Fairness Evaluation with Item Response Theory

TL;DR

A novel Fair-IRT framework to evaluate a set of predictive models on a set of individuals, while simultaneously eliciting specific parameters, namely, the ability to make fair predictions (a feature of predictive models), as well as the discrimination and difficulty of individuals that affect the prediction results.

Abstract

Item Response Theory (IRT) has been widely used in educational psychometrics to assess student ability, as well as the difficulty and discrimination of test questions. In this context, discrimination specifically refers to how effectively a question distinguishes between students of different ability levels, and it does not carry any connotation related to fairness. In recent years, IRT has been successfully used to evaluate the predictive performance of Machine Learning (ML) models, but this paper marks its first application in fairness evaluation. In this paper, we propose a novel Fair-IRT framework to evaluate a set of predictive models on a set of individuals, while simultaneously eliciting specific parameters, namely, the ability to make fair predictions (a feature of predictive models), as well as the discrimination and difficulty of individuals that affect the prediction results. Furthermore, we conduct a series of experiments to comprehensively understand the implications of these parameters for fairness evaluation. Detailed explanations for item characteristic curves (ICCs) are provided for particular individuals. We propose the flatness of ICCs to disentangle the unfairness between individuals and predictive models. The experiments demonstrate the effectiveness of this framework as a fairness evaluation tool. Two real-world case studies illustrate its potential application in evaluating fairness in both classification and regression tasks. Our paper aligns well with the Responsible Web track by proposing a Fair-IRT framework to evaluate fairness in ML models, which directly contributes to the development of a more inclusive, equitable, and trustworthy AI.

Figures (7)

• Figure 1: The general scenario in fairness evaluation. The dashed line denotes the two analysis directions: one for individuals and another for predictive models.
• Figure 2: (a) The scatter plot shows the discrimination parameter $\bm{a}_{j}$ and difficulty parameter $\bm{\delta}_{j}$ for each individual. The purple points indicate individuals with negative discrimination values (special individuals), while the green points indicate individuals with positive discrimination values (normal individuals). The size of the points increases as $\bm{\delta}_{j}$ approaches 0.5 and gradually decreases as $\bm{\delta}_{j}$ approaches 0 or 1; (b,c,d) Examples of ICCs generated by Fair-IRT for different values of discrimination and fixed range of difficulty (i.e., $0.4 < \bm{\delta}_{j} < 0.6$). Higher discriminations lead to steeper ICCs; (e) Examples of selected ICCs for different values of difficulty and fixed range of discrimination (i.e., $1.7 < \bm{a}_{j} < 2$).
• Figure 3: (a) The scatter plot shows the ${\hat{\text{STS}}}$ and ability parameter $\bm{\theta}_{i}$ for each predictive model; (b) Examples of selected individuals with flat ICCs. The shaded area indicates the ability range of the 20 selected predictive models.
• Figure 4: The plots for the Adult dataset: (a) The scatter plot shows the discrimination parameter $\bm{a}_{j}$ and the difficulty parameter $\bm{\delta}_{j}$ for each individual; (b) Examples of selected individuals with flat ICCs. The shaded area indicates the ability range of the 24 selected predictive models.
• Figure 5: The plots for the Law School dataset: (a) The scatter plot shows the discrimination parameter $\bm{a}_{j}$ and the difficulty parameter $\bm{\delta}_{j}$ for each individual; (b) Examples of selected individuals with flat ICCs. The shaded area indicates the ability range of the 15 selected predictive models.

Theorems & Definitions (4)

• Definition 1: Situation Test Score (STS)
• Definition 2: Individual Fairness (IF) dwork2012fairnessLouizosSLWZ15
• Definition 3: Counterfactual Fairness kusner2017counterfactual
• Definition 4: Equalised Score (ES)