treeig 0.1.6

Exact Integrated Gradients for tree ensembles.

TreeIG

TreeIG computes exact Integrated Gradients for tree-based models. It decomposes the change in a fitted tree model's scalar output between a baseline input $x_0$ and an observation $x$ into additive feature contributions.

For each observation, TreeIG returns feature attributions $\phi_j$ satisfying

$$\sum_j \phi_j = F(x) - F(x_0),$$

where $F$ is the scalar model output being explained. For regression models, $F$ is the prediction. For supported classifiers, $F$ is the raw margin/logit, not the predicted probability.

Integrated Gradients (Sundararajan, Taly, and Yan, 2017) defines feature attributions by integrating model gradients along a straight-line path from a baseline $x_0$ to the observation $x$.

At first glance, Integrated Gradients appears mismatched with piecewise-constant tree models: gradients vanish almost everywhere and are undefined at split boundaries. Hentschel (2026) shows that, for tree-based models, the path-integral of the gradients reduces to the sum of prediction jumps at split boundaries crossed along the integration path. The resulting attribution is exact — no Monte Carlo sampling, no numerical quadrature, no approximation parameters.

Because TreeIG replaces numerical quadrature and sampling with a finite sum over split crossings, it is fast in practice. For many real-world models — hundreds of trees, hundreds of features — attribution over thousands of observations completes in a few milliseconds on a modern laptop. (See the example notebook for timings.) For many typical use cases TreeIG is competitive with, and often faster than, TreeSHAP, which is itself considered fast.

TreeIG also includes TreeIGNumeric, a model-agnostic fallback that recovers the same crossing-sum attribution through numerical event detection when exact structural support is unavailable.

Installation

pip install treeig

Requires Python ≥ 3.9, NumPy, and Numba. Model backends (scikit-learn, XGBoost, LightGBM) are not installed automatically; install whichever you use.

Quickstart

import numpy as np
import treeig as tig

# model is a fitted supported tree model
x0 = X_train.mean(axis=0)
X_eval = X_test[:100]

ig = tig.TreeIG(model, baseline=x0)
phi = ig.attribute(X_eval)

phi has the same shape as X_eval. Row i, column j is the contribution of feature j to the model-output change from x_0 to X_eval[i].

For regression models, the completeness property holds exactly:

np.testing.assert_allclose(
    phi.sum(axis=1),
    model.predict(X_eval) - model.predict(x0.reshape(1, -1))[0],
)

Why TreeIG?

Standard Integrated Gradients defines feature contributions by integrating model gradients along a straight-line path from a baseline input to the observation. Tree models are piecewise constant, so ordinary gradients are zero almost everywhere and undefined at split boundaries.

TreeIG uses the tree structure directly. Along the interpolation path

$$ x(t) = x_0 + t,(x - x_0),\qquad 0 \le t \le 1, $$

a tree prediction changes only when the path crosses a split threshold. TreeIG finds those crossings exactly and assigns each prediction jump to the feature responsible for the crossing. For ensembles, contributions are summed across trees. The result is an exact additive decomposition without numerical quadrature.

The distributional-derivative perspective makes this precise. Along the interpolation path the prediction is piecewise constant, and its generalized derivative is a sum of localized impulses at split crossings. The path integral of each impulse is exactly the prediction jump at that crossing.

The top panel shows a step in the tree prediction along the interpolation path. The middle panel shows the corresponding distributional derivative: zero everywhere except at the split crossing. (Here, $\delta(t - t^\ast)$ is the Dirac delta distribution centered at $t^\ast$.) The bottom panel shows that the path integral localizes exactly at the crossing and recovers the prediction jump. TreeIG exploits the fact that integrated gradients applied to trees requires neither numerical differentiation nor numerical integration; it reduces to a simple sum of prediction steps along the integration path $x(t)$.

Standard numerical Integrated Gradients methods try to approximate these impulses using dense interpolation grids. TreeIG instead computes the split-crossing contributions analytically from the fitted tree structure. In this sense, TreeIG plays a role analogous to automatic differentiation for smooth models: rather than numerically searching for discontinuities, it uses the model's computational structure to evaluate the attribution integral exactly and efficiently. (The analogy understates the gain. Automatic differentiation removes derivative approximation but not the numerical quadrature used by Integrated Gradients. TreeIG exploits tree structure to evaluate the attribution integral itself exactly.)

Supported models

TreeIG currently supports tree models with finite numeric feature inputs.

Regression

• sklearn.tree.DecisionTreeRegressor
• sklearn.ensemble.RandomForestRegressor
• sklearn.ensemble.ExtraTreesRegressor
• sklearn.ensemble.GradientBoostingRegressor
• xgboost.XGBRegressor
• xgboost.Booster
• lightgbm.LGBMRegressor
• lightgbm.Booster

Classification (raw margins/logits only)

• sklearn.ensemble.GradientBoostingClassifier
• xgboost.XGBClassifier
• lightgbm.LGBMClassifier

For classification models, TreeIG attributes raw margins or logits. It does not attribute predicted probabilities because these are not additive across trees.

TreeIG computes exact path decompositions directly from the fitted tree structure. Since tree representations differ substantially across implementations, each model family requires customized parsing and routing logic.

Exact support not currently available

The exact TreeIG parser does not currently support:

• CatBoost;
• categorical splits;
• missing-value routing (use feature augmentation for missingness);
• probability-output attribution (because probability attribution is not additive);
• probability-averaging or vote-share classifiers such as DecisionTreeClassifier, RandomForestClassifier, and ExtraTreesClassifier (because they produce probabilities, not scores).

Many of these can still be attributed with the model-agnostic TreeIGNumeric, described below.

TreeIGNumeric

TreeIGNumeric is a model-agnostic fallback that recovers the crossing-sum attribution by numerically detecting prediction discontinuities along the integration path. It requires no access to model internals — only repeated evaluations of the prediction function — so it applies to many piecewise-constant models the exact parser does not support. Whenever a supported backend is available, exact TreeIG should be preferred.

TreeIGNumeric scans a numerical grid along the integration path to locate changes in the prediction, then uses local axis-aligned probes at each detected change to attribute the step to a feature. It preserves completeness for the detected changes and typically produces attributions very similar to exact TreeIG. Because it locates crossings numerically, multiple nearby crossings may occasionally be merged into a single event; exact TreeIG avoids this by enumerating crossings directly from the tree structure.

Two caveats on coverage:

• CatBoost and other encoded models. TreeIGNumeric removes the parsing barrier, but not the modeling one: interpolating a native categorical feature along the straight-line path is not meaningful, which is a property of Integrated Gradients itself, not of the implementation. TreeIGNumeric works on CatBoost (and similar) models with numeric or one-hot-encoded inputs.
• Probability-averaging classifiers. For models without an additive score (e.g. RandomForestClassifier), TreeIGNumeric explains a class probability, so completeness holds in probability space: $\sum_j \phi_j = p(x) - p(x_0)$.

import treeig as tig

ig = tig.TreeIGNumeric(model, baseline=x0)
phi, infos, summary = ig.explain(X_eval)

print(summary["mean_abs_residual"])

Diagnostics

Use explain when you want attributions together with completeness diagnostics.

ig = tig.TreeIG(model, baseline=x0)
phi, infos, summary = ig.explain(X_eval)

print(summary)

Each entry in infos contains diagnostics for one observation:

{
    "n_events":        ...,   # number of split-crossing events
    "endpoint_delta":  ...,   # F(x) - F(x0)
    "attribution_sum": ...,   # sum_j phi_j
    "residual":        ...,   # attribution_sum - endpoint_delta
    "abs_residual":    ...,
}

TreeIGNumeric returns the same fields plus n_coincident_events, the number of events at which multiple crossings were merged and allocated by the fallback rule. The summary dictionary reports aggregate residual and event-count statistics.

Classification targets

For binary additive-score classifiers, target=None and target=1 both attribute the positive-class margin. target=0 attributes the negative margin, implemented as the negative of the positive-class margin.

ig = tig.TreeIG(model, baseline=x0, target=1)
phi_pos = ig.attribute(X_eval)

ig = tig.TreeIG(model, baseline=x0, target=0)
phi_neg = ig.attribute(X_eval)

For multiclass classifiers, pass the class index explicitly.

ig = tig.TreeIG(model, baseline=x0, target=2)
phi_class_2 = ig.attribute(X_eval)

TreeIG attributes raw class margins. If probability-space explanations are needed, users should transform or interpret the margin-level contributions separately.

Functional interface

TreeIG also provides a direct functional interface.

phi, infos, summary = tig.compute(
    model,
    baseline=x0,
    X=X_eval,
)

Warmup

TreeIG uses Numba for fast parallel attribution kernels. The first call includes JIT compilation. You can compile in advance with warmup:

ig = tig.TreeIG(model, baseline=x0).warmup(X_eval[:3])
phi = ig.attribute(X_eval)

Subsequent calls on the same model are fast. Attribution for thousands of observations on a typical ensemble completes in well under a second after warmup.

Numerical conventions

TreeIG follows each backend's split-routing convention as closely as possible.

• scikit-learn trees route left when x[j] <= threshold;
• LightGBM numeric splits route left when x[j] <= threshold;
• XGBoost numeric splits route left when x[j] < threshold using float32-style comparisons.

Inputs must be finite numeric arrays. Missing-value routing is not currently implemented, so NaN and Inf values raise errors.

Baselines

The baseline $x_0$ defines the reference point for the decomposition. Common choices include the training-sample mean, a median or representative observation, a domain-specific neutral input, or a fixed benchmark case.

The attribution always explains the difference between the model output at the observation and the model output at the chosen baseline. Different baselines answer different questions.

Interpretation

For an observation $x$, TreeIG reports how much each feature contributes to moving the model output from $F(x_0)$ to $F(x)$ along the straight-line path from $x_0$ to $x$. Positive contributions increase the scalar output relative to the baseline; negative contributions decrease it. The contributions are additive by construction.

Relation to SHAP and TreeSHAP

TreeIG and TreeSHAP answer different attribution questions and generally produce different decompositions. Neither dominates the other.

TreeIG answers: "How much does feature $j$ contribute to the change in prediction as we move continuously from baseline $x_0$ to observation $x$?" The attribution is the integral of partial derivatives along the path from $x_0$ to $x$, which for piecewise-constant trees reduces exactly to a sum of prediction jumps at the split boundaries crossed along the path.

TreeSHAP answers: "How much does feature $j$ shift the expected prediction, averaged over all possible subsets of the other features?" The attribution is an average of discrete inclusion effects, where absent features are marginalized out over a background dataset. There is no path; the reference is the expected prediction over the background distribution.

The two differ in two ways. First, TreeIG takes a specific baseline input $x_0$ as its reference, while TreeSHAP uses a background distribution. Second, TreeIG measures contributions through calculus — integrating how the prediction changes as features move continuously from their baseline values — while TreeSHAP measures them through discrete feature inclusion, asking how much each feature changes the expected prediction when it enters a coalition.

The practical consequence is one of scope. SHAP's coalition construction is indifferent to the prediction surface between the background and the observation: a feature is either in the coalition or out, so the attribution is built from discrete switches and explores a wide neighborhood of hybrid inputs, many far from any natural path between real observations. IG instead follows a single path and accumulates exactly the prediction changes along it, evaluating the model only at convex combinations of two real inputs. SHAP explores a neighborhood; IG traces a path. SHAP's breadth gives sensitivity to model behavior across many feature combinations; IG's specificity gives a precise account of one trajectory through input space.

For a linear model with independent features and $x_0$ equal to the background mean, TreeIG and interventional SHAP coincide. (A linear model is not a tree, so the comparison is to SHAP generally rather than to TreeSHAP.) As the model becomes more nonlinear or the baseline $x_0$ diverges from the background distribution, the two increasingly disagree — reflecting genuine differences in the questions they answer rather than errors in either method.

Examples

XGBoost regression

import numpy as np
import xgboost as xgb
import treeig as tig

model = xgb.XGBRegressor(
    n_estimators=100,
    max_depth=3,
    learning_rate=0.05,
    objective="reg:squarederror",
    random_state=0,
)
model.fit(X_train, y_train)

x0 = X_train.mean(axis=0)
X_eval = X_test[:100]

ig = tig.TreeIG(model, baseline=x0).warmup(X_eval[:3])
phi, infos, summary = ig.explain(X_eval)

print(phi.shape)
print(summary["max_abs_residual"])

Multiclass classification margins

import lightgbm as lgb
import treeig as tig

model = lgb.LGBMClassifier(...)
model.fit(X_train, y_train)

x0 = X_train.mean(axis=0)
X_eval = X_test[:100]

# Attribute class-2 raw margin
ig = tig.TreeIG(model, baseline=x0, target=2)
phi = ig.attribute(X_eval)

Model-agnostic attribution

import treeig as tig

ig = tig.TreeIGNumeric(model, baseline=x0)
phi, infos, summary = ig.explain(X_eval)

print(summary["mean_abs_residual"])

Project status

TreeIG is production-ready for exact attribution of supported tree models in raw-output space. The current release covers the dominant tree ensemble backends in the Python ecosystem. TreeIGNumeric provides a model-agnostic fallback for unsupported piecewise-constant models.

Future extensions may include:

• exact structural support for CatBoost and other currently unsupported tree implementations;
• customized handling of categorical split structures and missing-value routing;
• alternative allocation rules for simultaneous multi-feature effects at coincident crossings.

Citation

If you use TreeIG in your work, please cite:

@misc{hentschel2026treeig,
  author = {Hentschel, Ludger},
  title  = {{TreeIG}: Exact Integrated Gradients for Tree-Based Models},
  year   = {2026},
  url    = {https://www.ludgerhentschel.com/PDFs/Hentschel%20'26g.pdf},
}

License

TreeIG is released under the terms in LICENSE.

References

TreeIG:

• Hentschel, Ludger. 2026. "TreeIG: Exact Integrated Gradients for Tree-Based Models." https://www.ludgerhentschel.com/Research.html and https://www.ludgerhentschel.com/Programs.html

Integrated Gradients:

• Sundararajan, Mukund, Ankur Taly, and Qiqi Yan. 2017. "Axiomatic Attribution for Deep Networks." International Conference on Machine Learning (ICML).

SHAP and TreeSHAP:

• Lundberg, Scott M., and Su-In Lee. 2017. "A Unified Approach to Interpreting Model Predictions." Advances in Neural Information Processing Systems (NeurIPS).

• Lundberg, Scott M., Gabriel Erion, and Su-In Lee. 2020. "From Local Explanations to Global Understanding with Explainable AI for Trees." Nature Machine Intelligence.

Popular implementations of Integrated Gradients for smooth models:

• Captum for PyTorch: https://captum.ai/
• TensorFlow Integrated Gradients: https://www.tensorflow.org/tutorials/interpretability/integrated_gradients