qshap: Fast Shapley Decomposition of $R^2$ for Gradient-Boosted Trees

Numerous methods have been developed to quantify feature attributions in individual predictions for tree ensembles. However, many applications require global measures of feature contributions to overall model performance. Although local attribution scores can be aggregated to characterize feature importance, such summaries do not directly decompose measures of predictive performance, such as $R^2$. This article introduces qshap, available in both R and Python, which provides Shapley decomposition of $R^2$ values for gradient-boosted decision trees (GBDTs) to quantify feature-specific contributions to model performance. By decomposing the quadratic loss of individual observations, qshap provides flexible tools to explore the importance of individual features and observations. qshap currently supports widely used GBDT implementations, including xgboost, lightgbm, and catboost, through a unified tree representation and efficient C++ backends. Its modular design can accommodate other GBDT implementations built from binary decision trees. In addition, we introduce a specialized backend for oblivious trees that exploits their symmetric structure to substantially accelerate computation.

CAS: A Causal Attribution Score for Local and Global Explainable Artificial Intelligence

Predictive explanation methods attribute a model output; they do not, by themselves, attribute an intervention effect on the real-world outcome. We introduce the Causal Attribution Score (CAS), a compact score architecture for causal explanation. CAS starts from an identified interventional coalition game, allocates the joint intervention contrast with causal Shapley contributions, and converts those raw outcome-scale effects into Local CAS, Signed Local CAS, and two complementary Global CAS summaries. The innovation is not a new Shapley formula, but a local-to-global causal reporting layer with an explicit intervention target. In the known-truth benchmark, eight repeated primary-interaction simulations (n = 2,200 each, three actions) gave mean Local CAS MAE of 0.107 for coalition-aware CAS, compared with 0.173 for one-at-a-time normalisation and 0.213 for a global normalised absolute ATE vector. The paired advantage over one-at-a-time normalisation increased from -0.003 under additivity to 0.091 under strong interactions. On both empirical DoubleML datasets, 401(k) eligibility/net financial assets (n = 9,915) and Pennsylvania reemployment bonus/unemployment duration (n = 5,099), predictive SHAP/TreeSHAP rankings differed materially from Feature-CAS rankings of treatment-effect modifiers. In Pennsylvania, dep1 (exactly one dependent) moved from predictive global rank 13 to Feature-CAS rank 2 and was the leading local Feature-CAS modifier. These results isolate the added value of separating what predicts the outcome from what explains heterogeneity in an estimated causal effect.

RelShap: Relationally Consistent Shapley Explanations

Machine learning pipelines commonly flatten relational data into single-table representations, discarding structural constraints. Widely used Shapley value-based feature attributions then rely on feature independence, evaluating the model on combinations that could never arise in the underlying data, producing misleading explanations. We propose RelShap, a framework that incorporates relational constraints and data provenance into Shapley value computation, restricting both background data and coalition evaluation to relationally valid configurations. The framework is estimator-agnostic and composes with Kernel SHAP, Monte Carlo, and Leverage SHAP without altering their sampling or weighting properties. Functional dependencies further induce equivalence classes over feature coalitions, which RelShap exploits to reduce runtime without changing Shapley values; we provide a combinatorial characterization of the expected speedup. Experiments across multiple datasets, models, and estimators show that RelShap produces explanations that are more faithful to the data-generating process, correctly identifying the dominant feature in controlled settings where existing methods, including Conditional SHAP and ManifoldShap, do not. Our code is available at: https://github.com/duneag2/relshap.

FADEx: Feature Attribution and Distortion-based Explanation of Dimensionality Reduction

Dimensionality Reduction (DR) is a fundamental tool for high-dimensional data exploration, reducing the complexity of latent spaces of machine learning models, and assisting in the explanation of complex opaque models. However, non-linear DR techniques often function as opaque transformations themselves, making it challenging to understand how individual features influence instance positioning in the reduced space. This lack of transparency complicates the analysis and interpretation of structural patterns, hindering the ability to reason about the organization of high-dimensional data based on the projected layout. In order to address this challenge, dimensionality reduction explanation methods have shown promise in improving the understanding of the observed groups and cluster structures. Unfortunately, existing DR explanation approaches tend to suffer from limitations such as multiple attributions per feature and restricted applicability to specific dimensionality reduction methods, which hinder their use. In this work, we propose FADEx, a novel local per-instance feature attribution method that leverages local linear approximation via first-order Taylor expansion and Singular Value Decomposition to provide explanations. FADEx computes the local linear models via weighted least squares, eliminating the need for out-of-sample data mapping, making it agnostic to the DR method, while simultaneously providing local feature attributions and distortion analysis. Through qualitative and quantitative evaluations, comparisons with existing methods, and case studies, we demonstrate FADEx's effectiveness and versatility in providing explanations and analytical resources for analyzing the behavior of DR methods. The results indicate FADEx yields robust and reliable explanations, outperforming existing approaches in several aspects.

Totally Positive Matrices and the Highest-Order Coefficients of the Characteristic Polynomial

We investigate the extent to which totally positive matrices can be distinguished through the highest-order coefficients of their characteristic polynomials. To identify the most informative coefficients, we also employed neural-network classifiers together with feature-attribution methods. Using datasets built from several structured totally positive families, including products of positive bidiagonal matrices, Vandermonde matrices, and Cauchy matrices, we find that the coefficients (a_{n-1}, a_{n-2}, a_{n-3}) already contain strong discriminatory information for separating totally positive from non-totally positive matrices in dimensions 5, 10, and 30. The resulting separation is markedly nonlinear and admits a natural geometric description in the corresponding three-dimensional coefficient space by means of Mahalanobis ellipsoids. These ellipsoids enclose the totally positive samples while excluding most non-totally positive ones. Moreover, different structured totally positive families exhibit distinct ellipsoidal signatures, and the separation between these signatures increases with the dimension. These observations lead us to formulate a conjecture on the geometric separation of structured totally positive families in the space determined by the three highest-order characteristic coefficients.

Feature Attribution-Based Explainability Analysis of Deep Learning Models in Predictive Process Monitoring

Predictive process monitoring supports the optimization and control of operational business processes by forecasting the future state or outcome of ongoing cases. While deep neural networks have achieved strong performance for these tasks by modeling sequential dependencies in event logs, their black-box nature limits trust and practical adoption. Feature attribution methods are often used to address this, but applying them directly poses a dilemma: event-level attributions impose high computational complexity for long traces, while explanations based on aggregated trace representations often fail to capture the underlying control-flow dynamics. To address this issue, we propose a local post-hoc explainability method for deep neural networks in outcome prediction. The method relies on a control-flow-aware segmentation algorithm that partitions a trace into meaningful segments and supports the computation of segment-level SHAP explanations. This makes it possible to identify which parts of a trace influence a prediction and which change points steer the case toward the predicted outcome. We assess the proposed segmentation method on a synthetic dataset with known process logic, where meaningful change points can be explicitly verified, and we demonstrate its usefulness on real-world event logs from a loan application process and an administrative process of a Dutch municipality.

Decision-Value Attribution in Predict-then-Optimize Systems

Predictive models are increasingly embedded in operational decision-making, yet standard explanation methods typically explain forecasts rather than the decisions those forecasts induce. This distinction is important in predict-then-optimize systems: large forecast changes may leave the optimizer's action unchanged, while small changes can alter the selected decision and its realized value. We propose Decision Value Attribution (DVA), a Shapley-based framework for attributing the value of a fixed prediction--optimization pipeline. The framework defines cooperative games whose payoff is the downstream decision value, allowing the players to be information sources, optimization or design parameters, or both. We present three variants: InfoDVA attributes value to features, DesignDVA attributes value to operational configurations, and Decision-Value Interactions (DVI) quantifies how information and design jointly create value. We further distinguish post-DVA, which evaluates decisions using realized outcomes, from pre-DVA, which evaluates decisions under the model's full prediction. This separation turns attribution into a decision-level diagnostic of whether the model's operational beliefs align with realized performance. The resulting attributions are expressed in the units of the operational objective and decompose the gain or loss relative to a baseline. Case studies in electricity storage arbitrage and emergency medical service coverage show that predictive explanations can be poor proxies for operational value, that DVA can guide targeted information-control interventions, and that optimization configurations determine when predictive information is decision-relevant.

Beyond Shapley: Efficient Computation of Asymmetric Shapley Values

We address the problem of explainability in machine learning models through feature attribution methods. In particular, we consider a variant of Shapley values known as Asymmetric Shapley Values (ASV), which enables the incorporation of causal knowledge into model-agnostic explanations through the use of a causal graph. We show that in certain contexts in which the computation of SHAP is $\#P$-hard, the exact computation of ASV can be done in polynomial time. To extend this algorithmic result, we introduce a notion of equivalence classes over the topological orderings of the underlying causal graph, which is useful to reduce the time to compute ASV. In particular, we present a polynomial-time algorithm (in the number of equivalence classes) to compute it whenever the causal graph is a rooted directed tree. Finally, we develop an algorithm for approximating ASV in arbitrary causal DAGs which relies on a procedure to sample topological orderings uniformly at random. To implement this sampling mechanism we leverage known algorithms as well as simpler alternatives. Our experimental results demonstrate the practical viability of the proposed approach in realistic causal structures.

Signed Evidence Flow: Conflict-Aware and Stability-Calibrated Data Analysis

Modern data analysis usually gives a prediction without showing whether the evidence behind it is clear, conflicting, or stable. Two cases can have the same fitted confidence even when one has mostly agreeing evidence and the other has strong support and strong opposition. We propose Signed Evidence Flow (SEF), which combines a fitted prediction rule with signed feature attributions to measure support, opposition, conflict, and perturbation stability. We prove that confidence determines conflict exactly when it also determines total evidence mass, derive the remaining conditional variance, and state when conflict can improve loss prediction beyond confidence and other audit variables. We also connect conflict to geometric decision fragility. Across healthcare, Covertype, black-box, finance, and ten external data sets, conflict sometimes separates risk among predictions that already appear confident. Cross-fitted tests show added error-ranking information beyond confidence and attribution entropy on several data sets, including two large finance tasks. The direction is not universal: in some tasks, lowconflict cases are riskier. We therefore introduce ScopeGate, a held-out permutation diagnostic that checks the direction before SEF is used for review triage. SEF is consequently an audit tool rather than a universal risk score: it describes evidence structure, while an independent calibration sample determines whether that structure is useful in the target population.

Feature Attribution in Directed Acyclic Graphs Using Edge Intervention

Shapley value-based feature attribution methods face challenges in scenarios involving complex feature interactions and causal relationships, even when a causal structure is provided. Existing methods typically adopt a node-centric view, attributing importance solely to individual features. Consequently, they often fail to simultaneously capture the externality and exogenous influence of features, leading to unreasonable interpretations. To overcome these limitations, we propose a novel feature attribution method called DAG-SHAP, which is based on edge intervention. DAG-SHAP treats each feature edge as an individual attribution object, ensuring that both externality and exogenous contributions of features are appropriately captured. Additionally, we introduce an approximation method for efficiently computing DAG-SHAP. Extensive experiments on both real and synthetic datasets validate the effectiveness of DAG-SHAP. Our code is available at https://github.com/ZJU-DIVER/DAG-SHAP.

Attribution via Distributional Paths for Information Revelation

Feature attribution methods explain predictions by assigning importance scores to input features. Path-based methods such as Integrated Gradients are especially appealing because they satisfy \textit{completeness}: attributions sum to the change in model output between a reference state and the input. Yet most path methods define this trajectory in input space, explaining a model through pointwise perturbed inputs along a chosen path. An input-space path integrates the model's raw response at each point it passes through, with no control over the resolution at which a feature is queried; the early, baseline-adjacent part of the trajectory contributes to the explanation on equal footing with the input itself. Here, we lift path attribution from input space to a space of structured probe distributions around the example of interest, and call our method Reveal-IG. Rather than traversing raw input values, Reveal-IG progressively reveals information about the input and attributes changes in the model's expected output along this distributional path. The result is a path-attribution framework that retains completeness with respect to the expected model response, and naturally accommodates multiscale image probes and feature-wise uncertainty in tabular data. Synthetic diagnostics show that Reveal-IG avoids path artifacts that affect input-space methods, and across ImageNet classification and tabular regression it produces stable, signed attributions -- leading on metrics that use attribution sign while remaining competitive on the rest.

Proxy-Based Approximation of Shapley and Banzhaf Interactions

Shapley and Banzhaf interactions capture the complex dynamics inherent in modern machine learning applications. However, current estimators for these higher-order interactions trade off between speed and accuracy. To overcome this limitation, we introduce ProxySHAP. ProxySHAP reconciles the high sample efficiency of tree-based proxy models with a principled path to consistency via residual correction. On a theoretical level, we derive a polynomial-time generalization of interventional TreeSHAP to compute exact interaction indices for tree ensembles, successfully bypassing exponential tree-depth dependencies in prior methods. Furthermore, we formally analyze the residual adjustment strategy, characterizing the specific conditions under which Maximum Sample Reuse (MSR) corrects proxy bias without its variance scaling exponentially with interaction size. Extensive benchmarking demonstrates that ProxySHAP sets a new state-of-the-art standard for approximation quality, including in large-scale applications with thousands of features. By achieving the lowest error in both small- and large-budget regimes, ProxySHAP significantly outperforms the prior best estimators ProxySPEX and KernelSHAP-IQ, while also delivering superior performance on downstream explainability tasks.

Manifold-Aligned Guided Integrated Gradients for Reliable Feature Attribution

Feature attribution is central to diagnosing and trusting deep neural networks, and Integrated Gradients (IG) is widely used due to its axiomatic properties. However, IG can yield unreliable explanations when the integration path between a baseline and the input passes through regions with noisy gradients. While Guided Integrated Gradients reduces this sensitivity by adaptively updating low-gradient-magnitude features, input-space guidance still produces intermediate inputs that deviate from the data manifold. To address this limitation, we propose \emph{Manifold-Aligned Guided Integrated Gradients} (MA-GIG), which constructs attribution paths in the latent space of a pre-trained variational autoencoder. By decoding intermediate latent states, MA-GIG biases the path toward the learned generative manifold and reduces exposure to implausible input-space regions. Through qualitative and quantitative evaluations, we demonstrate that MA-GIG produces faithful explanations by aggregating gradients on path features proximal to the input. Consequently, our method reduces off-manifold noise and outperforms prior path-based attribution methods across multiple datasets and classifiers. Our code is available at https://github.com/leekwoon/ma-gig/.