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Exploring the Whole Rashomon Set of Sparse Decision Trees (2209.08040v2)

Published 16 Sep 2022 in cs.LG and cs.AI

Abstract: In any given machine learning problem, there may be many models that could explain the data almost equally well. However, most learning algorithms return only one of these models, leaving practitioners with no practical way to explore alternative models that might have desirable properties beyond what could be expressed within a loss function. The Rashomon set is the set of these all almost-optimal models. Rashomon sets can be extremely complicated, particularly for highly nonlinear function classes that allow complex interaction terms, such as decision trees. We provide the first technique for completely enumerating the Rashomon set for sparse decision trees; in fact, our work provides the first complete enumeration of any Rashomon set for a non-trivial problem with a highly nonlinear discrete function class. This allows the user an unprecedented level of control over model choice among all models that are approximately equally good. We represent the Rashomon set in a specialized data structure that supports efficient querying and sampling. We show three applications of the Rashomon set: 1) it can be used to study variable importance for the set of almost-optimal trees (as opposed to a single tree), 2) the Rashomon set for accuracy enables enumeration of the Rashomon sets for balanced accuracy and F1-score, and 3) the Rashomon set for a full dataset can be used to produce Rashomon sets constructed with only subsets of the data set. Thus, we are able to examine Rashomon sets across problems with a new lens, enabling users to choose models rather than be at the mercy of an algorithm that produces only a single model.

Citations (43)

Summary

  • The paper introduces a novel method to enumerate the Rashomon set for sparse decision trees, offering a complete range of near-optimal models.
  • The methodology employs an innovative data structure and pre-pruning strategies to reduce the hypothesis space and computational complexity.
  • The results enable detailed variable importance analysis and robust cross-metric comparisons, aligning model choices with domain-specific needs.

Exploring the Whole Rashomon Set of Sparse Decision Trees: An Essay

The paper "Exploring the Whole Rashomon Set of Sparse Decision Trees" advances the conceptual and practical comprehension of model variety in decision tree-based machine learning. The authors introduce a novel approach to enumerate the Rashomon set, a collection of models that are nearly optimal in terms of their predictive performance, specifically for sparse decision trees. This contribution addresses a critical gap in the availability of model alternatives that potentially offer diverse properties in interpretability, fairness, or alignment with domain-specific constraints.

Core Contributions and Methodology

The Rashomon set concept, derived from the notion introduced by Leo Breiman, serves as a cornerstone of the paper. It encapsulates the viewpoint that multiple models can perform similarly well on a given dataset yet offer different interpretations and uses. This paper provides the first technique grounded in strong analytical bounds to fully enumerate the Rashomon set for any sparse decision trees—a non-trivial task due to the complex hypothesis space of decision trees.

The authors develop and employ a specialized data structure to represent this set efficiently. This data structure not only allows for the storage of the Rashomon set but also facilitates efficient querying and sampling, thus enabling practical applications such as variable importance analysis across the set. The methodology involves pruning large parts of the hypothesis space a priori by proving that certain sections do not contain any members of the Rashomon set. This is a significant computational advance, given the potential hypothesis space size involved in decision tree modeling.

Results and Applications

The approach enables practitioners and researchers to directly query aspects such as the size of the Rashomon set, variability in model predictions, the robustness of models when subsets of data are excluded, and construction of Rashomon sets for other performance metrics like balanced accuracy and F1-score. Notable applications include:

  1. Variable Importance: By examining the range of variable importances across the Rashomon set, the authors can characterize the overall importance of a variable, offering insights beyond single-model analyses.
  2. Cross-Metric Rashomon Sets: The method identifies models optimal concerning different metrics starting from the Rashomon set defined by accuracy, thus supporting decision-making in varied contexts and problem specifications.
  3. Robustness Analysis: The framework allows for the assessment of model performance stability when certain data subsets are removed, showcasing the Rashomon set’s utility in understanding robust decision-making dynamics.

Implications and Future Directions

The results are promising, suggesting that stakeholders are no longer limited to a singular model output. By providing an array of model choices, stakeholders can better align machine learning outcomes with domain-specific requirements or preferences. This capability not only augments the interpretability of AI systems but also paves the way for more thoughtful cross-validation methods where stakeholders can consider model stability and fairness over multiple viable options.

Further research might delve into extending these techniques to other complex model classes beyond decision trees, enhancing interoperability across various model paradigms. Additionally, integrating domain-specific constraints systematically into the Rashomon set enumeration process could yield customized decision trees that are both interpretable and optimally tuned to unique domains.

In conclusion, this paper marks a considerable advance in the domain of interpretable machine learning. By focusing on the Rashomon set for decision trees, the authors provide a conceptual and technical foundation that encourages the adoption and adaptation of multiple, high-performing models to meet specific needs, thus promoting a more nuanced use of machine learning in practice.

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