Primal path algorithm for compositional data analysis
This work addresses a computational bottleneck for researchers analyzing compositional data, such as in microbiome studies, but is incremental as it builds on existing regularization methods.
The paper tackles the computational inefficiency of regularized regression with compositional data by proposing an efficient solution path algorithm, which is extended to classification and shown to be faster than previous methods in high-dimensional cases.
Compositional data have two unique characteristics compared to typical multivariate data: the observed values are nonnegative and their summand is exactly one. To reflect these characteristics, a specific regularized regression model with linear constraints is commonly used. However, linear constraints incur additional computational time, which becomes severe in high-dimensional cases. As such, we propose an efficient solution path algorithm for a $l_1$ regularized regression with compositional data. The algorithm is then extended to a classification model with compositional predictors. We also compare its computational speed with that of previously developed algorithms and apply the proposed algorithm to analyze human gut microbiome data.