MuFidelity

MuFidelity is a fidelity metric measuring the correlation between important variables defined by the explanation method and the decline in the model score when these variables are reset to a baseline state.

Quote

[...] when we set particular features \(x_s\) to a baseline value \(x_0\) the change in predictor’s output should be proportional to the sum of attribution scores.

-- Evaluating and Aggregating Feature-based Model Explanations (2020)¹

Formally, given a predictor \(f\), an explanation function \(g\), a point \(x \in \mathbb{R}^n\) and a subset size \(k\) the MuFidelity metric is defined as:

\[ \mu F = \underset{S \subseteq \{1, ..., d\} \\ |S| = k}{Corr}( \sum_{i \in S} g(f, x)_i, f(x) - f(x_{[x_i = x_0 | i \in S]})) \]

Info

The better the method, the higher the score.

Example

from xplique.metrics import MuFidelity
from xplique.attributions import Saliency

# load images, labels and model
# ...
explainer = Saliency(model)
explanations = explainer(inputs, lablels)

metric = MuFidelity(model, inputs, labels)
score = metric.evaluate(explainations)

MuFidelity

Used to compute the fidelity correlation metric. This metric ensure there is a correlation between a random subset of pixels and their attribution score. For each random subset created, we set the pixels of the subset at a baseline state and obtain the prediction score. This metric measures the correlation between the drop in the score and the importance of the explanation.

__init__(self,
         model: Callable,
         inputs: Union[tf.Dataset, tf.Tensor, numpy.ndarray],
         targets: Union[tf.Tensor, numpy.ndarray, None] = None,
         batch_size: Optional[int] = 64,
         grid_size: Optional[int] = 9,
         subset_percent: float = 0.2,
         baseline_mode: Union[Callable, float] = 0.0,
         nb_samples: int = 200,
         operator: Optional[Callable] = None,
         activation: Optional[str] = None)

Parameters

• model : Callable

  • Model used for computing metric.

• inputs : Union[tf.Dataset, tf.Tensor, numpy.ndarray]

  • Input samples under study.

• targets : Union[tf.Tensor, numpy.ndarray, None] = None

  • One-hot encoded labels or regression target (e.g {+1, -1}), one for each sample.

• batch_size : Optional[int] = 64

  • Number of samples to explain at once, if None compute all at once.

• grid_size : Optional[int] = 9

  • If none, compute the original metric, else cut the image in (grid_size, grid_size) and each element of the subset will be a super pixel representing one element of the grid.

    You should use this when dealing with medium / large size images.

• subset_percent : float = 0.2

  • Percent of the image that will be set to baseline.

• baseline_mode : Union[Callable, float] = 0.0

  • Value of the baseline state, will be called with the a single input if it is a function.

• nb_samples : int = 200

  • Number of different subsets to try on each input to measure the correlation.

• operator : Optional[Callable] = None

  • Function g to explain, g take 3 parameters (f, x, y) and should return a scalar, with f the model, x the inputs and y the targets. If None, use the standard operator g(f, x, y) = f(x)[y].

• activation : Optional[str] = None

  • A string that belongs to [None, 'sigmoid', 'softmax']. Specify if we should add an activation layer once the model has been called. It is useful, for instance if you want to measure a 'drop of probability' by adding a sigmoid or softmax after getting your logits. If None does not add a layer to your model.

evaluate(self,
         explanations: Union[tf.Tensor, numpy.ndarray]) -> float

Evaluate the fidelity score.

Parameters

• explanations : Union[tf.Tensor, numpy.ndarray]

  • Explanation for the inputs, labels to evaluate.

Return

• fidelity_score : float

  • Metric score, average correlation between the drop in score when variables are set to a baseline state and the importance of these variables according to the explanations.

---

1. Evaluating and Aggregating Feature-based Model Explanations (2020) ↩