Rolling Shapley Values

Analytical computation of rolling and expanding Shapley values for time-series data. The 'rollshap' package decomposes the coefficient of determination (R-squared) of a linear regression into nonnegative contributions from each explanatory variable using the Shapley value from cooperative game theory (Shapley, 1953, ). For each window, the exact Shapley value is computed by fitting all subsets of the explanatory variables and averaging the marginal contribution to R-squared across all orderings, which returns an order-invariant attribution that sums to the full-model R-squared. Use cases include variable importance, factor attribution, and feature selection in time-series regression. The package supports rolling and expanding windows, weights, and handling of missing values via 'min_obs', 'complete_obs', and 'na_restore' arguments. The implementation uses the online and offline algorithms from the 'roll' package to compute rolling and expanding cross-products efficiently with parallelism across columns and windows provided by 'RcppParallel'.

rollshap

Overview

'rollshap' is a package that provides analytical computation of rolling and expanding Shapley values for time-series data.

The 'rollshap' package decomposes the coefficient of determination (R-squared) of a linear regression into nonnegative contributions from each explanatory variable using the Shapley value from cooperative game theory (Shapley, 1953, doi:10.1515/9781400881970-018). For each window, the exact Shapley value is computed by fitting all subsets of the explanatory variables and averaging the marginal contribution to R-squared across all orderings, which returns an order-invariant attribution that sums to the full-model R-squared. Use cases include:

Variable importance: rolling decomposition of explanatory power across factors or features
Factor attribution: quantifying the contribution of each factor to a model's fit through time
Feature selection: identifying variables whose marginal contribution is persistent or transient

The package supports rolling and expanding windows, weights, and handling of missing values via 'min_obs', 'complete_obs', and 'na_restore' arguments. The implementation uses the online and offline algorithms from the 'roll' package to compute rolling and expanding cross-products efficiently with parallelism across columns and windows provided by 'RcppParallel'.

Installation

Install the development version from GitHub:

# install.packages("devtools")
devtools::install_github("jasonjfoster/rollshap")

Usage

Load the package and supply a dataset:

library(rollshap) # roll (>= 1.1.7)

n <- 15
m <- 3
x <- matrix(rnorm(n * m), nrow = n, ncol = m)
y <- rnorm(n)
weights <- 0.9 ^ (n:1)

Then, to compute rolling and expanding Shapley values, use the roll_shap function:

# rolling Shapley values with complete windows
roll_shap(x, y, width = 5)

# rolling Shapley values with partial windows
roll_shap(x, y, width = 5, min_obs = 1)

# expanding Shapley values with partial windows
roll_shap(x, y, width = n, min_obs = 1)

# expanding Shapley values with partial windows and weights
roll_shap(x, y, width = n, min_obs = 1, weights = weights)

Note that handling of missing values is supported as well (see the min_obs, complete_obs, and na_restore arguments).

References

Shapley, L.S. (1953). "A Value for n-Person Games." In Contributions to the Theory of Games, Volume II, edited by H.W. Kuhn and A.W. Tucker, 307-317. Princeton University Press.