Efficient Computation of SHAP Explanations for Weighted Automata under Markovian Distributions

Core Concepts

The computation of SHAP explanations for the class of weighted automata and disjoint DNFs, which includes decision trees, can be performed efficiently under the assumption of Markovian distributions.

Abstract

The article investigates the computational complexity of the SHAP (Shapley Additive Explanations) score, a widely used framework for local interpretability of machine learning models. The authors focus on the case where the underlying model is a weighted automaton (WA) and the background data distribution is Markovian.
The key contributions are:

The authors provide a constructive proof showing that the computation of the SHAP score for the class of WAs is tractable under the Markovian assumption. This result extends the existing positive complexity results on SHAP score computation, which were mostly derived under the feature independence assumption.

The authors show that under the same Markovian assumption, the computation of the SHAP score for the class of disjoint DNFs (which includes decision trees) is also tractable. This is achieved by a polynomial-time reduction from the SHAP problem for disjoint DNFs to the SHAP problem for WAs.

The proof strategy involves decomposing the SHAP score computation into a set of operations over languages and seq2seq languages represented by WAs and weighted transducers (WTs). The authors then construct WAs and WTs that can compute these languages/seq2seq languages efficiently under the Markovian assumption.
This work provides a formal argument to substantiate the claim that WAs enjoy better transparency than their neural counterparts, as they allow for efficient SHAP score computation under realistic data distributions.

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On the tractability of SHAP explanations under Markovian distributions

by Reda Marzouk... at arxiv.org 05-07-2024

https://arxiv.org/pdf/2405.02936.pdf

Deeper Inquiries

What are the potential applications of the tractable SHAP explanations for weighted automata and disjoint DNFs under Markovian distributions

The tractable SHAP explanations for weighted automata and disjoint DNFs under Markovian distributions have various potential applications in the field of interpretable machine learning.

Sequential Models Interpretability: These explanations can provide insights into the decision-making process of sequential models, such as those used in natural language processing, speech processing, and image processing. Understanding the contribution of individual features in the context of sequential tasks can lead to improved model interpretability.

Model Transparency: By offering tractable explanations for weighted automata and disjoint DNFs, the transparency of these models can be enhanced. Stakeholders, including domain experts and end-users, can gain a better understanding of how these models arrive at their predictions.

Error Analysis: The SHAP explanations can help in error analysis by identifying the features that have the most influence on model predictions. This can aid in debugging and improving model performance.

Regulatory Compliance: In regulated industries where model interpretability is crucial, such as healthcare and finance, these tractable explanations can help ensure compliance with transparency and accountability requirements.

Feature Engineering: Understanding the impact of individual features on model predictions can guide feature selection and engineering efforts, leading to more effective model development.

Can the techniques developed in this work be extended to other families of models beyond weighted automata and disjoint DNFs

The techniques developed in this work for weighted automata and disjoint DNFs under Markovian distributions can potentially be extended to other families of models in the following ways:

Decision Trees: As shown in the corollary, the techniques can be extended to decision trees, a widely used class of models. By constructing an equivalent d-DNF from a decision tree, the SHAP score computation for decision trees under the Markovian assumption can be made tractable.

Neural Networks: While neural networks are more complex models, techniques from this work could be adapted to proxy interpretation models for neural networks. By approximating neural network behavior with weighted automata, similar tractable explanations could be derived.

Probabilistic Graphical Models: The concepts of Markovian distributions and weighted automata can be applied to probabilistic graphical models, enabling tractable explanations for models that incorporate probabilistic dependencies.

Reinforcement Learning Models: By formulating reinforcement learning models in a sequential framework, similar techniques could be used to provide interpretable explanations for these models under the Markovian assumption.

How do the theoretical results presented in this article relate to practical considerations in the deployment of interpretable machine learning models

The theoretical results presented in this article have several implications for the practical deployment of interpretable machine learning models:

Model Explainability: By demonstrating the tractability of SHAP explanations for specific model families under Markovian distributions, the article highlights the feasibility of providing interpretable explanations for complex models. This can enhance trust in AI systems and facilitate their adoption in real-world applications.

Regulatory Compliance: In industries where model interpretability is a regulatory requirement, the theoretical results offer a pathway to comply with transparency and accountability standards. Organizations can use these techniques to ensure that their models are explainable and auditable.

Model Debugging: The ability to compute SHAP scores efficiently for weighted automata and disjoint DNFs can aid in model debugging and error analysis. Understanding the impact of features on model predictions can help identify and rectify issues in the model.

Feature Importance: The results provide insights into the importance of individual features in model predictions. This information can guide feature engineering efforts and help data scientists make informed decisions about feature selection and model improvement.