Imputation Method based on Adaptive Group Lasso for High-dimensional Compositional Data with Missing Values

Compositional data usually refers to data on the individual components that make up a whole. Such data are common in many fields, especially in chemistry, biology, geology, and other scientific and engineering fields. However, in many real-life situations, a large number of missing values are often collected. The complexity of compositional data with missing values makes traditional estimation methods seem overwhelming. Therefore, how to effectively perform statistical inference on compositional data with missing values has attracted the attention of many scholars in recent years. The logarithmic scale transformation provides a possibility for compositional data, but this transformation has limited requirements on the components of the compositional data, such as not including or missing fixes and constraints. Therefore, it is of great significance to explore a new estimation method for composition data theoretically. In this paper, a compositional data imputation method based on the adaptive group least absolute shrinkage and selection operator (AGLasso) is proposed. AGLasso is able to adapt imputation methods to different data distributions and patterns based on the characteristics of the data. While traditional methods may result in lost or biased information, AGLasso attempts to impute while preserving data integrity. Through data analysis, the imputation effect of compositional data containing missing values is compared under different missing rates and correlation coefficients, and a comparative study is conducted with the Lasso imputation method, the adaptive Lasso imputation method and the group Lasso imputation method. The results show that adaptive group Lasso is superior to the other three interpolation methods. In domains such as healthcare data, where data quality has a huge impact on decision making, AGLasso can help improve data integrity and usability. And in the future, Generative Adversarial Network (GAN)-based imputation methods and novel deep learning methods using techniques such as self-encoders are expected to show more power in dealing with missing values.