# Conditional PED-ANOVA: Hyperparameter Importance in Hierarchical & Dynamic Search Spaces

arXiv: https://arxiv.org/abs/2601.20800 · HTML: https://mlsanity.com/paper/2601.20800/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 59 references that are in the map.
- First posted on arXiv 28 Jan 2026.

## Builds on (most cited first, 20 of 20)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Deep Reinforcement Learning that Matters](https://mlsanity.com/paper/1709.06560/) (2017)
- [Hyperband: A Novel Bandit-Based Approach to Hyperparameter Optimization](https://mlsanity.com/paper/1603.06560/) (2016)
- [OpenML: networked science in machine learning](https://mlsanity.com/paper/1407.7722/) (2014)
- [BOHB: Robust and Efficient Hyperparameter Optimization at Scale](https://mlsanity.com/paper/1807.01774/) (2018)
- [SMAC3: A Versatile Bayesian Optimization Package for Hyperparameter Optimization](https://mlsanity.com/paper/2109.09831/) (2021)
- [Auto-Sklearn 2.0: Hands-free AutoML via Meta-Learning](https://mlsanity.com/paper/2007.04074/) (2020)
- [On the State of the Art of Evaluation in Neural Language Models](https://mlsanity.com/paper/1707.05589/) (2017)
- [Tunability: Importance of Hyperparameters of Machine Learning Algorithms](https://mlsanity.com/paper/1802.09596/) (2018)
- [Surrogate NAS Benchmarks: Going Beyond the Limited Search Spaces of Tabular NAS Benchmarks](https://mlsanity.com/paper/2008.09777/) (2020)
- [Hyperparameter Importance Across Datasets](https://mlsanity.com/paper/1710.04725/) (2017)
- [YAHPO Gym -- An Efficient Multi-Objective Multi-Fidelity Benchmark for Hyperparameter Optimization](https://mlsanity.com/paper/2109.03670/) (2021)
- [Explaining Hyperparameter Optimization via Partial Dependence Plots](https://mlsanity.com/paper/2111.04820/) (2021)
- [BOAH: A Tool Suite for Multi-Fidelity Bayesian Optimization & Analysis of Hyperparameters](https://mlsanity.com/paper/1908.06756/) (2019)
- [Raiders of the Lost Architecture: Kernels for Bayesian Optimization in Conditional Parameter Spaces](https://mlsanity.com/paper/1409.4011/) (2014)
- [PED-ANOVA: Efficiently Quantifying Hyperparameter Importance in Arbitrary Subspaces](https://mlsanity.com/paper/2304.10255/) (2023)
- [Additive Tree-Structured Covariance Function for Conditional Parameter Spaces in Bayesian Optimization](https://mlsanity.com/paper/2006.11771/) (2020)
- [HyperSHAP: Shapley Values and Interactions for Explaining Hyperparameter Optimization](https://mlsanity.com/paper/2502.01276/) (2025)
- [DeepCAVE: A Visualization and Analysis Tool for Automated Machine Learning](https://mlsanity.com/paper/2512.01810/) (2025)

## Abstract (arXiv)

We propose conditional PED-ANOVA (condPED-ANOVA), a principled framework for estimating hyperparameter importance (HPI) in conditional search spaces, where the presence or domain of a hyperparameter can depend on other hyperparameters. Although the original PED-ANOVA provides a fast and efficient way to estimate HPI within the top-performing regions of the search space, it assumes a fixed, unconditional search space and therefore cannot properly handle conditional hyperparameters. To address this, we introduce a conditional HPI for top-performing regions and derive a closed-form estimator that accurately reflects conditional activation and domain changes. Experiments show that naive adaptations of existing HPI estimators yield misleading or uninterpretable importances in conditional settings, whereas condPED-ANOVA consistently provides meaningful importances that reflect the underlying conditional structure. Our code is publicly available at https://github.com/kAIto47802/condPED-ANOVA.