Global Surrogate Models

A gradient-boosted tree ensemble with 800 trees produces excellent predictions but no human can read 800 trees and say what the model "believes." A global surrogate model sidesteps that by training a second, deliberately simple model — a shallow decision tree or a linear regression — to predict the outputs of the first model, not the original labels. If the simple model can reproduce the complex model's predictions well, its readable logic becomes an approximate window into the complex model's behavior.

How it works

The recipe has three steps: generate a large set of inputs (the original training data, or fresh samples spanning the input space), run the complex "black box" model on each to get its predictions, then fit an interpretable model — most often a shallow decision tree, capped at depth 3 or 4 — to predict those black-box outputs from the same features. The surrogate's own accuracy at matching the black box, often reported as $R^2$ for regression or agreement rate for classification, tells you how much to trust its explanation. A surrogate with $R^2 = 0.95$ is a decent proxy; one with $R^2 = 0.4$ is telling you the black box's logic doesn't collapse into anything simple, which is itself useful information.

Worked example

A quant firm has a neural network that scores 2,000 stocks daily on expected next-week return using twelve features. To understand the model's broad logic, they sample 50,000 (feature, prediction) pairs from a year of scores and fit a depth-3 decision tree to predict the network's score from the same twelve features. The tree achieves $R^2 = 0.81$ against the network's outputs and its first split is on 60-day price momentum above or below a threshold, the second split on short-interest percentile. Reading the tree, the desk learns the network's dominant behavior is roughly "buy momentum unless short interest is very high" — a genuinely useful summary, even though the tree misses the remaining 19% of the network's more intricate, higher-order interactions.

What this means in practice

Global surrogates are cheap, model-agnostic, and give a whole-model summary rather than a single prediction's explanation, which is exactly what a risk committee often wants before approving a strategy: "roughly, what is this model doing?" They're a starting point, not a substitute for the real model — trading decisions should never be routed through the surrogate itself, only through the audited black box, with the surrogate serving as documentation and a sanity check.