Kernel SHAP is a method that uses the LIME framework to compute Shapley Values. Setting the loss function, weighting kernel and regularization terms appropriately in the LIME framework allows theoretically obtaining Shapley Values more efficiently than directly computing Shapley Values.
More information regarding this method and proof of equivalence can be found in the original paper here: https://arxiv.org/abs/1705.07874
forward_func (callable) – The forward function of the model or any modification of it
attribute(inputs, baselines=None, target=None, additional_forward_args=None, feature_mask=None, n_samples=25, perturbations_per_eval=1, return_input_shape=True, show_progress=False)¶
This method attributes the output of the model with given target index (in case it is provided, otherwise it assumes that output is a scalar) to the inputs of the model using the approach described above, training an interpretable model based on KernelSHAP and returning a representation of the interpretable model.
It is recommended to only provide a single example as input (tensors with first dimension or batch size = 1). This is because LIME / KernelShap is generally used for sample-based interpretability, training a separate interpretable model to explain a model’s prediction on each individual example.
A batch of inputs can also be provided as inputs, similar to other perturbation-based attribution methods. In this case, if forward_fn returns a scalar per example, attributions will be computed for each example independently, with a separate interpretable model trained for each example. Note that provided similarity and perturbation functions will be provided each example separately (first dimension = 1) in this case. If forward_fn returns a scalar per batch (e.g. loss), attributions will still be computed using a single interpretable model for the full batch. In this case, similarity and perturbation functions will be provided the same original input containing the full batch.
The number of interpretable features is determined from the provided feature mask, or if none is provided, from the default feature mask, which considers each scalar input as a separate feature. It is generally recommended to provide a feature mask which groups features into a small number of interpretable features / components (e.g. superpixels in images).
inputs (tensor or tuple of tensors) – Input for which KernelShap is computed. If forward_func takes a single tensor as input, a single input tensor should be provided. If forward_func takes multiple tensors as input, a tuple of the input tensors should be provided. It is assumed that for all given input tensors, dimension 0 corresponds to the number of examples, and if multiple input tensors are provided, the examples must be aligned appropriately.
baselines (scalar, tensor, tuple of scalars or tensors, optional) –
Baselines define the reference value which replaces each feature when the corresponding interpretable feature is set to 0. Baselines can be provided as:
a single tensor, if inputs is a single tensor, with exactly the same dimensions as inputs or the first dimension is one and the remaining dimensions match with inputs.
a single scalar, if inputs is a single tensor, which will be broadcasted for each input value in input tensor.
a tuple of tensors or scalars, the baseline corresponding to each tensor in the inputs’ tuple can be:
either a tensor with matching dimensions to corresponding tensor in the inputs’ tuple or the first dimension is one and the remaining dimensions match with the corresponding input tensor.
or a scalar, corresponding to a tensor in the inputs’ tuple. This scalar value is broadcasted for corresponding input tensor.
In the cases when baselines is not provided, we internally use zero scalar corresponding to each input tensor. Default: None
Output indices for which surrogate model is trained (for classification cases, this is usually the target class). If the network returns a scalar value per example, no target index is necessary. For general 2D outputs, targets can be either:
a single integer or a tensor containing a single integer, which is applied to all input examples
a list of integers or a 1D tensor, with length matching the number of examples in inputs (dim 0). Each integer is applied as the target for the corresponding example.
For outputs with > 2 dimensions, targets can be either:
A single tuple, which contains #output_dims - 1 elements. This target index is applied to all examples.
A list of tuples with length equal to the number of examples in inputs (dim 0), and each tuple containing #output_dims - 1 elements. Each tuple is applied as the target for the corresponding example.
additional_forward_args (any, optional) – If the forward function requires additional arguments other than the inputs for which attributions should not be computed, this argument can be provided. It must be either a single additional argument of a Tensor or arbitrary (non-tuple) type or a tuple containing multiple additional arguments including tensors or any arbitrary python types. These arguments are provided to forward_func in order following the arguments in inputs. For a tensor, the first dimension of the tensor must correspond to the number of examples. It will be repeated for each of n_steps along the integrated path. For all other types, the given argument is used for all forward evaluations. Note that attributions are not computed with respect to these arguments. Default: None
feature_mask (tensor or tuple of tensors, optional) – feature_mask defines a mask for the input, grouping features which correspond to the same interpretable feature. feature_mask should contain the same number of tensors as inputs. Each tensor should be the same size as the corresponding input or broadcastable to match the input tensor. Values across all tensors should be integers in the range 0 to num_interp_features - 1, and indices corresponding to the same feature should have the same value. Note that features are grouped across tensors (unlike feature ablation and occlusion), so if the same index is used in different tensors, those features are still grouped and added simultaneously. If None, then a feature mask is constructed which assigns each scalar within a tensor as a separate feature. Default: None
n_samples (int, optional) – The number of samples of the original model used to train the surrogate interpretable model. Default: 50 if n_samples is not provided.
perturbations_per_eval (int, optional) – Allows multiple samples to be processed simultaneously in one call to forward_fn. Each forward pass will contain a maximum of perturbations_per_eval * #examples samples. For DataParallel models, each batch is split among the available devices, so evaluations on each available device contain at most (perturbations_per_eval * #examples) / num_devices samples. If the forward function returns a single scalar per batch, perturbations_per_eval must be set to 1. Default: 1
return_input_shape (bool, optional) – Determines whether the returned tensor(s) only contain the coefficients for each interp- retable feature from the trained surrogate model, or whether the returned attributions match the input shape. When return_input_shape is True, the return type of attribute matches the input shape, with each element containing the coefficient of the corresponding interpretable feature. All elements with the same value in the feature mask will contain the same coefficient in the returned attributions. If return_input_shape is False, a 1D tensor is returned, containing only the coefficients of the trained interpretable model, with length num_interp_features.
show_progress (bool, optional) – Displays the progress of computation. It will try to use tqdm if available for advanced features (e.g. time estimation). Otherwise, it will fallback to a simple output of progress. Default: False
- attributions (tensor or tuple of tensors):
The attributions with respect to each input feature. If return_input_shape = True, attributions will be the same size as the provided inputs, with each value providing the coefficient of the corresponding interpretale feature. If return_input_shape is False, a 1D tensor is returned, containing only the coefficients of the trained interpreatable models, with length num_interp_features.
- Return type
tensor or tuple of tensors of attributions
>>> # SimpleClassifier takes a single input tensor of size Nx4x4, >>> # and returns an Nx3 tensor of class probabilities. >>> net = SimpleClassifier()
>>> # Generating random input with size 1 x 4 x 4 >>> input = torch.randn(1, 4, 4)
>>> # Defining KernelShap interpreter >>> ks = KernelShap(net) >>> # Computes attribution, with each of the 4 x 4 = 16 >>> # features as a separate interpretable feature >>> attr = ks.attribute(input, target=1, n_samples=200)
>>> # Alternatively, we can group each 2x2 square of the inputs >>> # as one 'interpretable' feature and perturb them together. >>> # This can be done by creating a feature mask as follows, which >>> # defines the feature groups, e.g.: >>> # +---+---+---+---+ >>> # | 0 | 0 | 1 | 1 | >>> # +---+---+---+---+ >>> # | 0 | 0 | 1 | 1 | >>> # +---+---+---+---+ >>> # | 2 | 2 | 3 | 3 | >>> # +---+---+---+---+ >>> # | 2 | 2 | 3 | 3 | >>> # +---+---+---+---+ >>> # With this mask, all inputs with the same value are set to their >>> # baseline value, when the corresponding binary interpretable >>> # feature is set to 0. >>> # The attributions can be calculated as follows: >>> # feature mask has dimensions 1 x 4 x 4 >>> feature_mask = torch.tensor([[[0,0,1,1],[0,0,1,1], >>> [2,2,3,3],[2,2,3,3]]])
>>> # Computes KernelSHAP attributions with feature mask. >>> attr = ks.attribute(input, target=1, feature_mask=feature_mask)
- Perturbations are sampled by the following process:
- Choose k (number of selected features), based on the distribution
p(k) = (M - 1) / (k * (M - k))
where M is the total number of features in the interpretable space
- Randomly select a binary vector with k ones, each sample is equally
likely. This is done by generating a random vector of normal values and thresholding based on the top k elements.
Since there are M choose k vectors with k ones, this weighted sampling is equivalent to applying the Shapley kernel for the sample weight, defined as: k(M, k) = (M - 1) / (k * (M - k) * (M choose k))