Cumulative deviation of a subpopulation from the full population

Journal of Big Data


Assessing equity in treatment of a subpopulation often involves assigning numerical “scores” to all individuals in the full population such that similar individuals get similar scores; matching via propensity scores or appropriate covariates is common, for example. Given such scores, individuals with similar scores may or may not attain similar outcomes independent of the individuals’ memberships in the subpopulation. The traditional graphical methods for visualizing inequities are known as “reliability diagrams” or “calibrations plots,” which bin the scores into a partition of all possible values, and for each bin plot both the average outcomes for only individuals in the subpopulation as well as the average outcomes for all individuals; comparing the graph for the subpopulation with that for the full population gives some sense of how the averages for the subpopulation deviate from the averages for the full population. Unfortunately, real data sets contain only finitely many observations, limiting the usable resolution of the bins, and so the conventional methods can obscure important variations due to the binning. Fortunately, plotting cumulative deviation of the subpopulation from the full population as proposed in this paper sidesteps the problematic coarse binning. The cumulative plots encode subpopulation deviation directly as the slopes of secant lines for the graphs. Slope is easy to perceive even when the constant offsets of the secant lines are irrelevant. The cumulative approach avoids binning that smooths over deviations of the subpopulation from the full population. Such cumulative aggregation furnishes both high-resolution graphical methods and simple scalar summary statistics (analogous to those of Kuiper and of Kolmogorov and Smirnov used in statistical significance testing for comparing probability distributions).

Related Publications

All Publications

Interspeech - October 12, 2021

LiRA: Learning Visual Speech Representations from Audio through Self-supervision

Pingchuan Ma, Rodrigo Mira, Stavros Petridis, Björn W. Schuller, Maja Pantic

ICML - July 18, 2021

Latency-Aware Neural Architecture Search with Multi-Objective Bayesian Optimization

David Eriksson, Pierce I-Jen Chuang, Samuel Daulton, Peng Xia, Akshat Shrivastava, Arun Babu, Shicong Zhao, Ahmed Aly, Ganesh Venkatesh, Maximilian Balandat

ISAAC - December 5, 2021

On the Extended TSP Problem

Julián Mestre, Sergey Pupyrev, Seeun William Umboh

IEEE Transactions on Image Processing Journal - March 9, 2021

Inspirational Adversarial Image Generation

Baptiste Rozière, Morgane Rivière, Olivier Teytaud, Jérémy Rapin, Yann LeCun, Camille Couprie

To help personalize content, tailor and measure ads, and provide a safer experience, we use cookies. By clicking or navigating the site, you agree to allow our collection of information on and off Facebook through cookies. Learn more, including about available controls: Cookies Policy