Efficient Algorithms for Computing Locally-Minimal Probabilistic Explanations of Complex Machine Learning Models

Core Concepts

This paper proposes novel efficient algorithms for computing locally-minimal probabilistic abductive explanations (LmPAXp) for complex machine learning models, including random forests and binarized neural networks. The proposed algorithms provide high-quality approximations of probabilistic abductive explanations in practice.

Abstract

The paper addresses the challenge of providing trustworthy and rigorous explanations for complex machine learning models, particularly in high-stakes domains. It focuses on the computation of probabilistic abductive explanations (PAXp), which trade off the strong theoretical guarantees of rigor of abductive explanations for smaller explanation sizes.
The key contributions are:

Two new algorithms for computing approximate locally-minimal PAXp explanations:

One based on approximate model counting
One based on sampling with probabilistic guarantees

Experimental evaluation of the proposed algorithms on random forests and binarized neural networks:

The results demonstrate the practical efficiency of the proposed algorithms.
For random forests, the LmPAXp explanations are significantly shorter than plain abductive explanations, while maintaining high precision.
For binarized neural networks, the LmPAXp explanations are up to two-thirds shorter than abductive explanations.

The paper first provides background on formal explainability, including abductive explanations (AXp) and probabilistic abductive explanations (PAXp). It then details the logic encodings for random forests and binarized neural networks.
The core of the paper describes the two proposed algorithms for computing LmPAXp explanations. The first approach uses approximate model counting to estimate the probability of the explanation. The second approach uses Monte Carlo sampling with PAC guarantees.
The experimental results demonstrate the effectiveness of the proposed algorithms in producing succinct and high-quality probabilistic explanations for complex machine learning models, outperforming the baseline approach for decision trees.

Stats

The average length of LmPAXp explanations for random forests is 26-94% smaller than plain abductive explanations, with an average precision of 0.97 or higher.
The average length of LmPFFAXp explanations for random forests is 16-85% smaller than formal feature attribution abductive explanations.
For binarized neural networks, the LmPAXp explanations are up to two-thirds shorter than abductive explanations.

Quotes

"Probabilistic abductive explanations trade off the strong theoretical guarantees of rigor of abductive explanations for smaller explanation sizes, while still ensuring the quality of approximate explanations."
"A surprising experimental observation [20] is that, in the case of decision trees and other graph-based classifiers, locally-minimal explanations are in most cases also subset-minimal explanations — reported results show for decision trees that in 99.8% cases computed approximate explanations are proved that are subset minimal."

Key Insights Distilled From

Locally-Minimal Probabilistic Explanations

by Yacine Izza,... at arxiv.org 05-07-2024

https://arxiv.org/pdf/2312.11831.pdf

Deeper Inquiries

What are the theoretical guarantees or bounds on the quality of the locally-minimal probabilistic explanations produced by the proposed algorithms

The proposed algorithms for computing locally-minimal probabilistic explanations offer guarantees of rigor in terms of the quality of the explanations produced. Specifically, the algorithms aim to find explanations that are locally-minimal, meaning that they are minimal if at most one feature is allowed to be removed. This approach helps in reducing the size of the explanations while still maintaining a high level of accuracy.
In the context provided, the experimental results demonstrate that the locally-minimal probabilistic explanations generated by the algorithms offer high-quality approximations of the probabilistic abductive explanations in practice. The results show that in the case of decision trees and other graph-based classifiers, locally-minimal explanations are often subset-minimal explanations, with a high percentage of cases where computed approximate explanations are proven to be subset minimal. This indicates that the algorithms are effective in producing explanations that are both concise and accurate.

How would the performance and quality of the explanations change if the tolerance and confidence parameters in the approximate model counting and sampling approaches were varied

The performance and quality of the explanations produced by the approximate model counting and sampling approaches can be influenced by varying the tolerance and confidence parameters.
Performance:

Tolerance:

Increasing the tolerance parameter may lead to a larger approximation error in the number of solutions computed by the model counting or sampling methods. A higher tolerance allows for a more relaxed approximation, which can result in faster computation times but potentially lower precision in the explanations.
Decreasing the tolerance parameter would result in a smaller approximation error but may require more computational resources and time to achieve a higher level of accuracy in the explanations.

Confidence:

A higher confidence level in the approximation guarantees would require more computational effort to ensure that the computed explanations meet the specified level of confidence.
Lower confidence levels may result in faster computation times but with a trade-off in the reliability and accuracy of the explanations.
Quality:

Tolerance:

Varying the tolerance parameter can impact the precision of the explanations. A higher tolerance may allow for more flexibility in the approximation, potentially leading to less precise explanations.
Lower tolerance values can result in more accurate and precise explanations but may require more computational resources and time to achieve.

Confidence:

Adjusting the confidence parameter can affect the reliability of the explanations. A higher confidence level ensures a higher level of certainty in the accuracy of the explanations.
Lower confidence levels may introduce more uncertainty in the quality of the explanations, potentially leading to less reliable results.
Overall, finding the right balance between tolerance and confidence parameters is crucial in optimizing the performance and quality of the explanations generated by the algorithms.

Can the proposed techniques be extended to other types of complex machine learning models beyond random forests and binarized neural networks

The proposed techniques for computing locally-minimal probabilistic explanations can be extended to other types of complex machine learning models beyond random forests and binarized neural networks. The key lies in formulating the logic encodings of the classifiers and adapting the algorithms for approximate model counting and sampling to suit the specific characteristics of the new models.
Extension to Other Models:

Deep Learning Models: Techniques can be adapted to handle deep learning models such as convolutional neural networks (CNNs) or recurrent neural networks (RNNs). The logic encodings would need to capture the structure and operations of these models, and the algorithms can be modified to accommodate the complexity of deep learning architectures.

Ensemble Methods: The techniques can be applied to ensemble methods like gradient boosting machines, AdaBoost, or stacking models. The logic encodings would need to represent the ensemble structure, and the algorithms can be tailored to handle the combination of multiple base learners.

Support Vector Machines (SVMs): The methods can be extended to SVMs by encoding the decision boundaries and support vectors in a logical form. The algorithms can then be adjusted to compute locally-minimal explanations for SVMs.

Clustering Algorithms: Techniques can be adapted for clustering algorithms like K-means or hierarchical clustering. The logic encodings would need to capture the clustering process, and the algorithms can be modified to find concise explanations for cluster assignments.
By customizing the logic encodings and algorithms to suit the specific characteristics and complexities of different machine learning models, the proposed techniques can be effectively extended to a wide range of models for generating locally-minimal probabilistic explanations.