Counterfactual Inference

The first step in the three-step counterfactual inference process. Abduction uses the observed factual evidence to compute the posterior distribution over the exogenous noise variables (U) in a Structural Causal Model. This step explains the specific unobserved randomness that led to the actual outcome. Without abduction, you cannot personalize the counterfactual to the specific individual or unit; you would only compute a generic interventional distribution.

The second step where the structural causal model is physically modified to simulate the hypothetical intervention. This is formalized using the do-operator and involves 'graph surgery': removing all incoming edges to the intervened variable and setting its value to a constant. This breaks the natural causal flow and ensures the effect of the intervention is isolated from confounding factors. This step transforms the original model into a mutilated sub-model representing the counterfactual world.

The final step where the updated noise posteriors from the abduction step are passed through the surgically altered model from the action step. By propagating these specific noise values forward through the modified structural equations, the model calculates the precise outcome that would have occurred for that specific unit under the hypothetical scenario. This distinguishes counterfactual inference from standard interventional queries, which average over the entire population noise distribution.

A special case of inference where the structural equations are assumed to have no unobserved randomness. In this scenario, the abduction step is trivial because the noise variables are uniquely identified from the observations. The counterfactual outcome is a single deterministic value rather than a distribution. This is common in algorithmic recourse systems where the model's prediction function is fully known and deterministic, simplifying the computation of the nearest counterfactual.

The general case where structural equations involve unobserved exogenous noise, leading to a distribution over potential counterfactual outcomes. The result is not a single value but a probability distribution reflecting the inherent uncertainty about the unit's unobserved characteristics. This is crucial for counterfactual fairness assessments, where we must compute the probability that an individual would have received a different decision had their sensitive attribute been different, accounting for all possible latent profiles consistent with their observed data.

A computational architecture for performing counterfactual inference in deep learning models. It involves constructing a single neural network that encodes both the factual and counterfactual worlds simultaneously, sharing the noise variables between them. The factual network computes the abduction, while the counterfactual network applies the intervention and prediction. This allows gradient-based optimization to generate counterfactual explanations directly, bypassing the need for explicit probabilistic inference in complex, high-dimensional models.