9 research outputs found
Improving weighted least squares inference
These days, it is common practice to base inference about the coefficients in a hetoskedastic linear model on the ordinary least squares estimator in conjunction with using heteroskedasticity consistent standard errors. Even when the true form of heteroskedasticity is unknown, heteroskedasticity consistent standard errors can also used to base valid inference on a weighted least squares estimator and using such an estimator can provide large gains in efficiency over the ordinary least squares estimator. However, intervals based on asymptotic approximations with plug-in standard errors often have coverage that is below the nominal level, especially for small sample sizes. Similarly, tests can have null rejection probabilities that are above the nominal level. It is shown that under unknown hereroskedasticy, a bootstrap approximation to the sampling distribution of the weighted least squares estimator is valid, which allows for inference with improved finite-sample properties. For testing linear constraints, permutations tests are proposed which are exact when the error distribution is symmetric and is asymptotically valid otherwise. Another concern that has discouraged the use of weighting is that the weighted least squares estimator may be less efficient than the ordinary least squares estimator when the model used to estimate the unknown form of the heteroskedasticity is misspecified. To address this problem, a new estimator is proposed that is asymptotically at least as efficient as both the ordinary and the weighted least squares estimator. Simulation studies demonstrate the attractive finite-sample properties of this new estimator as well as the improvements in performance realized by bootstrap confidence intervals
Detection and Mitigation of Algorithmic Bias via Predictive Rate Parity
Recently, numerous studies have demonstrated the presence of bias in machine
learning powered decision-making systems. Although most definitions of
algorithmic bias have solid mathematical foundations, the corresponding bias
detection techniques often lack statistical rigor, especially for non-iid data.
We fill this gap in the literature by presenting a rigorous non-parametric
testing procedure for bias according to Predictive Rate Parity, a commonly
considered notion of algorithmic bias. We adapt traditional asymptotic results
for non-parametric estimators to test for bias in the presence of dependence
commonly seen in user-level data generated by technology industry applications
and illustrate how these approaches can be leveraged for mitigation. We further
propose modifications of this methodology to address bias measured through
marginal outcome disparities in classification settings and extend notions of
predictive rate parity to multi-objective models. Experimental results on real
data show the efficacy of the proposed detection and mitigation methods
Improving weighted least squares inference
These days, it is common practice to base inference about the coefficients in a hetoskedastic linear model on the ordinary least squares estimator in conjunction with using heteroskedasticity consistent standard errors. Even when the true form of heteroskedasticity is unknown, heteroskedasticity consistent standard errors can also used to base valid inference on a weighted least squares estimator and using such an estimator can provide large gains in efficiency over the ordinary least squares estimator. However, intervals based on asymptotic approximations with plug-in standard errors often have coverage that is below the nominal level, especially for small sample sizes. Similarly, tests can have null rejection probabilities that are above the nominal level. In this paper, it is shown that under unknown hereroskedasticy, a bootstrap approximation to the sampling distribution of the weighted least squares estimator is valid, which allows for inference with improved finite-sample properties. For testing linear constraints, permutations tests are proposed which are exact when the error distribution is symmetric and is asymptotically valid otherwise. Another concern that has discouraged the use of weighting is that the weighted least squares estimator may be less efficient than the ordinary least squares estimator when the model used to estimate the unknown form of the heteroskedasticity is misspecified. To address this problem, a new estimator is proposed that is asymptotically at least as efficient as both the ordinary and the weighted least squares estimator. Simulation studies demonstrate the attractive finite-sample properties of this new estimator as well as the improvements in performance realized by bootstrap confidence intervals
Long-term Dynamics of Fairness Intervention in Connection Recommender Systems
Recommender system fairness has been studied from the perspectives of a
variety of stakeholders including content producers, the content itself and
recipients of recommendations. Regardless of which type of stakeholders are
considered, most works in this area assess the efficacy of fairness
intervention by evaluating a single fixed fairness criterion through the lens
of a one-shot, static setting. Yet recommender systems constitute dynamical
systems with feedback loops from the recommendations to the underlying
population distributions which could lead to unforeseen and adverse
consequences if not taken into account. In this paper, we study a connection
recommender system patterned after the systems employed by web-scale social
networks and analyze the long-term effects of intervening on fairness in the
recommendations. We find that, although seemingly fair in aggregate, common
exposure and utility parity interventions fail to mitigate amplification of
biases in the long term. We theoretically characterize how certain fairness
interventions impact the bias amplification dynamics in a stylized P\'{o}lya
urn model.Comment: Conference on Artificial Intelligence, Ethics, and Society (AIES
2022