# Quantifying Model Complexity via Functional Decomposition for Better Post-Hoc Interpretability

arXiv: https://arxiv.org/abs/1904.03867 · HTML: https://mlsanity.com/paper/1904.03867/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Apr 2019.

## Built on by (most cited first, 22 of 22)

- [Hyperparameter Optimization: Foundations, Algorithms, Best Practices and Open Challenges](https://mlsanity.com/paper/2107.05847/) (2021)
- [YAHPO Gym -- An Efficient Multi-Objective Multi-Fidelity Benchmark for Hyperparameter Optimization](https://mlsanity.com/paper/2109.03670/) (2021)
- [SHAP-IQ: Unified Approximation of any-order Shapley Interactions](https://mlsanity.com/paper/2303.01179/) (2023)
- [Explainable Artificial Intelligence Approaches: A Survey](https://mlsanity.com/paper/2101.09429/) (2021)
- [Trust in AI: Progress, Challenges, and Future Directions](https://mlsanity.com/paper/2403.14680/) (2024)
- [From plane crashes to algorithmic harm: applicability of safety engineering frameworks for responsible ML](https://mlsanity.com/paper/2210.03535/) (2022)
- [Comparing Explanation Methods for Traditional Machine Learning Models Part 1: An Overview of Current Methods and Quantifying Their Disagreement](https://mlsanity.com/paper/2211.08943/) (2022)
- [Position: A Call to Action for a Human-Centered AutoML Paradigm](https://mlsanity.com/paper/2406.03348/) (2024)
- [DALE: Differential Accumulated Local Effects for efficient and accurate global explanations](https://mlsanity.com/paper/2210.04542/) (2022)
- [Statistical Multicriteria Benchmarking via the GSD-Front](https://mlsanity.com/paper/2406.03924/) (2024)
- [Interpreting and generalizing deep learning in physics-based problems with functional linear models](https://mlsanity.com/paper/2307.04569/) (2023)
- [Improving Interpretability via Explicit Word Interaction Graph Layer](https://mlsanity.com/paper/2302.02016/) (2023)
- [Multi-Objective Optimization of Performance and Interpretability of Tabular Supervised Machine Learning Models](https://mlsanity.com/paper/2307.08175/) (2023)
- [Marginal Effects for Non-Linear Prediction Functions](https://mlsanity.com/paper/2201.08837/) (2022)
- [Explainability in Process Outcome Prediction: Guidelines to Obtain Interpretable and Faithful Models](https://mlsanity.com/paper/2203.16073/) (2022)
- [A Collection of Quality Diversity Optimization Problems Derived from Hyperparameter Optimization of Machine Learning Models](https://mlsanity.com/paper/2204.14061/) (2022)
- [Mind the Gap: Measuring Generalization Performance Across Multiple Objectives](https://mlsanity.com/paper/2212.04183/) (2022)
- [Statistical inference using machine learning and classical techniques based on accumulated local effects (ALE)](https://mlsanity.com/paper/2310.09877/) (2023)
- [Comparing Explanation Methods for Traditional Machine Learning Models Part 2: Quantifying Model Explainability Faithfulness and Improvements with Dimensionality Reduction](https://mlsanity.com/paper/2211.10378/) (2022)
- [Machine Learning Workflow to Explain Black-box Models for Early Alzheimer's Disease Classification Evaluated for Multiple Datasets](https://mlsanity.com/paper/2205.05907/) (2022)
- [Application of Machine Learning Methods in Inferring Surface Water Groundwater Exchanges using High Temporal Resolution Temperature Measurements](https://mlsanity.com/paper/2201.00726/) (2022)
- [Evaluating Explanation Methods by the Predictors They Induce](https://mlsanity.com/paper/2609.20058/) (2026)

## Abstract (arXiv)

Post-hoc model-agnostic interpretation methods such as partial dependence plots can be employed to interpret complex machine learning models. While these interpretation methods can be applied regardless of model complexity, they can produce misleading and verbose results if the model is too complex, especially w.r.t. feature interactions. To quantify the complexity of arbitrary machine learning models, we propose model-agnostic complexity measures based on functional decomposition: number of features used, interaction strength and main effect complexity. We show that post-hoc interpretation of models that minimize the three measures is more reliable and compact. Furthermore, we demonstrate the application of these measures in a multi-objective optimization approach which simultaneously minimizes loss and complexity.