Partial Dependence & ICE Plot Explorer

Feature To Explain

Model & Data

Interaction strength k 0.40

Instances N 18

Show ICE curves per instance

Live Readouts

PDP range

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ICE spread (σ)

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Instances used

Response surface f(x₁,x₂)

ICE curve — one instance, other feature held fixed

PDP — average over all instances

How it works

The bars form a model's response surface y = f(x₁, x₂) over a grid. For a chosen feature x_j, the Partial Dependence Plot averages the model's output over the marginal distribution of the other feature x_{-j}, using the n instances actually sampled here as the empirical distribution:

PDP_j(x) = (1/n) · Σ_i f(x, x_{-j}^(i))

Each term in that sum, plotted on its own instead of averaged, is one ICE curve:

ICE_i(x) = f(x, x_{-j}^(i))

With no interaction (k = 0) every instance's curve has the same shape, just shifted — the amber ICE curves sit parallel and the white PDP line summarizes them perfectly. As |k| grows, the interaction term k·x₁·x₂ makes each instance's curve tilt by a different amount depending on its fixed x_{-j} value, so the ICE curves fan out and the single PDP average starts to hide real, instance-specific behaviour — exactly the failure mode the article describes ("PDP assumes independence, can be misleading under correlation/interaction").

Vary x₁ / Vary x₂ — choose which axis is swept to build the PDP/ICE curves; the other feature is held at each instance's own sampled value.
Interaction strength k — coefficient of the k·x₁·x₂ term in the underlying model; watch the ICE spread readout grow with |k|.
Instances N — how many sampled data points (and ICE curves) the PDP is averaged over.
Resample instances — draws a fresh random set of (x₁,x₂) sample points from the surface.

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