In selection processes such as hiring, promotion, and college admissions, implicit bias toward socially-salient attributes such as race, gender, or sexual orientation produces persistent inequality and reduces utility for the decision-maker. Recent works show that interventions like the Rooney Rule, which require a minimum quota of individuals from each affected group, are very effective in improving utility when individuals belong to at most one affected group. However, in several settings, individuals belong to multiple affected groups and, consequently, face more extreme implicit bias due to this intersectionality. We consider independently drawn utilities and show that, with intersectionality, the aforementioned non-intersectional constraints only recover part of the utility achievable in the absence of implicit bias. On the other hand, we show that appropriate lower-bound constraints on the intersections recover almost all the utility achievable in the absence of implicit bias. And, hence, offer an advantage over non-intersectional approaches to reducing inequality.
This paper introduces the problem of coresets for regression problems to panel data settings. We first define coresets for several variants of regression problems with panel data and then present efficient algorithms to construct coresets of size that depend polynomially on 1/ε (where ε is the error parameter) and the number of regression parameters – independent of the number of individuals in the panel data or the time units each individual is observed for. Our approach is based on the Feldman-Langberg framework in which a key step is to upper bound the “total sensitivity” that is roughly the sum of maximum influences of all individual-time pairs taken over all possible choices of regression parameters. Empirically, we assess our approach with synthetic and real-world datasets; the coreset sizes constructed using our approach are much smaller than the full dataset and coresets indeed accelerate the running time of computing the regression objective.
We study the problem of constructing coresets for clustering problems with time series data. This problem has gained importance across many fields including biology, medicine, and economics due to the proliferation of sensors for real-time measurement and rapid drop in storage costs. In particular, we consider the setting where the time series data on N entities is generated from a Gaussian mixture model with autocorrelations over k clusters in Rd. Our main contribution is an algorithm to construct coresets for the maximum likelihood objective for this mixture model. Our algorithm is efficient, and, under a mild assumption on the covariance matrices of the Gaussians, the size of the coreset is independent of the number of entities N and the number of observations for each entity, and depends only polynomially on k, d and 1/ε, where ε is the error parameter. We empirically assess the performance of our coresets with synthetic data.