kernelshap {kernelshap}

Kernel SHAP

Description

Efficient implementation of Kernel SHAP, see Lundberg and Lee (2017), and Covert and Lee (2021), abbreviated by CL21. For up to p=8 features, the resulting Kernel SHAP values are exact regarding the selected background data. For larger p, an almost exact hybrid algorithm involving iterative sampling is used, see Details.

Usage

kernelshap(object, ...)

## Default S3 method:
kernelshap(
  object,
  X,
  bg_X,
  pred_fun = stats::predict,
  feature_names = colnames(X),
  bg_w = NULL,
  exact = length(feature_names) <= 8L,
  hybrid_degree = 1L + length(feature_names) %in% 4:16,
  paired_sampling = TRUE,
  m = 2L * length(feature_names) * (1L + 3L * (hybrid_degree == 0L)),
  tol = 0.005,
  max_iter = 100L,
  parallel = FALSE,
  parallel_args = NULL,
  verbose = TRUE,
  ...
)

## S3 method for class 'ranger'
kernelshap(
  object,
  X,
  bg_X,
  pred_fun = function(m, X, ...) stats::predict(m, X, ...)$predictions,
  feature_names = colnames(X),
  bg_w = NULL,
  exact = length(feature_names) <= 8L,
  hybrid_degree = 1L + length(feature_names) %in% 4:16,
  paired_sampling = TRUE,
  m = 2L * length(feature_names) * (1L + 3L * (hybrid_degree == 0L)),
  tol = 0.005,
  max_iter = 100L,
  parallel = FALSE,
  parallel_args = NULL,
  verbose = TRUE,
  ...
)

Arguments

object

Fitted model object.

...

Additional arguments passed to pred_fun(object, X, ...).

X

(n \times p) matrix or data.frame with rows to be explained. The columns should only represent model features, not the response (but see feature_names on how to overrule this).

bg_X

Background data used to integrate out "switched off" features, often a subset of the training data (typically 50 to 500 rows) It should contain the same columns as X. In cases with a natural "off" value (like MNIST digits), this can also be a single row with all values set to the off value.

pred_fun

Prediction function of the form ⁠function(object, X, ...)⁠, providing K \ge 1 predictions per row. Its first argument represents the model object, its second argument a data structure like X. Additional (named) arguments are passed via .... The default, stats::predict(), will work in most cases.

feature_names

Optional vector of column names in X used to calculate SHAP values. By default, this equals colnames(X). Not supported if X is a matrix.

bg_w

Optional vector of case weights for each row of bg_X.

exact

If TRUE, the algorithm will produce exact Kernel SHAP values with respect to the background data. In this case, the arguments hybrid_degree, m, paired_sampling, tol, and max_iter are ignored. The default is TRUE up to eight features, and FALSE otherwise.

hybrid_degree

Integer controlling the exactness of the hybrid strategy. For 4 \le p \le 16, the default is 2, otherwise it is 1. Ignored if exact = TRUE.

• 0: Pure sampling strategy not involving any exact part. It is strictly worse than the hybrid strategy and should therefore only be used for studying properties of the Kernel SHAP algorithm.

• 1: Uses all 2p on-off vectors z with \sum z \in \{1, p-1\} for the exact part, which covers at least 75% of the mass of the Kernel weight distribution. The remaining mass is covered by random sampling.

• 2: Uses all p(p+1) on-off vectors z with \sum z \in \{1, 2, p-2, p-1\}. This covers at least 92% of the mass of the Kernel weight distribution. The remaining mass is covered by sampling. Convergence usually happens in the minimal possible number of iterations of two.

• k>2: Uses all on-off vectors with \sum z \in \{1, \dots, k, p-k, \dots, p-1\}.

paired_sampling

Logical flag indicating whether to do the sampling in a paired manner. This means that with every on-off vector z, also 1-z is considered. CL21 shows its superiority compared to standard sampling, therefore the default (TRUE) should usually not be changed except for studying properties of Kernel SHAP algorithms. Ignored if exact = TRUE.

m

Even number of on-off vectors sampled during one iteration. The default is 2p, except when hybrid_degree == 0. Then it is set to 8p. Ignored if exact = TRUE.

tol

Tolerance determining when to stop. Following CL21, the algorithm keeps iterating until \textrm{max}(\sigma_n)/(\textrm{max}(\beta_n) - \textrm{min}(\beta_n)) < \textrm{tol}, where the \beta_n are the SHAP values of a given observation, and \sigma_n their standard errors. For multidimensional predictions, the criterion must be satisfied for each dimension separately. The stopping criterion uses the fact that standard errors and SHAP values are all on the same scale. Ignored if exact = TRUE.

max_iter

If the stopping criterion (see tol) is not reached after max_iter iterations, the algorithm stops. Ignored if exact = TRUE.

parallel

If TRUE, use parallel foreach::foreach() to loop over rows to be explained. Must register backend beforehand, e.g., via 'doFuture' package, see README for an example. Parallelization automatically disables the progress bar.

parallel_args

Named list of arguments passed to foreach::foreach(). Ideally, this is NULL (default). Only relevant if parallel = TRUE. Example on Windows: if object is a GAM fitted with package 'mgcv', then one might need to set parallel_args = list(.packages = "mgcv").

verbose

Set to FALSE to suppress messages and the progress bar.

Details

Pure iterative Kernel SHAP sampling as in Covert and Lee (2021) works like this:

1. A binary "on-off" vector z is drawn from \{0, 1\}^p such that its sum follows the SHAP Kernel weight distribution (normalized to the range \{1, \dots, p-1\}).

2. For each j with z_j = 1, the j-th column of the original background data is replaced by the corresponding feature value x_j of the observation to be explained.

3. The average prediction v_z on the data of Step 2 is calculated, and the average prediction v_0 on the background data is subtracted.

4. Steps 1 to 3 are repeated m times. This produces a binary m \times p matrix Z (each row equals one of the z) and a vector v of shifted predictions.

5. v is regressed onto Z under the constraint that the sum of the coefficients equals v_1 - v_0, where v_1 is the prediction of the observation to be explained. The resulting coefficients are the Kernel SHAP values.

This is repeated multiple times until convergence, see CL21 for details.

A drawback of this strategy is that many (at least 75%) of the z vectors will have \sum z \in \{1, p-1\}, producing many duplicates. Similarly, at least 92% of the mass will be used for the p(p+1) possible vectors with \sum z \in \{1, 2, p-2, p-1\}. This inefficiency can be fixed by a hybrid strategy, combining exact calculations with sampling.

The hybrid algorithm has two steps:

1. Step 1 (exact part): There are 2p different on-off vectors z with \sum z \in \{1, p-1\}, covering a large proportion of the Kernel SHAP distribution. The degree 1 hybrid will list those vectors and use them according to their weights in the upcoming calculations. Depending on p, we can also go a step further to a degree 2 hybrid by adding all p(p-1) vectors with \sum z \in \{2, p-2\} to the process etc. The necessary predictions are obtained along with other calculations similar to those described in CL21.

2. Step 2 (sampling part): The remaining weight is filled by sampling vectors z according to Kernel SHAP weights renormalized to the values not yet covered by Step 1. Together with the results from Step 1 - correctly weighted - this now forms a complete iteration as in CL21. The difference is that most mass is covered by exact calculations. Afterwards, the algorithm iterates until convergence. The output of Step 1 is reused in every iteration, leading to an extremely efficient strategy.

If p is sufficiently small, all possible 2^p-2 on-off vectors z can be evaluated. In this case, no sampling is required and the algorithm returns exact Kernel SHAP values with respect to the given background data. Since kernelshap() calculates predictions on data with MN rows (N is the background data size and M the number of z vectors), p should not be much higher than 10 for exact calculations. For similar reasons, degree 2 hybrids should not use p much larger than 40.

Value

An object of class "kernelshap" with the following components:

• S: (n \times p) matrix with SHAP values or, if the model output has dimension K > 1, a list of K such matrices.

• X: Same as input argument X.

• baseline: Vector of length K representing the average prediction on the background data.

• SE: Standard errors corresponding to S (and organized like S).

• n_iter: Integer vector of length n providing the number of iterations per row of X.

• converged: Logical vector of length n indicating convergence per row of X.

• m: Integer providing the effective number of sampled on-off vectors used per iteration.

• m_exact: Integer providing the effective number of exact on-off vectors used per iteration.

• prop_exact: Proportion of the Kernel SHAP weight distribution covered by exact calculations.

• exact: Logical flag indicating whether calculations are exact or not.

• txt: Summary text.

• predictions: (n \times K) matrix with predictions of X.

• algorithm: "kernelshap".

Methods (by class)

• kernelshap(default): Default Kernel SHAP method.

• kernelshap(ranger): Kernel SHAP method for "ranger" models, see Readme for an example.

References

1. Scott M. Lundberg and Su-In Lee. A unified approach to interpreting model predictions. Proceedings of the 31st International Conference on Neural Information Processing Systems, 2017.

2. Ian Covert and Su-In Lee. Improving KernelSHAP: Practical Shapley Value Estimation Using Linear Regression. Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:3457-3465, 2021.

Examples

# MODEL ONE: Linear regression
fit <- lm(Sepal.Length ~ ., data = iris)

# Select rows to explain (only feature columns)
X_explain <- iris[1:2, -1]

# Select small background dataset (could use all rows here because iris is small) 
set.seed(1)
bg_X <- iris[sample(nrow(iris), 100), ]

# Calculate SHAP values
s <- kernelshap(fit, X_explain, bg_X = bg_X)
s

# MODEL TWO: Multi-response linear regression
fit <- lm(as.matrix(iris[, 1:2]) ~ Petal.Length + Petal.Width + Species, data = iris)
s <- kernelshap(fit, iris[1:4, 3:5], bg_X = bg_X)
summary(s)

# Non-feature columns can be dropped via 'feature_names'
s <- kernelshap(
  fit, 
  iris[1:4, ],
  bg_X = bg_X, 
  feature_names = c("Petal.Length", "Petal.Width", "Species")
)
s