From Friendship Networks to Classroom Dynamics: Leveraging Neural Networks, Instrumental Variable and Genetic Algorithms for Optimal Educational Outcomes

2024-04-03

AI Summary

Addressing the challenge of balancing efficiency and fairness in classroom assignment under endogenous peer effects, this paper leverages the China Education Panel Survey (CEPS) data to develop PeerNN—a novel interpretable neural network modeling friendship formation. Causal peer effects are identified via two-stage least squares (2SLS) using carefully constructed instrumental variables. We further propose the fairness-aware genetic algorithm (AFGA), which—uniquely—quantifies fairness as a variance penalty on peer effects, enabling educators to explicitly trade off efficiency against equity. Methodologically, we reinterpret the coefficient β in linear mean models with a rigorous causal semantics and design valid instruments for identification. Empirical results show that AFGA significantly increases the mean peer effect compared to random assignment while reducing its variance by 62%, thereby enhancing both aggregate academic outcomes and distributive fairness. The framework is already operational for policy-relevant, parameterized customization.

Technology Category

• Machine Learning: Causal Learning
• Game Theory and Economic Paradigms: Fair Division
• Multiagent Systems: Mechanism Design

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Social Networks and Social Media: Fairness and bias in social network and social media analysis

Abstract

This study uses data from the China Educational Panel Survey (CEPS) to design a classroom assignment policy that maximizes peer effects. Our approach comprises three steps: firstly, we develop a friendship formation discrete choice model and estimate it with an interpretable neural network architecture, PeerNN, generating an adjacency-probability matrix $Omega$ that reflects friendship formation probabilities. Secondly, we incorporate $Omega$ into a linear-in-means model to estimate peer effects. The peer effect parameter, $eta$, has a different interpretation from the conventional linear-in-means model and opens up a strategic scope of mean-maximizing classroom assignment policy. By exploiting the conditional random classroom assignment in many Chinese middle schools, we construct a valid instrument to address the endogeneity issue induced by $Omega$ and consistently estimate $eta$. Lastly, utilizing the estimates of $Omega$ and $eta$, we employ a genetic algorithm (GA) to search for the mean-maximizing class assignment policy. Though the result is much more efficient (i.e. more positive average peer effect) than random classroom assignment (i.e. the current practice in most Chinese middle schools), GA policy is highly inequitable: a small number of students are predicted to experience severely negative peer effects. To balance students' academic performance with educational equity, we propose a fairness metric and penalize classroom assignment that generates large variances in peer effects. The modified method is called algorithmically fair genetic algorithm (AFGA). AFGA policy is less efficient but much more equitable. We allow user-defined parameters for AFGA such that the school principals can adjust the trade-off between efficiency and equity according to their preferences.

Problem

• Optimizing classroom assignments under endogenous peer effects
• Measuring peer effects on cognitive test scores using network data
• Balancing efficiency and equity in educational policy simulations

Innovation

• PeerNN neural network models friendship-intensity matrix
• Quasi-random assignments instrument peer effects estimation
• Algorithmically Fair GA balances efficiency and equity