🔍 Counterfactual Explanations

Counterfactual Explanations#

Explaining a decision by the smallest input change that would flip it.

Important

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What it is#

A counterfactual explanation shows how a prediction would change if the input were different, answering: what minimal change to this input would flip the model’s decision? It borrows the causal idea of a counterfactual — what would have happened if …?

The formal definition#

Given an instance $x$ with prediction $f(x)$, a counterfactual is an alternative $x'$ that changes the outcome yet stays as close as possible to $x$:

\[\min_{x'} \; d(x, x') \quad \text{s.t.} \quad f(x') = y_{\text{desired}},\]

with $f(x') \neq f(x)$ and $d(\cdot)$ a distance metric (L1, L2 or a feature-specific cost).

A worked example#

For a denied loan, a counterfactual might say: if income rose by $5,000, or the credit score were 650 instead of 600, the loan would be approved — actionable recourse. Good counterfactuals are valid (they flip the prediction), proximal and sparse (few, small changes), actionable (realistic and controllable — “get older” is not), and diverse (several options).

Methods and uses#

They are generated by optimisation, gradient search (for differentiable models) or generative models (VAE, GAN) for realism, via libraries like alibi and dice-ml. They power user recourse (“what must I change?”), fairness audits (do minority groups need unfairly large changes for the same decision?) and model debugging — but they can be unrealistic (e.g. “if gender changed”), are non-unique, and need domain constraints to stay valid and fair.

Theme: Explainability & Governance · All terminology

Hint

Mind map — connected ideas

SHAP (SHapley Additive exPlanations) · LIME (Local Interpretable Model-agnostic Explanations) · Causal Effect · Causal Inference · Post-hoc Explainability · Equalized Odds (Fairness)

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More in Explainability & Governance

Basel III · Fair Lending laws · High-Stakes Domains · LIME (Local Interpretable Model-agnostic Explanations) · Post-hoc Explainability · SHAP (SHapley Additive exPlanations)