Recipe: KernelSHAP Basics¶

What you'll build: KernelSHAP explaining a purely linear network. For a linear model the true Shapley values have a known closed form, so you can check the explainer's output exactly.

CMake target: kernel_shap_basics_recipe (examples/recipes/kernel_shap_basics.cpp).

Run it: ./build/kernel_shap_basics_recipe (Windows: build\Release\kernel_shap_basics_recipe.exe).

Code¶

LinearModule linear(3, 1, &backend);
linear.set_weight({2.0f, -3.0f, 5.0f});
linear.set_bias({100.0f});  // deliberately large/irrelevant

ExplainerContext ctx({&linear});
auto predict = [&ctx](const Tensor& x) { return ctx.forward_pass(x); };

Tensor input(Shape({1, 3}), &backend, {1.0f, 2.0f, 3.0f});
Tensor baseline(Shape({1, 3}), &backend, {0.0f, 0.0f, 0.0f});

KernelSHAP shap;
Attribution attr = shap.explain(predict, input, baseline, /*target_index=*/0, &backend);

Full source: examples/recipes/kernel_shap_basics.cpp.

Expected output¶

KernelSHAP recipe -- linear network f(x) = 2*x0 - 3*x1 + 5*x2 + 100

feature  phi (SHAP)    w*(x-b)
x0           2.0000     2.0000
x1          -6.0000    -6.0000
x2          15.0000    15.0000
...

What's happening¶

For a linear model, the Shapley value of feature i is exactly w_i * (x_i - baseline_i). KernelSHAP::explain() evaluates every coalition (each mix of "present" and "baseline" features). It weights each coalition by the SHAP kernel and solves a weighted regression.

On a linear model this recovers the closed form exactly: the phi column matches w*(x-b) to four decimal places. The large bias appears in every coalition's f(S), so it cancels out.