Log-ratio Lasso: Scalable, Sparse Estimation for Log-ratio Models

TL;DR

This paper introduces a scalable method for sparse estimation of log-ratio models, enabling efficient feature selection in high-dimensional biological data, with improved predictive accuracy and interpretability.

Contribution

It presents a novel low-dimensional embedding of the log-ratio space and a two-step penalized fitting procedure for highly sparse, interpretable models.

Findings

Achieves highly sparse models with biologically relevant features

Improves predictive accuracy over less interpretable methods

Demonstrates effectiveness on cancer proteomics data

Abstract

Positive-valued signal data is common in many biological and medical applications, where the data are often generated from imaging techniques such as mass spectrometry. In such a setting, the relative intensities of the raw features are often the scientifically meaningful quantities, so it is of interest to identify relevant features that take the form of log-ratios of the raw inputs. When including the log-ratios of all pairs of predictors, the dimensionality of this predictor space becomes large, so computationally efficient statistical procedures are required. We introduce an embedding of the log-ratio parameter space into a space of much lower dimension and develop efficient penalized fitting procedure using this more tractable representation. This procedure serves as the foundation for a two-step fitting procedure that combines a convex filtering step with a second non-convex pruning step to yield highly sparse solutions. On a cancer proteomics data set we find that these methods fit highly sparse models with log-ratio features of known biological relevance while greatly improving upon the predictive accuracy of less interpretable methods.