Implements gradient SHAP based on the implementation from SHAP’s primary author. For reference, please, view:

A Unified Approach to Interpreting Model Predictions http://papers.nips.cc/paper7062-a-unified-approach-to-interpreting-model-predictions

GradientShap approximates SHAP values by computing the expectations of gradients by randomly sampling from the distribution of baselines/references. It adds white noise to each input sample n_samples times, selects a random baseline from baselines’ distribution and a random point along the path between the baseline and the input, and computes the gradient of outputs with respect to those selected random points. The final SHAP values represent the expected values of gradients * (inputs - baselines).

GradientShap makes an assumption that the input features are independent and that the explanation model is linear, meaning that the explanations are modeled through the additive composition of feature effects. Under those assumptions, SHAP value can be approximated as the expectation of gradients that are computed for randomly generated n_samples input samples after adding gaussian noise n_samples times to each input for different baselines/references.

In some sense it can be viewed as an approximation of integrated gradients by computing the expectations of gradients for different baselines.

Current implementation uses Smoothgrad from NoiseTunnel in order to randomly draw samples from the distribution of baselines, add noise to input samples and compute the expectation (smoothgrad).

Parameters
• forward_func (function) – The forward function of the model or any modification of it.

• multiply_by_inputs (bool, optional) –

Indicates whether to factor model inputs’ multiplier in the final attribution scores. In the literature this is also known as local vs global attribution. If inputs’ multiplier isn’t factored in then this type of attribution method is also called local attribution. If it is, then that type of attribution method is called global. More detailed can be found here: https://arxiv.org/abs/1711.06104

In case of gradient shap, if multiply_by_inputs is set to True, the sensitivity scores of scaled inputs are being multiplied by (inputs - baselines).

attribute(inputs: TensorOrTupleOfTensorsGeneric, baselines: Union[TensorOrTupleOfTensorsGeneric, Callable[..., TensorOrTupleOfTensorsGeneric]], n_samples: int = 5, stdevs: Union[float, Tuple[float, ...]] = 0.0, target: TargetType = None, additional_forward_args: Any = None, *, return_convergence_delta: Literal[True]) Tuple[TensorOrTupleOfTensorsGeneric, Tensor][source]
attribute(inputs: TensorOrTupleOfTensorsGeneric, baselines: Union[TensorOrTupleOfTensorsGeneric, Callable[..., TensorOrTupleOfTensorsGeneric]], n_samples: int = 5, stdevs: Union[float, Tuple[float, ...]] = 0.0, target: TargetType = None, additional_forward_args: Any = None, return_convergence_delta: Literal[False] = False) TensorOrTupleOfTensorsGeneric
Parameters
• inputs (tensor or tuple of tensors) – Input for which SHAP attribution values are 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 (tensor, tuple of tensors, callable) –

Baselines define the starting point from which expectation is computed and can be provided as:

• a single tensor, if inputs is a single tensor, with the first dimension equal to the number of examples in the baselines’ distribution. The remaining dimensions must match with input tensor’s dimension starting from the second dimension.

• a tuple of tensors, if inputs is a tuple of tensors, with the first dimension of any tensor inside the tuple equal to the number of examples in the baseline’s distribution. The remaining dimensions must match the dimensions of the corresponding input tensor starting from the second dimension.

• callable function, optionally takes inputs as an argument and either returns a single tensor or a tuple of those.

It is recommended that the number of samples in the baselines’ tensors is larger than one.

• n_samples (int, optional) – The number of randomly generated examples per sample in the input batch. Random examples are generated by adding gaussian random noise to each sample. Default: 5 if n_samples is not provided.

• stdevs (float, or a tuple of floats optional) – The standard deviation of gaussian noise with zero mean that is added to each input in the batch. If stdevs is a single float value then that same value is used for all inputs. If it is a tuple, then it must have the same length as the inputs tuple. In this case, each stdev value in the stdevs tuple corresponds to the input with the same index in the inputs tuple. Default: 0.0

• target (int, tuple, tensor or list, optional) –

Output indices for which gradients are computed (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.

Default: None

• 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 can contain a tuple of ND tensors or any arbitrary python type of any shape. In case of the ND tensor the first dimension of the tensor must correspond to the batch size. It will be repeated for each n_steps for each randomly generated input sample. Note that the gradients are not computed with respect to these arguments. Default: None

• return_convergence_delta (bool, optional) – Indicates whether to return convergence delta or not. If return_convergence_delta is set to True convergence delta will be returned in a tuple following attributions. Default: False

Returns

• attributions (tensor or tuple of tensors):

Attribution score computed based on GradientSHAP with respect to each input feature. Attributions will always be the same size as the provided inputs, with each value providing the attribution of the corresponding input index. If a single tensor is provided as inputs, a single tensor is returned. If a tuple is provided for inputs, a tuple of corresponding sized tensors is returned.

• delta (tensor, returned if return_convergence_delta=True):

This is computed using the property that the total sum of forward_func(inputs) - forward_func(baselines) must be very close to the total sum of the attributions based on GradientSHAP. Delta is calculated for each example in the input after adding n_samples times gaussian noise to each of them. Therefore, the dimensionality of the deltas tensor is equal to the number of examples in the input * n_samples The deltas are ordered by each input example and n_samples noisy samples generated for it.

Return type

attributions or 2-element tuple of attributions, delta

Examples:

>>> # ImageClassifier takes a single input tensor of images Nx3x32x32,
>>> # and returns an Nx10 tensor of class probabilities.
>>> net = ImageClassifier()
>>> input = torch.randn(3, 3, 32, 32, requires_grad=True)
>>> # choosing baselines randomly
>>> baselines = torch.randn(20, 3, 32, 32)
>>> # Computes gradient shap for the input
>>> # Attribution size matches input size: 3x3x32x32