Generative Adversarial Networks for High-Dimensional Item Factor Analysis: A Deep Adversarial Learning Algorithm

TL;DR

This paper addresses parameter estimation in high-dimensional item factor analysis by integrating adversarial variational Bayes (AVB) with an importance-weighted extension (IWAVB). AVB replaces the explicit KL term in variational inference with a discriminator-driven adversarial loss, enabling a flexible, implicit posterior for latent traits, while IWAVB sharpens the marginal likelihood approximation via importance weighting. Across simulations and a large-scale Big-Five dataset, IWAVB demonstrates higher or comparable likelihoods and competitive parameter recovery, particularly under multimodal latent distributions, albeit with higher computational cost and some stability considerations. The approach offers a path to scalable, multimodal IFA that can incorporate complex data types beyond structured responses, potentially enhancing psychometric analyses and integration with multimodal data.

Abstract

Advances in deep learning and representation learning have transformed item factor analysis (IFA) in the item response theory (IRT) literature by enabling more efficient and accurate parameter estimation. Variational Autoencoders (VAEs) have been one of the most impactful techniques in modeling high-dimensional latent variables in this context. However, the limited expressiveness of the inference model based on traditional VAEs can still hinder the estimation performance. We introduce Adversarial Variational Bayes (AVB) algorithms as an improvement to VAEs for IFA with improved flexibility and accuracy. By bridging the strengths of VAEs and Generative Adversarial Networks (GANs), AVB incorporates an auxiliary discriminator network to reframe the estimation process as a two-player adversarial game and removes the restrictive assumption of standard normal distributions in the inference model. Theoretically, AVB can achieve similar or higher likelihood compared to VAEs. A further enhanced algorithm, Importance-weighted Adversarial Variational Bayes (IWAVB) is proposed and compared with Importance-weighted Autoencoders (IWAE). In an exploratory analysis of empirical data, IWAVB demonstrated superior expressiveness by achieving a higher likelihood compared to IWAE. In confirmatory analysis with simulated data, IWAVB achieved similar mean-square error results to IWAE while consistently achieving higher likelihoods. When latent variables followed a multimodal distribution, IWAVB outperformed IWAE. With its innovative use of GANs, IWAVB is shown to have the potential to extend IFA to handle large-scale data, facilitating the potential integration of psychometrics and multimodal data analysis.

Figures (11)

• Figure 1: Ten handwritten images sampled from model (a) GAN, (b) WGAN, (c) VAE, and (d) VAE-GAN. Adapted from mi2018probe.
• Figure 2: Distribution of latent variables for VAE and AVB trained on a simple synthetic dataset containing samples from 4 different labels.
• Figure 3: Schematic illustration of a standard Generative Adversarial Network. In some GAN variants, real data serve only as true samples and are not fed into the generator. However, in the AVB application to IFA, the generator and discriminator take item response data as input, and the discriminator distinguishes between samples in the latent space.
• Figure 4: Schematic comparison of the encoder and decoder designs for the AVB method and a standard VAE.
• Figure 5: Parameter MSE and bias comparison for IWAVB and IWAE methods based on 100 replications of simulation with 5-dimensional latent variables following normal distribution.

Theorems & Definitions (2)

• Theorem 2.1: mescheder2017adversarial
• Theorem 2.2: mescheder2017adversarial