We describe a data-driven discovery method that leverages Simpson's paradox to uncover interesting patterns in behavioral data. Our method systematically disaggregates data to identify subgroups within a population whose behavior deviates significantly from the rest of the population. Given an outcome of interest and a set of covariates, the method follows three steps. First, it disaggregates data into subgroups, by conditioning on a particular covariate, so as minimize the variation of the outcome within the subgroups. Next, it models the outcome as a linear function of another covariate, both in the subgroups and in the aggregate data. Finally, it compares trends to identify disaggregations that produce subgroups with different behaviors from the aggregate. We illustrate the method by applying it to three real-world behavioral datasets, including Q &A site Stack Exchange and online learning platforms Khan Academy and Duolingo.
Simpson's paradox @cite_11 @cite_9 often confounds analysis of heterogeneous data, especially social and behavioral data. According to the paradox, an association observed in data that has been aggregated over the entire population may be different from, and even opposite to, associations existing in the subgroups comprising the population. Failure to take this paradox into account can distort conclusions of analysis. Arguably the most famous example of Simpson's paradox arose from a lawsuit alleging gender discrimination at UC Berkeley @cite_16 . Analysis of the aggregate admissions data for the school revealed a statistically significant bias against women: a smaller fraction of female applicants were admitted. However, when admissions data was disaggregated by department, women were shown to have parity, and even a slight advantage in some departments, over men. The paradox arose because departments that female applicants prefer have lower admissions rates for both genders.
@cite_9 @cite_16 @cite_11
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Examination of aggregate data on graduate admissions to the University of California, Berkeley, for fall 1973 shows a clear but misleading pattern of bias against female applicants. Examination of the disaggregated data reveals few decision-making units that show statistically significant departures from expected frequencies of female admissions, and about as many units appear to favor women as to favor men. If the data are properly pooled, taking into account the autonomy of departmental decision making, thus correcting for the tendency of women to apply to graduate departments that are more difficult for applicants of either sex to enter, there is a small but statistically significant bias in favor of women. The graduate departments that are easier to enter tend to be those that require more mathematics in the undergraduate preparatory curriculum. The bias in the aggregated data stems not from any pattern of discrimination on the part of admissions committees, which seem quite fair on the whole, but apparently from prior screening at earlier levels of the educational system. Women are shunted by their socialization and education toward fields of graduate study that are generally more crowded, less productive of completed degrees, and less well funded, and that frequently offer poorer professional employment prospects. T his document is the report of a workshop that convened a group of experts to discuss the recruitment and retention of women in Computer Science and Engineering (CSE) Graduate Programs. (1) Participants included long-time members of the CSE academic and research communities, social scientists engaged in relevant research, and directors of successful retention efforts. (2) The report is a compendium of the experience and expertise of workshop participants, rather than the result of a full-scale, scholarly study into the range of issues. Its goal is to provide departments with practical advice on recruitment and retention in the form of a set of specific recommendations. Women are significantly underrepresented in CSE academic departments [5][40]. As computing technology becomes increasingly pervasive, this underrepresentation translates into a loss of opportunity for individuals, a loss of talent to the workforce, and a loss of creativity in shaping the future of society. While there are many causes of this underrepresentation some rooted in early socialization and primary educational experiences academic departments at the university level nevertheless can have an effect [6][7]. In particular, an improvement at the graduate level in recruitment and retention (and thus in graduation rates) would enable more women to move into visible and influential positions in the CSE community. The increasing presence of these women would provide positive role models and mentors. In order to treat all students fairly, educators must pay attention to gender-based traits. Although in characterizing behaviors one must be careful to acknowledge the existence of individual differences and to avoid stereotyping, there is a large body of information on gender traits. There is strong evidence, for example, that women, even though they perform at the same levels, have less confidence in their abilities and individual accomplishments than men [2][17][36][39][43]. Women are often less aggressive than male students in promoting themselves, attempting new or challenging activities, and pursuing awards or fellowships. There is evidence that females come to computing as only one interest among many, and are thus less single-minded than their male counterparts [27]. Often women report feeling "out of place" in the male-dominated, hacker culture [3] [22] [28]. In light of such differences, some of our recommendations are gender-specific. Most, however, are not. The adoption of our recommendations would improve the educational environment for all students. The recommendations are given in two sections, the first This paper addresses the discovery of surprising patterns. Recently, several authors have addressed the task of discovering surprising prediction rules. However, we do not focus on prediction rules, but rather on a quite different kind of pattern, namely the occurrence of Simpson’s paradox. Intuitively, the fact that this is a paradox suggests that it has a great potential to be a surprising pattern for the user. With this motivation, we make the detection of Simpson’s paradox the central goal of a data mining algorithm explicitly designed to discover surprising patterns. We present computational results showing surprising occurrences of the paradox in some public-domain data sets. In addition, we propose a method for ranking the discovered instances of the paradox in decreasing order of estimated degree of surprisingness. In recent years, automated data-driven decision-making systems have enjoyed a tremendous success in a variety of fields (e.g., to make product recommendations, or to guide the production of entertainment). More recently, these algorithms are increasingly being used to assist socially sensitive decision-making (e.g., to decide who to admit into a degree program or to prioritize individuals for public housing). Yet, these automated tools may result in discriminative decision-making in the sense that they may treat individuals unfairly or unequally based on membership to a category or a minority, resulting in disparate treatment or disparate impact and violating both moral and ethical standards. This may happen when the training dataset is itself biased (e.g., if individuals belonging to a particular group have historically been discriminated upon). However, it may also happen when the training dataset is unbiased, if the errors made by the system affect individuals belonging to a category or minority differently (e.g., if misclassification rates for Blacks are higher than for Whites). In this paper, we unify the definitions of unfairness across classification and regression. We propose a versatile mixed-integer optimization framework for learning optimal and fair decision trees and variants thereof to prevent disparate treatment and or disparate impact as appropriate. This translates to a flexible schema for designing fair and interpretable policies suitable for socially sensitive decision-making. We conduct extensive computational studies that show that our framework improves the state-of-the-art in the field (which typically relies on heuristics) to yield non-discriminative decisions at lower cost to overall accuracy.