Individual Conditional Expectation (ICE)

Intuition

"What would the model predict for this person if only their age changed?" Keep everything else fixed, sweep one feature over a range, and plot the prediction. That curve is an ICE curve.

Precise explanation

For a model predict(X) -> (n,), an instance $x$, feature $j$ and grid values $g_1..g_m$: build $m$ copies of $x$, set column $j$ to $g_k$ in copy $k$, and predict all copies in one batch. Black-box: only predictions are needed, not model internals (model-agnostic). Caveat: if features are correlated, some grid points create unrealistic inputs (e.g. 5 rooms in a 20 m² flat).

Figure (original): each line is one instance; different shapes reveal interactions that an average (PDP, XA-06) would hide.

Worked example

predict(X) = X[:,0]·X[:,1]; x = [2, 3]; vary feature 0 over [0, 1, 2] → [0, 3, 6] (slope = 3 = this instance's x₁ value).

Common mistakes

• Modifying the original instance in place.
• Calling the model once per grid point in a Python loop (slow for real models).
• Interpreting ICE as causal effects in the real world.

Why this matters

ICE curves are the building block of partial dependence (XA-06) and a practical "what-if" tool.

References

• Interpretable Machine Learning (3rd edition) — Christoph Molnar (S024)