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.

Creating models from past observations and ensuring their effectiveness on new data is the essence of machine learning. However, selecting models that generalize well remains a challenging task. Related to this topic, the Rashomon Effect refers to cases where multiple models perform similarly well for a given learning problem. This often occurs in real-world scenarios, like the manufacturing process or medical diagnosis, where diverse patterns in data lead to multiple high-performing solutions. We propose the Rashomon Ensemble, a method that strategically selects models from these diverse high-performing solutions to improve generalization. By grouping models based on both their performance and explanations, we construct ensembles that maximize diversity while maintaining predictive accuracy. This selection ensures that each model covers a distinct region of the solution space, making the ensemble more robust to distribution shifts and variations in unseen data. We validate our approach on both open and proprietary collaborative real-world datasets, demonstrating up to 0.20+ AUROC improvements in scenarios where the Rashomon ratio is large. Additionally, we demonstrate tangible benefits for businesses in various real-world applications, highlighting the robustness, practicality, and effectiveness of our approach.

The Rashomon set is the set of these all almost-optimal models. Rashomon sets can be large in size and complicated in structure, particularly for highly nonlinear function classes that allow complex interaction terms, such as decision trees.

Evaluating the performance of closely matched machine learning(ML) models under specific conditions has long been a focus of researchers in the field of machine learning. The Rashomon set is a collection of closely matched ML models, encompassing a wide range of models with similar accuracies but different structures. Traditionally, the analysis of these sets has focused on vertical structural analysis, which involves comparing the corresponding features at various levels within the ML models. However, there has been a lack of effective visualization methods for horizontally comparing multiple models with specific features. We propose the VAR visualization solution. VAR uses visualization to perform comparisons of ML models within the Rashomon set. This solution combines heatmaps and scatter plots to facilitate the comparison. With the help of VAR, ML model developers can identify the optimal model under specific conditions and better understand the Rashomon set's overall characteristics.

This phenomenon--often called the Rashomon effect [7], predictive multiplicity [22], or model multiplicity [5]--has wide-ranging implications for both understanding and improving fairness, as these equally accurate models often differ substantially in other properties such as fairness [21, 28] or model simplicity [29-31]. As prior work has pointed out, this multiplicity of models can be viewed as both a fairness opportunity and a concern [5, 10]. On the positive side, legal scholarship has pointed to the fact that model multiplicity is relevant to how to interpret and enforce U.S. anti-discrimination law, and specifically, can strengthen the disparate impact doctrine to more effectively combat algorithmic discrimination [3]. In a recent paper, Black et al. [3] suggest that the phenomenon of model multiplicity could support a reading of the disparate impact doctrine that requires companies to proactively search the set of equally accurate models for less discriminatory alternatives that have equivalent accuracy to a base model deemed acceptable for deployment from a model performance perspective. On the negative side, several scholars have pointed out that facially similar models, with equivalent accuracy but differences in their individual predictions, can suggest that some model decisions are arbitrary since they seem to be made on the basis of model choice that does not impact performance (e.g., a <1% change in a model's training set accuracy) [2, 17, 22]. This arbitrariness can impact model explanations and recourse as well: individuals with decisions that are unstable across small model changes may not receive reliable explanations for their model outcome, or ways to change it [4, 6, 25]. Further, if there is a group-based asymmetry of arbitrariness-e.g., if female loan applicants have more arbitrariness in their decisions than male loan applicants-- this could lead to a group-based equity concern in and of itself. Understanding the extent of the benefits and risks of model multiplicity relies upon an understanding of the properties of the Rashomon set, or the set of approximately equally accurate models for a given prediction task, i.e., equally accurate up to

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.

Today, as increasingly complex predictive models are developed, simple rule sets remain a crucial tool to obtain interpretable predictions and drive high-stakes decision making. However, a single rule set provides a partial representation of a learning task. An emerging paradigm in interpretable machine learning aims at exploring the Rashomon set of all models exhibiting near-optimal performance. Existing work on Rashomon-set exploration focuses on exhaustive search of the Rashomon set for particular classes of models, which can be a computationally challenging task. On the other hand, exhaustive enumeration leads to redundancy that often is not necessary, and a representative sample or an estimate of the size of the Rashomon set is sufficient for many applications. In this work, we propose, for the first time, efficient methods to explore the Rashomon set of rule set models with or without exhaustive search. Extensive experiments demonstrate the effectiveness of the proposed methods in a variety of scenarios.

Post-hoc global/local feature attribution methods are progressively being employed to understand the decisions of complex machine learning models. Yet, because of limited amounts of data, it is possible to obtain a diversity of models with good empirical performance but that provide very different explanations for the same prediction, making it hard to derive insight from them. In this work, instead of aiming at reducing the under-specification of model explanations, we fully embrace it and extract logical statements about feature attributions that are consistent across all models with good empirical performance (i.e. all models in the Rashomon Set). We show that partial orders of local/global feature importance arise from this methodology enabling more nuanced interpretations by allowing pairs of features to be incomparable when there is no consensus on their relative importance. We prove that every relation among features present in these partial orders also holds in the rankings provided by existing approaches. Finally, we present three use cases employing hypothesis spaces with tractable Rashomon Sets (Additive models, Kernel Ridge, and Random Forests) and show that partial orders allow one to extract consistent local and global interpretations of models despite their under-specification.

In any given machine learning problem, there might be many models that 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 by a loss function. The Rashomon set is the set of these all almost-optimal models. Rashomon sets can be large in size and complicated in structure, 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.

Given thousands of equally accurate machine learning (ML) models, how can users choose among them? A recent ML technique enables domain experts and data scientists to generate a complete Rashomon set for sparse decision trees--a huge set of almost-optimal interpretable ML models. To help ML practitioners identify models with desirable properties from this Rashomon set, we develop TimberTrek, the first interactive visualization system that summarizes thousands of sparse decision trees at scale. Two usage scenarios highlight how TimberTrek can empower users to easily explore, compare, and curate models that align with their domain knowledge and values. Our open-source tool runs directly in users' computational notebooks and web browsers, lowering the barrier to creating more responsible ML models. TimberTrek is available at the following public demo link: https://poloclub.github.io/timbertrek.