用对抗学习提升高维项目反应理论中的潜变量估计精度。
Generative Adversarial Networks for High-Dimensional Item Factor Analysis: A Deep Adversarial Learning Algorithm
- 结合VAE与GAN思想，用判别器重构潜变量估计过程。
- 在真实数据上，新模型似然值高于IWAE；模拟数据中误差相当但似然更高。
- 特别适合处理多模态分布的潜变量，适用于大规模心理测量数据。
深度学习和表征学习的进步推动了项目反应理论（IRT）中项目因子分析（IFA）的发展，实现了更高效、更准确的参数估计。变分自编码器（VAEs）是该领域最有效的技术之一，用于建模高维潜变量。然而，传统VAE推断模型表达能力有限，仍制约估计性能。本文提出对抗变分贝叶斯（AVB）算法，作为VAE的改进方法，提升了灵活性与准确性。通过融合VAE与生成对抗网络（GAN）的优势，AVB引入辅助判别器网络，将估计过程重构为双玩家对抗博弈，并去除了推断模型中标准正态分布的限制性假设。理论上，AVB可达到与VAE相当或更高的似然值。进一步提出重要性加权对抗变分贝叶斯（IWAVB），并与重要性加权自编码器（IWAE）对比。在真实数据探索性分析中，IWAVB展现出更高似然值；在模拟数据验证中，其均方误差与IWAE相当，但始终获得更高似然值。当潜变量服从多模态分布时，IWAVB显著优于IWAE。该方法利用GAN思想，具备扩展IFA以处理大规模数据的潜力，促进心理测量学与多模态数据分析的融合。
原文摘要 · Abstract (English)
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.
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