Generative Models for Missing Data

Missing data poses an ubiquitous challenge across a wide range of applications, stemming from a multitude of causes that are both diverse and context-dependent. The prevailing issue is that most advanced data analysis techniques are primarily tailored for complete datasets, thereby underscoring the indispensable need for effective imputation methods. In this chapter, we embark on an extensive exploration of missing data from a statistical perspective, offering a holistic review of its intricate nature. Our investigation encompasses a deep dive into the various mechanisms underlying missing data, shedding light on their ignorability and identifiability-fundamental concepts essential for understanding and addressing this pervasive issue. Moreover, we present a succinct yet comprehensive overview of influential classical imputation methods, showcasing their contributions to the field. Building upon this foundation, we delve into the latest advancements in generative models, a burgeoning area that holds great promise for learning from and imputing missing data. By harnessing the power of generative models, we aim to unlock novel insights and methodologies that can tackle the challenges posed by missing data. Furthermore, we introduce an approach that specifically addresses the critical problem of nonparametric identifiability in nonignorable missing data through the innovative use of generative models. This novel approach aims to overcome the limitations associated with alternative generative models and provides a potential solution to this challenging issue. To enhance the clarity of our proposed method, we supplement our discourse with curated numerical examples that distinguish its effectiveness from other baselines in specific scenarios. Through the exploration, we hope to pave the way for further research and advancements in this critical domain, ultimately leading to more accurate and reliable analyses and interpretations of incomplete datasets.