Explain the output of machine learning models with dependence-aware (conditional/observational) Shapley values
Source:R/explain.R
explain.Rd
Computes dependence-aware Shapley values for observations in x_explain
from the specified
model
by using the method specified in approach
to estimate the conditional expectation.
See Aas et al. (2021)
for a thorough introduction to dependence-aware prediction explanation with Shapley values.
Usage
explain(
model,
x_explain,
x_train,
approach,
phi0,
iterative = NULL,
max_n_coalitions = NULL,
group = NULL,
n_MC_samples = 1000,
seed = 1,
verbose = "basic",
predict_model = NULL,
get_model_specs = NULL,
prev_shapr_object = NULL,
asymmetric = FALSE,
causal_ordering = NULL,
confounding = NULL,
extra_computation_args = list(),
iterative_args = list(),
output_args = list(),
...
)
Arguments
- model
Model object. Specifies the model whose predictions we want to explain. Run
get_supported_models()
for a table of which modelsexplain
supports natively. Unsupported models can still be explained by passingpredict_model
and (optionally)get_model_specs
, see details for more information.- x_explain
Matrix or data.frame/data.table. Contains the the features, whose predictions ought to be explained.
- x_train
Matrix or data.frame/data.table. Contains the data used to estimate the (conditional) distributions for the features needed to properly estimate the conditional expectations in the Shapley formula.
- approach
Character vector of length
1
or one less than the number of features. All elements should, either be"gaussian"
,"copula"
,"empirical"
,"ctree"
,"vaeac"
,"categorical"
,"timeseries"
,"independence"
,"regression_separate"
, or"regression_surrogate"
. The two regression approaches can not be combined with any other approach. See details for more information.- phi0
Numeric. The prediction value for unseen data, i.e. an estimate of the expected prediction without conditioning on any features. Typically we set this value equal to the mean of the response variable in our training data, but other choices such as the mean of the predictions in the training data are also reasonable.
- iterative
Logical or NULL If
NULL
(default), the argument is set toTRUE
if there are more than 5 features/groups, andFALSE
otherwise. If eventuallyTRUE
, the Shapley values are estimated iteratively in an iterative manner. This provides sufficiently accurate Shapley value estimates faster. First an initial number of coalitions is sampled, then bootsrapping is used to estimate the variance of the Shapley values. A convergence criterion is used to determine if the variances of the Shapley values are sufficiently small. If the variances are too high, we estimate the number of required samples to reach convergence, and thereby add more coalitions. The process is repeated until the variances are below the threshold. Specifics related to the iterative process and convergence criterion are set throughiterative_args
.- max_n_coalitions
Integer. The upper limit on the number of unique feature/group coalitions to use in the iterative procedure (if
iterative = TRUE
). Ifiterative = FALSE
it represents the number of feature/group coalitions to use directly. The quantity refers to the number of unique feature coalitions ifgroup = NULL
, and group coalitions ifgroup != NULL
.max_n_coalitions = NULL
corresponds tomax_n_coalitions=2^n_features
.- group
List. If
NULL
regular feature wise Shapley values are computed. If provided, group wise Shapley values are computed.group
then has length equal to the number of groups. The list element contains character vectors with the features included in each of the different groups. See Jullum et al. (2021) for more information on group wise Shapley values.- n_MC_samples
Positive integer. For most approaches, it indicates the maximum number of samples to use in the Monte Carlo integration of every conditional expectation. For
approach="ctree"
,n_MC_samples
corresponds to the number of samples from the leaf node (see an exception related to thectree.sample
argumentsetup_approach.ctree()
). Forapproach="empirical"
,n_MC_samples
is the \(K\) parameter in equations (14-15) of Aas et al. (2021), i.e. the maximum number of observations (with largest weights) that is used, see also theempirical.eta
argumentsetup_approach.empirical()
.- seed
Positive integer. Specifies the seed before any randomness based code is being run. If
NULL
no seed is set in the calling environment.- verbose
String vector or NULL. Specifies the verbosity (printout detail level) through one or more of strings
"basic"
,"progress"
,"convergence"
,"shapley"
and"vS_details"
."basic"
(default) displays basic information about the computation which is being performed."progress
displays information about where in the calculation process the function currently is. #'"convergence"
displays information on how close to convergence the Shapley value estimates are (only wheniterative = TRUE
) ."shapley"
displays intermediate Shapley value estimates and standard deviations (only wheniterative = TRUE
)the final estimates.
"vS_details"
displays information about the v_S estimates. This is most relevant forapproach %in% c("regression_separate", "regression_surrogate", "vaeac"
).NULL
means no printout. Note that any combination of four strings can be used. E.g.verbose = c("basic", "vS_details")
will display basic information + details about the v(S)-estimation process.
- predict_model
Function. The prediction function used when
model
is not natively supported. (Runget_supported_models()
for a list of natively supported models.) The function must have two arguments,model
andnewdata
which specify, respectively, the model and a data.frame/data.table to compute predictions for. The function must give the prediction as a numeric vector.NULL
(the default) uses functions specified internally. Can also be used to override the default function for natively supported model classes.- get_model_specs
Function. An optional function for checking model/data consistency when
model
is not natively supported. (Runget_supported_models()
for a list of natively supported models.) The function takesmodel
as argument and provides a list with 3 elements:- labels
Character vector with the names of each feature.
- classes
Character vector with the classes of each features.
- factor_levels
Character vector with the levels for any categorical features.
If
NULL
(the default) internal functions are used for natively supported model classes, and the checking is disabled for unsupported model classes. Can also be used to override the default function for natively supported model classes.- prev_shapr_object
shapr
object or string. If an object of classshapr
is provided, or string with a path to where intermediate results are stored, then the function will use the previous object to continue the computation. This is useful if the computation is interrupted or you want higher accuracy than already obtained, and therefore want to continue the iterative estimation. See the general usage for examples.- asymmetric
Logical. Not applicable for (regular) non-causal or asymmetric explanations. If
FALSE
(default),explain
computes regular symmetric Shapley values, IfTRUE
, thenexplain
compute asymmetric Shapley values based on the (partial) causal ordering given bycausal_ordering
. That is,explain
only uses the feature combinations/coalitions that respect the causal ordering when computing the asymmetric Shapley values. Ifasymmetric
isTRUE
andconfounding
isNULL
(default), thenexplain
computes asymmetric conditional Shapley values as specified in Frye et al. (2020). Ifconfounding
is provided, i.e., notNULL
, thenexplain
computes asymmetric causal Shapley values as specified in Heskes et al. (2020).- causal_ordering
List. Not applicable for (regular) non-causal or asymmetric explanations.
causal_ordering
is an unnamed list of vectors specifying the components of the partial causal ordering that the coalitions must respect. Each vector represents a component and contains one or more features/groups identified by their names (strings) or indices (integers). Ifcausal_ordering
isNULL
(default), no causal ordering is assumed and all possible coalitions are allowed. No causal ordering is equivalent to a causal ordering with a single component that includes all features (list(1:n_features)
) or groups (list(1:n_groups)
) for feature-wise and group-wise Shapley values, respectively. For feature-wise Shapley values andcausal_ordering = list(c(1, 2), c(3, 4))
, the interpretation is that features 1 and 2 are the ancestors of features 3 and 4, while features 3 and 4 are on the same level. Note: All features/groups must be included in thecausal_ordering
without any duplicates.- confounding
Logical vector. Not applicable for (regular) non-causal or asymmetric explanations.
confounding
is a vector of logicals specifying whether confounding is assumed or not for each component in thecausal_ordering
. IfNULL
(default), then no assumption about the confounding structure is made andexplain
computes asymmetric/symmetric conditional Shapley values, depending on the value ofasymmetric
. Ifconfounding
is a single logical, i.e.,FALSE
orTRUE
, then this assumption is set globally for all components in the causal ordering. Otherwise,confounding
must be a vector of logicals of the same length ascausal_ordering
, indicating the confounding assumption for each component. Whenconfounding
is specified, thenexplain
computes asymmetric/symmetric causal Shapley values, depending on the value ofasymmetric
. Theapproach
cannot beregression_separate
andregression_surrogate
as the regression-based approaches are not applicable to the causal Shapley value methodology.- extra_computation_args
Named list. Specifies extra arguments related to the computation of the Shapley values. See
get_extra_comp_args_default()
for description of the arguments and their default values.- iterative_args
Named list. Specifies the arguments for the iterative procedure. See
get_iterative_args_default()
for description of the arguments and their default values.- output_args
Named list. Specifies certain arguments related to the output of the function. See
get_output_args_default()
for description of the arguments and their default values.- ...
Arguments passed on to
setup_approach.categorical
,setup_approach.copula
,setup_approach.ctree
,setup_approach.empirical
,setup_approach.gaussian
,setup_approach.independence
,setup_approach.regression_separate
,setup_approach.regression_surrogate
,setup_approach.timeseries
,setup_approach.vaeac
categorical.joint_prob_dt
Data.table. (Optional) Containing the joint probability distribution for each combination of feature values.
NULL
means it is estimated from thex_train
andx_explain
.categorical.epsilon
Numeric value. (Optional) If
categorical.joint_probability_dt
is not supplied, probabilities/frequencies are estimated usingx_train
. If certain observations occur inx_explain
and NOT inx_train
, then epsilon is used as the proportion of times that these observations occurs in the training data. In theory, this proportion should be zero, but this causes an error later in the Shapley computation.internal
List. Not used directly, but passed through from
explain()
.ctree.mincriterion
Numeric scalar or vector. Either a scalar or vector of length equal to the number of features in the model. The value is equal to 1 - \(\alpha\) where \(\alpha\) is the nominal level of the conditional independence tests. If it is a vector, this indicates which value to use when conditioning on various numbers of features. The default value is 0.95.
ctree.minsplit
Numeric scalar. Determines minimum value that the sum of the left and right daughter nodes required for a split. The default value is 20.
ctree.minbucket
Numeric scalar. Determines the minimum sum of weights in a terminal node required for a split The default value is 7.
ctree.sample
Boolean. If
TRUE
(default), then the method always samplesn_MC_samples
observations from the leaf nodes (with replacement). IfFALSE
and the number of observations in the leaf node is less thann_MC_samples
, the method will take all observations in the leaf. IfFALSE
and the number of observations in the leaf node is more thann_MC_samples
, the method will samplen_MC_samples
observations (with replacement). This means that there will always be sampling in the leaf unlesssample = FALSE
and the number of obs in the node is less thann_MC_samples
.empirical.type
Character. (default =
"fixed_sigma"
) Should be equal to either"independence"
,"fixed_sigma"
,"AICc_each_k"
"AICc_full"
."independence"
is deprecated. Useapproach = "independence"
instead."fixed_sigma"
uses a fixed bandwidth (set throughempirical.fixed_sigma
) in the kernel density estimation."AICc_each_k"
and"AICc_full"
optimize the bandwidth using the AICc criterion, with respectively one bandwidth per coalition size and one bandwidth for all coalition sizes.empirical.eta
Numeric scalar. Needs to be
0 < eta <= 1
. The default value is 0.95. Represents the minimum proportion of the total empirical weight that data samples should use. If e.g.eta = .8
we will choose theK
samples with the largest weight so that the sum of the weights accounts for 80\eta
is the \(\eta\) parameter in equation (15) of Aas et al. (2021).empirical.fixed_sigma
Positive numeric scalar. The default value is 0.1. Represents the kernel bandwidth in the distance computation used when conditioning on all different coalitions. Only used when
empirical.type = "fixed_sigma"
empirical.n_samples_aicc
Positive integer. Number of samples to consider in AICc optimization. The default value is 1000. Only used for
empirical.type
is either"AICc_each_k"
or"AICc_full"
.empirical.eval_max_aicc
Positive integer. Maximum number of iterations when optimizing the AICc. The default value is 20. Only used for
empirical.type
is either"AICc_each_k"
or"AICc_full"
.empirical.start_aicc
Numeric. Start value of the
sigma
parameter when optimizing the AICc. The default value is 0.1. Only used forempirical.type
is either"AICc_each_k"
or"AICc_full"
.empirical.cov_mat
Numeric matrix. (Optional) The covariance matrix of the data generating distribution used to define the Mahalanobis distance.
NULL
means it is estimated fromx_train
.gaussian.mu
Numeric vector. (Optional) Containing the mean of the data generating distribution.
NULL
means it is estimated from thex_train
.gaussian.cov_mat
Numeric matrix. (Optional) Containing the covariance matrix of the data generating distribution.
NULL
means it is estimated from thex_train
.regression.model
A
tidymodels
object of classmodel_specs
. Default is a linear regression model, i.e.,parsnip::linear_reg()
. See tidymodels for all possible models, and see the vignette for how to add new/own models. Note, to make it easier to callexplain()
from Python, theregression.model
parameter can also be a string specifying the model which will be parsed and evaluated. For example,"parsnip::rand_forest(mtry = hardhat::tune(), trees = 100, engine = "ranger", mode = "regression")"
is also a valid input. It is essential to include the package prefix if the package is not loaded.regression.tune_values
Either
NULL
(default), a data.frame/data.table/tibble, or a function. The data.frame must contain the possible hyperparameter value combinations to try. The column names must match the names of the tunable parameters specified inregression.model
. Ifregression.tune_values
is a function, then it should take one argumentx
which is the training data for the current coalition and returns a data.frame/data.table/tibble with the properties described above. Using a function allows the hyperparameter values to change based on the size of the coalition See the regression vignette for several examples. Note, to make it easier to callexplain()
from Python, theregression.tune_values
can also be a string containing an R function. For example,"function(x) return(dials::grid_regular(dials::mtry(c(1, ncol(x)))), levels = 3))"
is also a valid input. It is essential to include the package prefix if the package is not loaded.regression.vfold_cv_para
Either
NULL
(default) or a named list containing the parameters to be sent torsample::vfold_cv()
. See the regression vignette for several examples.regression.recipe_func
Either
NULL
(default) or a function that that takes in arecipes::recipe()
object and returns a modifiedrecipes::recipe()
with potentially additional recipe steps. See the regression vignette for several examples. Note, to make it easier to callexplain()
from Python, theregression.recipe_func
can also be a string containing an R function. For example,"function(recipe) return(recipes::step_ns(recipe, recipes::all_numeric_predictors(), deg_free = 2))"
is also a valid input. It is essential to include the package prefix if the package is not loaded.regression.surrogate_n_comb
Positive integer. Specifies the number of unique coalitions to apply to each training observation. The default is the number of sampled coalitions in the present iteration. Any integer between 1 and the default is allowed. Larger values requires more memory, but may improve the surrogate model. If the user sets a value lower than the maximum, we sample this amount of unique coalitions separately for each training observations. That is, on average, all coalitions should be equally trained.
timeseries.fixed_sigma
Positive numeric scalar. Represents the kernel bandwidth in the distance computation. The default value is 2.
timeseries.bounds
Numeric vector of length two. Specifies the lower and upper bounds of the timeseries. The default is
c(NULL, NULL)
, i.e. no bounds. If one or both of these bounds are notNULL
, we restrict the sampled time series to be between these bounds. This is useful if the underlying time series are scaled between 0 and 1, for example.vaeac.depth
Positive integer (default is
3
). The number of hidden layers in the neural networks of the masked encoder, full encoder, and decoder.vaeac.width
Positive integer (default is
32
). The number of neurons in each hidden layer in the neural networks of the masked encoder, full encoder, and decoder.vaeac.latent_dim
Positive integer (default is
8
). The number of dimensions in the latent space.vaeac.lr
Positive numeric (default is
0.001
). The learning rate used in thetorch::optim_adam()
optimizer.vaeac.activation_function
An
torch::nn_module()
representing an activation function such as, e.g.,torch::nn_relu()
(default),torch::nn_leaky_relu()
,torch::nn_selu()
, ortorch::nn_sigmoid()
.vaeac.n_vaeacs_initialize
Positive integer (default is
4
). The number of different vaeac models to initiate in the start. Pick the best performing one aftervaeac.extra_parameters$epochs_initiation_phase
epochs (default is2
) and continue training that one.vaeac.epochs
Positive integer (default is
100
). The number of epochs to train the final vaeac model. This includesvaeac.extra_parameters$epochs_initiation_phase
, where the default is2
.vaeac.extra_parameters
Named list with extra parameters to the
vaeac
approach. Seevaeac_get_extra_para_default()
for description of possible additional parameters and their default values.
Value
Object of class c("shapr", "list")
. Contains the following items:
shapley_values_est
data.table with the estimated Shapley values with explained observation in the rows and features along the columns. The column
none
is the prediction not devoted to any of the features (given by the argumentphi0
)shapley_values_sd
data.table with the standard deviation of the Shapley values reflecting the uncertainty. Note that this only reflects the coalition sampling part of the kernelSHAP procedure, and is therefore by definition 0 when all coalitions is used. Only present when
extra_computation_args$compute_sd=TRUE
, which is the default wheniterative = TRUE
internal
List with the different parameters, data, functions and other output used internally.
pred_explain
Numeric vector with the predictions for the explained observations
MSEv
List with the values of the MSEv evaluation criterion for the approach. See the MSEv evaluation section in the general usage for details.
timing
List containing timing information for the different parts of the computation.
init_time
andend_time
gives the time stamps for the start and end of the computation.total_time_secs
gives the total time in seconds for the complete execution ofexplain()
.main_timing_secs
gives the time in seconds for the main computations.iter_timing_secs
gives for each iteration of the iterative estimation, the time spent on the different parts iterative estimation routine.
Details
The shapr
package implements kernelSHAP estimation of dependence-aware Shapley values with
eight different Monte Carlo-based approaches for estimating the conditional distributions of the data.
These are all introduced in the
general usage.
(From R: vignette("general_usage", package = "shapr")
).
Moreover,
Aas et al. (2021)
gives a general introduction to dependence-aware Shapley values, and the three approaches "empirical"
,
"gaussian"
, "copula"
, and also discusses "independence"
.
Redelmeier et al. (2020) introduces the approach "ctree"
.
Olsen et al. (2022) introduces the "vaeac"
approach.
Approach "timeseries"
is discussed in
Jullum et al. (2021).
shapr
has also implemented two regression-based approaches "regression_separate"
and "regression_surrogate"
,
as described in Olsen et al. (2024).
It is also possible to combine the different approaches, see the
general usage for more information.
The package also supports the computation of causal and asymmetric Shapley values as introduced by
Heskes et al. (2020) and
Frye et al. (2020).
Asymmetric Shapley values were proposed by
Heskes et al. (2020) as a way to incorporate causal knowledge in
the real world by restricting the possible feature combinations/coalitions when computing the Shapley values to
those consistent with a (partial) causal ordering.
Causal Shapley values were proposed by
Frye et al. (2020) as a way to explain the total effect of features
on the prediction, taking into account their causal relationships, by adapting the sampling procedure in shapr
.
The package allows for parallelized computation with progress updates through the tightly connected
future::future and progressr::progressr packages.
See the examples below.
For iterative estimation (iterative=TRUE
), intermediate results may also be printed to the console
(according to the verbose
argument).
Moreover, the intermediate results are written to disk.
This combined batch computing of the v(S) values, enables fast and accurate estimation of the Shapley values
in a memory friendly manner.
Examples
if (FALSE) { # \dontrun{
# Load example data
data("airquality")
airquality <- airquality[complete.cases(airquality), ]
x_var <- c("Solar.R", "Wind", "Temp", "Month")
y_var <- "Ozone"
# Split data into test- and training data
data_train <- head(airquality, -3)
data_explain <- tail(airquality, 3)
x_train <- data_train[, x_var]
x_explain <- data_explain[, x_var]
# Fit a linear model
lm_formula <- as.formula(paste0(y_var, " ~ ", paste0(x_var, collapse = " + ")))
model <- lm(lm_formula, data = data_train)
# Explain predictions
p <- mean(data_train[, y_var])
# (Optionally) enable parallelization via the future package
if (requireNamespace("future", quietly = TRUE)) {
future::plan("multisession", workers = 2)
}
# (Optionally) enable progress updates within every iteration via the progressr package
if (requireNamespace("progressr", quietly = TRUE)) {
progressr::handlers(global = TRUE)
}
# Empirical approach
explain1 <- explain(
model = model,
x_explain = x_explain,
x_train = x_train,
approach = "empirical",
phi0 = p,
n_MC_samples = 1e2
)
# Gaussian approach
explain2 <- explain(
model = model,
x_explain = x_explain,
x_train = x_train,
approach = "gaussian",
phi0 = p,
n_MC_samples = 1e2
)
# Gaussian copula approach
explain3 <- explain(
model = model,
x_explain = x_explain,
x_train = x_train,
approach = "copula",
phi0 = p,
n_MC_samples = 1e2
)
# ctree approach
explain4 <- explain(
model = model,
x_explain = x_explain,
x_train = x_train,
approach = "ctree",
phi0 = p,
n_MC_samples = 1e2
)
# Combined approach
approach <- c("gaussian", "gaussian", "empirical")
explain5 <- explain(
model = model,
x_explain = x_explain,
x_train = x_train,
approach = approach,
phi0 = p,
n_MC_samples = 1e2
)
# Print the Shapley values
print(explain1$shapley_values_est)
# Plot the results
if (requireNamespace("ggplot2", quietly = TRUE)) {
plot(explain1)
plot(explain1, plot_type = "waterfall")
}
# Group-wise explanations
group_list <- list(A = c("Temp", "Month"), B = c("Wind", "Solar.R"))
explain_groups <- explain(
model = model,
x_explain = x_explain,
x_train = x_train,
group = group_list,
approach = "empirical",
phi0 = p,
n_MC_samples = 1e2
)
print(explain_groups$shapley_values_est)
# Separate and surrogate regression approaches with linear regression models.
explain_separate_lm <- explain(
model = model,
x_explain = x_explain,
x_train = x_train,
phi0 = p,
approach = "regression_separate",
regression.model = parsnip::linear_reg()
)
explain_surrogate_lm <- explain(
model = model,
x_explain = x_explain,
x_train = x_train,
phi0 = p,
approach = "regression_surrogate",
regression.model = parsnip::linear_reg()
)
# Iterative estimation
# For illustration purposes only. By default not used for such small dimensions as here
# Gaussian approach
explain_iterative <- explain(
model = model,
x_explain = x_explain,
x_train = x_train,
approach = "gaussian",
phi0 = p,
n_MC_samples = 1e2,
iterative = TRUE,
iterative_args = list(initial_n_coalitions = 10)
)
} # }