algorithmic Decision Making in the Presence of Unmeasured Confounding

On a variety of complex decision-making tasks, from doctors prescribing treatment to judges setting bail, machine learning algorithms have been shown to outperform expert human judgments. One complication, however, is that it is often difficult to anticipate the effects of algorithmic policies prior to deployment, making the decision to adopt them risky. In particular, one generally cannot use historical data to directly observe what would have happened had the actions recommended by the algorithm been taken. One standard strategy is to model potential outcomes for alternative decisions assuming that there are no unmeasured confounders (i.e., to assume ignorability). But if this ignorability assumption is violated, the predicted and actual effects of an algorithmic policy can diverge sharply. In this paper we present a flexible, Bayesian approach to gauge the sensitivity of predicted policy outcomes to unmeasured confounders. We show that this policy evaluation problem is a generalization of estimating heterogeneous treatment effects in observational studies, and so our methods can immediately be applied to that setting. Finally, we show, both theoretically and empirically, that under certain conditions it is possible to construct near-optimal algorithmic policies even when ignorability is violated. We demonstrate the efficacy of our methods on a large dataset of judicial actions, in which one must decide whether defendants awaiting trial should be required to pay bail or can be released without payment.

stat.ME↗

arXiv2017

Simple rules for complex decisions

From doctors diagnosing patients to judges setting bail, experts often base their decisions on experience and intuition rather than on statistical models. While understandable, relying on intuition over models has often been found to result in inferior outcomes. Here we present a new method, select-regress-and-round, for constructing simple rules that perform well for complex decisions. These rules take the form of a weighted checklist, can be applied mentally, and nonetheless rival the performance of modern machine learning algorithms. Our method for creating these rules is itself simple, and can be carried out by practitioners with basic statistics knowledge. We demonstrate this technique with a detailed case study of judicial decisions to release or detain defendants while they await trial. In this application, as in many policy settings, the effects of proposed decision rules cannot be directly observed from historical data: if a rule recommends releasing a defendant that the judge in reality detained, we do not observe what would have happened under the proposed action. We address this key counterfactual estimation problem by drawing on tools from causal inference. We find that simple rules significantly outperform judges and are on par with decisions derived from random forests trained on all available features. Generalizing to 22 varied decision-making domains, we find this basic result replicates. We conclude with an analytical framework that helps explain why these simple decision rules perform as well as they do.

stat.AP↗

arXiv2012

CR singular images of generic submanifolds under holomorphic maps

The purpose of this paper is to organize some results on the local geometry of CR singular real-analytic manifolds that are images of CR manifolds via a CR map that is a diffeomorphism onto its image. We find a necessary (sufficient in dimension 2) condition for the diffeomorphism to extend to a finite holomorphic map. The multiplicity of this map is a biholomorphic invariant that is precisely the Moser invariant of the image when it is a Bishop surface with vanishing Bishop invariant. In higher dimensions, we study Levi-flat CR singular images and we prove that the set of CR singular points must be large, and in the case of codimension 2, necessarily Levi-flat or complex. We also show that there exist real-analytic CR functions on such images that satisfy the tangential CR conditions at the singular points, yet fail to extend to holomorphic functions in a neighborhood. We provide many examples to illustrate the phenomena that arise.

math.CV↗

arXiv2010

Partial Rigidity of CR Embeddings of Real Hypersurfaces into Hyperquadrics with Small Signature Difference

We study the rigidity of holomorphic mappings from a neighborhood of a Levi-nondegenerate CR hypersurface $M$ with signature $l$ into a hyperquadric $Q_{l'}^{N} \subseteq \mathbb{CP}^{N+1}$ of larger dimension and signature. We show that if the CR complexity of $M$ is not too large then the image of $M$ under any such mapping is contained in a complex plane with dimension independent of $N$. This result follows from two theorems, the first demonstrating that for sufficiently degenerate mappings, the image of $M$ is contained in a plane, and the second relating the degeneracy of mappings into different quadrics.

math.CV↗