Bridging extrinsic and intrinsic variable importance

Variable importance may describe either intrinsic predictive information in a population or extrinsic importance for a fitted prediction rule. Quantifying the uncertainty in variable importance estimates is critical for interpretation. Methods for estimating intrinsic variable importance (we will refer to these as VIMP) and the minipatch leave-one-covariate-out procedure (MPLOCO) target intrinsic and extrinsic importance, respectively, and provide methods for computing standard errors. These two approaches have a shared structure, comparing prediction performance with and without features, but the relationship between them has not been formally characterized. We establish conditions under which the two perspectives align. Under squared-error loss, if the fitted full and reduced learners converge to their oracle counterparts sufficiently fast, then MPLOCO is asymptotically equivalent to VIMP. We provide further conditions extending this result to general loss functions and formalize grouped MPLOCO for potentially overlapping feature groups. Through simulations, we show that VIMP and MPLOCO agree most closely when the fitted learner is well aligned with the data-generating mechanism. In a high-dimensional grouped simulation, both procedures identified the signal-containing groups. In an analysis of HIV-1 VRC01 neutralization sensitivity, both methods placed the same three biologically relevant feature groups among their highest-ranked groups. These results clarify when intrinsic and extrinsic importance can be interpreted similarly and when they provide complementary information.

Variable Importance Identification Through Lazy Training for Binary Classification

Deep neural networks have been widely used in many applications (e.g., computer vision and natural language processing); however, understanding their explainability remains a challenging task. Recently, substantial research has been devoted to improving the explainability of deep neural networks, with most of this work focusing on the regression framework. In this paper, we instead focus on the binary classification framework and adopt a variable-importance framework combined with the idea of lazy training to propose an efficient algorithm for identifying important features. From a theoretical perspective, our method relies on only a minimal set of assumptions and achieves well-controlled error rates. The validity of the proposed method and algorithm is examined through extensive simulation studies and real-data applications.

Longitudinal Random Forests for Sparse and Irregular Response Trajectories

Longitudinal studies often collect data at sparse, irregular, and unequally spaced time points. Such heterogeneity is often driven by subject-specific covariates, yet existing methods have been restricted to a scalar endpoint value, completely neglecting the underlying response trajectories. We propose a novel Longitudinal Random Forest (LRF) framework that leverages tree-based ensemble machine learning with adaptive node-wise longitudinal trajectory estimation. The LRF framework makes five methodological contributions. it captures each subject's individual response trajectory while simultaneously accommodating within-node correlation, between-node heterogeneity, and nonlinear and interactive covariate effects. It introduces a novel trajectory-based splitting criterion that maximizes trajectory separation while incorporating a size-weighted penalty; it provides two variants, Principal Analysis by Conditional Expectation (LRF-PACE) and adaptive linear mixed-effects models (LRF-adaptiveLMM), which employ nonparametric and semiparametric node-wise smoothers, respectively, while learning covariate effects in a data-driven manner. It provides a comprehensive interpretation of covariates using both the classical trajectory-based permutation variable importance measure (PVIM) and a newly proposed finite-way interaction frequency count, and it not only predicts entire trajectories for new subjects but also forecasts future trajectories for existing subjects. Extensive simulation studies demonstrate that LRF achieves superior performance over several competing methods, even under severe sparsity. The practical significance of the LRF framework lies in its ability to address five important clinical questions.

Correcting Variable Importance Scored by Random Forests

Variable importance produced by Random Forests (RF) is used widely in statistical data analysis, and has played an important role in a variety of tasks such as assisting model interpretation, model selection and diagnosis, and cost-bounded learning etc. However, the calculation of variable importance in RF does not take into account of the correlations among variables, and variables that are correlated to many other variables tend to receive a lower importance index or being completely masked (i.e., with an importance index near zero) by other strongly correlated variables. To prevent influence from unwanted correlated variables in calculating variable importance, we propose to group variables by their conditional correlations (conditional on the response variable). We explore two computationally efficient options, with one grouping variables individually, and then separates the variable of interest from all correlated variables, while the other uses clustering to group variables according to their pair-wise conditional correlations. Our experiments show that both lead to sensible corrections to the importance of variables.