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Cynthia Rudin

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AAAI Conference 2026 Conference Paper

AutoSchA: Automatic Hierarchical Music Representations via Multi-Relational Node Isolation

  • Stephen Ni-Hahn
  • Rico Zhu
  • Jerry Yin
  • Yue Jiang
  • Cynthia Rudin
  • Simon Mak

Hierarchical representations provide powerful and principled approaches for analyzing many musical genres. Such representations have been broadly studied in music theory, for instance via Schenkerian analysis (SchA). Hierarchical music analyses, however, are highly cost-intensive; the analysis of a single piece of music requires a great deal of time and effort from trained experts. The representation of hierarchical analyses in a computer-readable format is also a further challenge. Given recent developments in hierarchical deep learning and increasing quantities of computer-readable data, there is great promise in extending such work for an automatic hierarchical representation framework. This paper thus introduces a novel approach, AutoSchA, which extends recent developments in graph neural networks (GNNs) for hierarchical music analysis. AutoSchA features three key contributions: 1) a new graph learning framework for hierarchical music representation, 2) a new graph pooling mechanism based on node isolation that directly optimizes learned pooling assignments, and 3) a state-of-the-art architecture that integrates such developments for automatic hierarchical music analysis. We show, in a suite of experiments, that AutoSchA performs comparably to human experts when analyzing Baroque fugue subjects.

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AAAI Conference 2026 Conference Paper

Resolving Predictive Multiplicity for the Rashomon Set

  • Parian Haghighat
  • Hadis Anahideh
  • Cynthia Rudin

The existence of multiple, equally accurate models for a given predictive task leads to predictive multiplicity, where a ``Rashomon set'' of models achieve similar accuracy but diverge in their individual predictions. This inconsistency undermines trust in high-stakes applications where we want consistent predictions. We propose three approaches to reduce inconsistency among predictions for the members of the Rashomon set. The first approach is outlier correction. An outlier has a label that none of the good models are capable of predicting correctly. Outliers can cause the Rashomon set to have high variance predictions in a local area, so fixing them can lower variance. Our second approach is local patching. In a local region around a test point, models may disagree with each other because some of them are biased. We can detect and fix such biases using a validation set, which also reduces multiplicity. Our third approach is pairwise reconciliation, where we find pairs of models that disagree on a region around the test point. We modify predictions that disagree, making them less biased. These three approaches can be used together or separately, and they each have distinct advantages. The reconciled predictions can then be distilled into a single interpretable model for real-world deployment. In experiments across multiple datasets, our methods reduce disagreement metrics while maintaining competitive accuracy.

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JMLR Journal 2025 Journal Article

"What is Different Between These Datasets?" A Framework for Explaining Data Distribution Shifts

  • Varun Babbar*
  • Zhicheng Guo*
  • Cynthia Rudin

The performance of machine learning models relies heavily on the quality of input data, yet real-world applications often face significant data-related challenges. A common issue arises when curating training data or deploying models: two datasets from the same domain may exhibit differing distributions. While many techniques exist for detecting such distribution shifts, there is a lack of comprehensive methods to explain these differences in a human-understandable way beyond opaque quantitative metrics. To bridge this gap, we propose a versatile framework of interpretable methods for comparing datasets. Using a variety of case studies, we demonstrate the effectiveness of our approach across diverse data modalities—including tabular data, text data, images, time-series signals – in both low and high-dimensional settings. These methods complement existing techniques by providing actionable and interpretable insights to better understand and address distribution shifts. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2025. ( edit, beta )

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NeurIPS Conference 2025 Conference Paper

Data Fusion for Partial Identification of Causal Effects

  • Quinn Lanners
  • Cynthia Rudin
  • Alexander Volfovsky
  • Harsh Parikh

Data fusion techniques integrate information from heterogeneous data sources to improve learning, generalization, and decision-making across data sciences. In causal inference, these methods leverage rich observational data to improve causal effect estimation, while maintaining the trustworthiness of randomized controlled trials. Existing approaches often relax the strong "no unobserved confounding" assumption by instead assuming exchangeability of counterfactual outcomes across data sources. However, when both assumptions simultaneously fail—a common scenario in practice—current methods cannot identify or estimate causal effects. We address this limitation by proposing a novel partial identification framework that enables researchers to answer key questions such as: Is the causal effect positive/negative? and How severe must assumption violations be to overturn this conclusion? Our approach introduces interpretable sensitivity parameters that quantify assumption violations and derives corresponding causal effect bounds. We develop doubly robust estimators for these bounds and operationalize breakdown frontier analysis to understand how causal conclusions change as assumption violations increase. We apply our framework to the Project STAR study, which investigates the effect of classroom size on students’ third-grade standardized test performance. Our analysis reveals that the Project STAR results are robust to simultaneous violations of key assumptions, both on average and across various subgroups of interest. This strengthens confidence in the study's conclusions despite potential unmeasured biases in the data.

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AAAI Conference 2025 Conference Paper

Dimension Reduction with Locally Adjusted Graphs

  • Yingfan Wang
  • Yiyang Sun
  • Haiyang Huang
  • Cynthia Rudin

Dimension reduction (DR) algorithms have proven to be extremely useful for gaining insight into large-scale high-dimensional datasets, particularly finding clusters in transcriptomic data. The initial phase of these DR methods often involves converting the original high-dimensional data into a graph. In this graph, each edge represents the similarity or dissimilarity between pairs of data points. However, this graph is frequently suboptimal due to unreliable high-dimensional distances and the limited information extracted from the high-dimensional data. This problem is exacerbated as the dataset size increases. If we reduce the size of the dataset by selecting points for a specific sections of the embeddings, the clusters observed through DR are more separable since the extracted subgraphs are more reliable. In this paper, we introduce LocalMAP, a new dimensionality reduction algorithm that dynamically and locally adjusts the graph to address this challenge. By dynamically extracting subgraphs and updating the graph on-the-fly, LocalMAP is capable of identifying and separating real clusters within the data that other DR methods may overlook or combine. We demonstrate the benefits of LocalMAP through a case study on biological datasets, highlighting its utility in helping users more accurately identify clusters for real-world problems.

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AAAI Conference 2025 Conference Paper

How Your Location Relates to Health: Variable Importance and Interpretable Machine Learning for Environmental and Sociodemographic Data

  • Ishaan Maitra
  • Raymond Lin
  • Eric Chen
  • Jon Donnelly
  • Sanja Scepanovic
  • Cynthia Rudin

Health outcomes depend on complex environmental and sociodemographic factors whose effects change over location and time. Only recently has fine-grained spatial and temporal data become available to study these effects, namely the MEDSAT dataset of English health, environmental, and sociodemographic information. Leveraging this new resource, we use a variety of variable importance techniques to robustly identify the most informative predictors across multiple health outcomes. We then develop an interpretable machine learning framework based on Generalized Additive Models (GAMs) and Multiscale Geographically Weighted Regression (MGWR) to analyze both local and global spatial dependencies of each variable on various health outcomes. Our findings identify NO2 as a global predictor for asthma, hypertension, and anxiety, alongside other outcome-specific predictors related to occupation, marriage, and vegetation. Regional analyses reveal local variations with air pollution and solar radiation, with notable shifts during COVID. This comprehensive approach provides actionable insights for addressing health disparities, and advocates for the integration of interpretable machine learning in public health.

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ICML Conference 2025 Conference Paper

Leveraging Predictive Equivalence in Decision Trees

  • Hayden McTavish
  • Zachery Boner
  • Jon Donnelly
  • Margo I. Seltzer
  • Cynthia Rudin

Decision trees are widely used for interpretable machine learning due to their clearly structured reasoning process. However, this structure belies a challenge we refer to as predictive equivalence: a given tree’s decision boundary can be represented by many different decision trees. The presence of models with identical decision boundaries but different evaluation processes makes model selection challenging. The models will have different variable importance and behave differently in the presence of missing values, but most optimization procedures will arbitrarily choose one such model to return. We present a boolean logical representation of decision trees that does not exhibit predictive equivalence and is faithful to the underlying decision boundary. We apply our representation to several downstream machine learning tasks. Using our representation, we show that decision trees are surprisingly robust to test-time missingness of feature values; we address predictive equivalence’s impact on quantifying variable importance; and we present an algorithm to optimize the cost of reaching predictions.

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ICML Conference 2025 Conference Paper

Near-Optimal Decision Trees in a SPLIT Second

  • Varun Babbar
  • Hayden McTavish
  • Cynthia Rudin
  • Margo I. Seltzer

Decision tree optimization is fundamental to interpretable machine learning. The most popular approach is to greedily search for the best feature at every decision point, which is fast but provably suboptimal. Recent approaches find the global optimum using branch and bound with dynamic programming, showing substantial improvements in accuracy and sparsity at great cost to scalability. An ideal solution would have the accuracy of an optimal method and the scalability of a greedy method. We introduce a family of algorithms called SPLIT (SParse Lookahead for Interpretable Trees) that moves us significantly forward in achieving this ideal balance. We demonstrate that not all sub-problems need to be solved to optimality to find high quality trees; greediness suffices near the leaves. Since each depth adds an exponential number of possible trees, this change makes our algorithms orders of magnitude faster than existing optimal methods, with negligible loss in performance. We extend this algorithm to allow scalable computation of sets of near-optimal trees (i. e. , the Rashomon set).

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AAAI Conference 2024 Conference Paper

Evaluating Pre-trial Programs Using Interpretable Machine Learning Matching Algorithms for Causal Inference

  • Travis Seale-Carlisle
  • Saksham Jain
  • Courtney Lee
  • Caroline Levenson
  • Swathi Ramprasad
  • Brandon Garrett
  • Sudeepa Roy
  • Cynthia Rudin

After a person is arrested and charged with a crime, they may be released on bail and required to participate in a community supervision program while awaiting trial. These 'pre-trial programs' are common throughout the United States, but very little research has demonstrated their effectiveness. Researchers have emphasized the need for more rigorous program evaluation methods, which we introduce in this article. We describe a program evaluation pipeline that uses recent interpretable machine learning techniques for observational causal inference, and demonstrate these techniques in a study of a pre-trial program in Durham, North Carolina. Our findings show no evidence that the program either significantly increased or decreased the probability of new criminal charges. If these findings replicate, the criminal-legal system needs to either improve pre-trial programs or consider alternatives to them. The simplest option is to release low-risk individuals back into the community without subjecting them to any restrictions or conditions. Another option is to assign individuals to pre-trial programs that incentivize pro-social behavior. We believe that the techniques introduced here can provide researchers the rigorous tools they need to evaluate these programs.

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NeurIPS Conference 2024 Conference Paper

FastSurvival: Hidden Computational Blessings in Training Cox Proportional Hazards Models

  • Jiachang Liu
  • Rui Zhang
  • Cynthia Rudin

Survival analysis is an important research topic with applications in healthcare, business, and manufacturing. One essential tool in this area is the Cox proportional hazards (CPH) model, which is widely used for its interpretability, flexibility, and predictive performance. However, for modern data science challenges such as high dimensionality (both $n$ and $p$) and high feature correlations, current algorithms to train the CPH model have drawbacks, preventing us from using the CPH model at its full potential. The root cause is that the current algorithms, based on the Newton method, have trouble converging due to vanishing second order derivatives when outside the local region of the minimizer. To circumvent this problem, we propose new optimization methods by constructing and minimizing surrogate functions that exploit hidden mathematical structures of the CPH model. Our new methods are easy to implement and ensure monotonic loss decrease and global convergence. Empirically, we verify the computational efficiency of our methods. As a direct application, we show how our optimization methods can be used to solve the cardinality-constrained CPH problem, producing very sparse high-quality models that were not previously practical to construct. We list several extensions that our breakthrough enables, including optimization opportunities, theoretical questions on CPH's mathematical structure, as well as other CPH-related applications.

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NeurIPS Conference 2024 Conference Paper

Improving Decision Sparsity

  • Yiyang Sun
  • Tong Wang
  • Cynthia Rudin

Sparsity is a central aspect of interpretability in machine learning. Typically, sparsity is measured in terms of the size of a model globally, such as the number of variables it uses. However, this notion of sparsity is not particularly relevant for decision making; someone subjected to a decision does not care about variables that do not contribute to the decision. In this work, we dramatically expand a notion of decision sparsity called the Sparse Explanation Value (SEV) so that its explanations are more meaningful. SEV considers movement along a hypercube towards a reference point. By allowing flexibility in that reference and by considering how distances along the hypercube translate to distances in feature space, we can derive sparser and more meaningful explanations for various types of function classes. We present cluster-based SEV and its variant tree-based SEV, introduce a method that improves credibility of explanations, and propose algorithms that optimize decision sparsity in machine learning models.

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NeurIPS Conference 2024 Conference Paper

Interpretable Generalized Additive Models for Datasets with Missing Values

  • Hayden McTavish
  • Jon Donnelly
  • Margo Seltzer
  • Cynthia Rudin

Many important datasets contain samples that are missing one or more feature values. Maintaining the interpretability of machine learning models in the presence of such missing data is challenging. Singly or multiply imputing missing values complicates the model’s mapping from features to labels. On the other hand, reasoning on indicator variables that represent missingness introduces a potentially large number of additional terms, sacrificing sparsity. We solve these problems with M-GAM, a sparse, generalized, additive modeling approach that incorporates missingness indicators and their interaction terms while maintaining sparsity through $\ell_0$ regularization. We show that M-GAM provides similar or superior accuracy to prior methods while significantly improving sparsity relative to either imputation or naïve inclusion of indicator variables.

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NeurIPS Conference 2024 Conference Paper

Interpretable Image Classification with Adaptive Prototype-based Vision Transformers

  • Chiyu Ma
  • Jon Donnelly
  • Wenjun Liu
  • Soroush Vosoughi
  • Cynthia Rudin
  • Chaofan Chen

We present ProtoViT, a method for interpretable image classification combining deep learning and case-based reasoning. This method classifies an image by comparing it to a set of learned prototypes, providing explanations of the form ``this looks like that. '' In our model, a prototype consists of parts, which can deform over irregular geometries to create a better comparison between images. Unlike existing models that rely on Convolutional Neural Network (CNN) backbones and spatially rigid prototypes, our model integrates Vision Transformer (ViT) backbones into prototype based models, while offering spatially deformed prototypes that not only accommodate geometric variations of objects but also provide coherent and clear prototypical feature representations with an adaptive number of prototypical parts. Our experiments show that our model can generally achieve higher performance than the existing prototype based models. Our comprehensive analyses ensure that the prototypes are consistent and the interpretations are faithful.

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JBHI Journal 2024 Journal Article

Learning From Alarms: A Robust Learning Approach for Accurate Photoplethysmography-Based Atrial Fibrillation Detection Using Eight Million Samples Labeled With Imprecise Arrhythmia Alarms

  • Cheng Ding
  • Zhicheng Guo
  • Cynthia Rudin
  • Ran Xiao
  • Amit Shah
  • Duc H. Do
  • Randall J Lee
  • Gari Clifford

Atrial fibrillation (AF) is a common cardiac arrhythmia with serious health consequences if not detected and treated early. Detecting AF using wearable devices with photoplethysmography (PPG) sensors and deep neural networks has demonstrated some success using proprietary algorithms in commercial solutions. However, to improve continuous AF detection in ambulatory settings towards a population-wide screening use case, we face several challenges, one of which is the lack of large-scale labeled training data. To address this challenge, we propose to leverage AF alarms from bedside patient monitors to label concurrent PPG signals, resulting in the largest PPG-AF dataset so far (8. 5 M 30-second records from 24, 100 patients) and demonstrating a practical approach to build large labeled PPG datasets. Furthermore, we recognize that the AF labels thus obtained contain errors because of false AF alarms generated from imperfect built-in algorithms from bedside monitors. Dealing with label noise with unknown distribution characteristics in this case requires advanced algorithms. We, therefore, introduce and open-source a novel loss design, the cluster membership consistency (CMC) loss, to mitigate label errors. By comparing CMC with state-of-the-art methods selected from a noisy label competition, we demonstrate its superiority in handling label noise in PPG data, resilience to poor-quality signals, and computational efficiency.

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NeurIPS Conference 2024 Conference Paper

Navigating the Effect of Parametrization for Dimensionality Reduction

  • Haiyang Huang
  • Yingfan Wang
  • Cynthia Rudin

Parametric dimensionality reduction methods have gained prominence for their ability to generalize to unseen datasets, an advantage that traditional non-parametric approaches typically lack. Despite their growing popularity, there remains a prevalent misconception among practitioners about the equivalence in performance between parametric and non-parametric methods. Here, we show that these methods are not equivalent -- parametric methods retain global structure but lose significant local details. To explain this, we provide evidence that parameterized approaches lack the ability to repulse negative samples, and the choice of loss function also has an impact. Addressing these issues, we developed a new parametric method, ParamRepulsor, that incorporates Hard Negative Mining and a loss function that applies a strong repulsive force. This new method achieves state-of-the-art performance on local structure preservation for parametric methods without sacrificing the fidelity of global structural representation. Our code is available at https: //github. com/hyhuang00/ParamRepulsor.

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ICML Conference 2024 Conference Paper

Position: Amazing Things Come From Having Many Good Models

  • Cynthia Rudin
  • Chudi Zhong
  • Lesia Semenova
  • Margo I. Seltzer
  • Ronald Parr
  • Jiachang Liu 0001
  • Srikar Katta
  • Jon Donnelly

The Rashomon Effect, coined by Leo Breiman, describes the phenomenon that there exist many equally good predictive models for the same dataset. This phenomenon happens for many real datasets and when it does, it sparks both magic and consternation, but mostly magic. In light of the Rashomon Effect, this perspective piece proposes reshaping the way we think about machine learning, particularly for tabular data problems in the nondeterministic (noisy) setting. We address how the Rashomon Effect impacts (1) the existence of simple-yet-accurate models, (2) flexibility to address user preferences, such as fairness and monotonicity, without losing performance, (3) uncertainty in predictions, fairness, and explanations, (4) reliable variable importance, (5) algorithm choice, specifically, providing advanced knowledge of which algorithms might be suitable for a given problem, and (6) public policy. We also discuss a theory of when the Rashomon Effect occurs and why. Our goal is to illustrate how the Rashomon Effect can have a massive impact on the use of machine learning for complex problems in society.

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NeurIPS Conference 2024 Conference Paper

Using Noise to Infer Aspects of Simplicity Without Learning

  • Zachery Boner
  • HARRY CHEN
  • Lesia Semenova
  • Ronald Parr
  • Cynthia Rudin

Noise in data significantly influences decision-making in the data science process. In fact, it has been shown that noise in data generation processes leads practitioners to find simpler models. However, an open question still remains: what is the degree of model simplification we can expect under different noise levels? In this work, we address this question by investigating the relationship between the amount of noise and model simplicity across various hypothesis spaces, focusing on decision trees and linear models. We formally show that noise acts as an implicit regularizer for several different noise models. Furthermore, we prove that Rashomon sets (sets of near-optimal models) constructed with noisy data tend to contain simpler models than corresponding Rashomon sets with non-noisy data. Additionally, we show that noise expands the set of ``good'' features and consequently enlarges the set of models that use at least one good feature. Our work offers theoretical guarantees and practical insights for practitioners and policymakers on whether simple-yet-accurate machine learning models are likely to exist, based on knowledge of noise levels in the data generation process.

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NeurIPS Conference 2023 Conference Paper

A Path to Simpler Models Starts With Noise

  • Lesia Semenova
  • HARRY CHEN
  • Ronald Parr
  • Cynthia Rudin

The Rashomon set is the set of models that perform approximately equally well on a given dataset, and the Rashomon ratio is the fraction of all models in a given hypothesis space that are in the Rashomon set. Rashomon ratios are often large for tabular datasets in criminal justice, healthcare, lending, education, and in other areas, which has practical implications about whether simpler models can attain the same level of accuracy as more complex models. An open question is why Rashomon ratios often tend to be large. In this work, we propose and study a mechanism of the data generation process, coupled with choices usually made by the analyst during the learning process, that determines the size of the Rashomon ratio. Specifically, we demonstrate that noisier datasets lead to larger Rashomon ratios through the way that practitioners train models. Additionally, we introduce a measure called pattern diversity, which captures the average difference in predictions between distinct classification patterns in the Rashomon set, and motivate why it tends to increase with label noise. Our results explain a key aspect of why simpler models often tend to perform as well as black box models on complex, noisier datasets.

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NeurIPS Conference 2023 Conference Paper

Exploring and Interacting with the Set of Good Sparse Generalized Additive Models

  • Chudi Zhong
  • Zhi Chen
  • Jiachang Liu
  • Margo Seltzer
  • Cynthia Rudin

In real applications, interaction between machine learning models and domain experts is critical; however, the classical machine learning paradigm that usually produces only a single model does not facilitate such interaction. Approximating and exploring the Rashomon set, i. e. , the set of all near-optimal models, addresses this practical challenge by providing the user with a searchable space containing a diverse set of models from which domain experts can choose. We present algorithms to efficiently and accurately approximate the Rashomon set of sparse, generalized additive models with ellipsoids for fixed support sets and use these ellipsoids to approximate Rashomon sets for many different support sets. The approximated Rashomon set serves as a cornerstone to solve practical challenges such as (1) studying the variable importance for the model class; (2) finding models under user-specified constraints (monotonicity, direct editing); and (3) investigating sudden changes in the shape functions. Experiments demonstrate the fidelity of the approximated Rashomon set and its effectiveness in solving practical challenges.

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JMLR Journal 2023 Journal Article

Globally-Consistent Rule-Based Summary-Explanations for Machine Learning Models: Application to Credit-Risk Evaluation

  • Cynthia Rudin
  • Yaron Shaposhnik

We develop a method for understanding specific predictions made by (global) predictive models by constructing (local) models tailored to each specific observation (these are also called “explanations" in the literature). Unlike existing work that “explains” specific observations by approximating global models in the vicinity of these observations, we fit models that are globally-consistent with predictions made by the global model on past data. We focus on rule-based models (also known as association rules or conjunctions of predicates), which are interpretable and widely used in practice. We design multiple algorithms to extract such rules from discrete and continuous datasets, and study their theoretical properties. Finally, we apply these algorithms to multiple credit-risk models trained on the Explainable Machine Learning Challenge data from FICO and demonstrate that our approach effectively produces sparse summary-explanations of these models in seconds. Our approach is model-agnostic (that is, can be used to explain any predictive model), and solves a minimum set cover problem to construct its summaries. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2023. ( edit, beta )

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NeurIPS Conference 2023 Conference Paper

OKRidge: Scalable Optimal k-Sparse Ridge Regression

  • Jiachang Liu
  • Sam Rosen
  • Chudi Zhong
  • Cynthia Rudin

We consider an important problem in scientific discovery, namely identifying sparse governing equations for nonlinear dynamical systems. This involves solving sparse ridge regression problems to provable optimality in order to determine which terms drive the underlying dynamics. We propose a fast algorithm, OKRidge, for sparse ridge regression, using a novel lower bound calculation involving, first, a saddle point formulation, and from there, either solving (i) a linear system or (ii) using an ADMM-based approach, where the proximal operators can be efficiently evaluated by solving another linear system and an isotonic regression problem. We also propose a method to warm-start our solver, which leverages a beam search. Experimentally, our methods attain provable optimality with run times that are orders of magnitude faster than those of the existing MIP formulations solved by the commercial solver Gurobi.

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AAAI Conference 2023 Conference Paper

Optimal Sparse Regression Trees

  • Rui Zhang
  • Rui Xin
  • Margo Seltzer
  • Cynthia Rudin

Regression trees are one of the oldest forms of AI models, and their predictions can be made without a calculator, which makes them broadly useful, particularly for high-stakes applications. Within the large literature on regression trees, there has been little effort towards full provable optimization, mainly due to the computational hardness of the problem. This work proposes a dynamic programming-with-bounds approach to the construction of provably-optimal sparse regression trees. We leverage a novel lower bound based on an optimal solution to the k-Means clustering algorithm on one dimensional data. We are often able to find optimal sparse trees in seconds, even for challenging datasets that involve large numbers of samples and highly-correlated features.

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NeurIPS Conference 2023 Conference Paper

The Rashomon Importance Distribution: Getting RID of Unstable, Single Model-based Variable Importance

  • Jon Donnelly
  • Srikar Katta
  • Cynthia Rudin
  • Edward Browne

Quantifying variable importance is essential for answering high-stakes questions in fields like genetics, public policy, and medicine. Current methods generally calculate variable importance for a given model trained on a given dataset. However, for a given dataset, there may be many models that explain the target outcome equally well; without accounting for all possible explanations, different researchers may arrive at many conflicting yet equally valid conclusions given the same data. Additionally, even when accounting for all possible explanations for a given dataset, these insights may not generalize because not all good explanations are stable across reasonable data perturbations. We propose a new variable importance framework that quantifies the importance of a variable across the set of all good models and is stable across the data distribution. Our framework is extremely flexible and can be integrated with most existing model classes and global variable importance metrics. We demonstrate through experiments that our framework recovers variable importance rankings for complex simulation setups where other methods fail. Further, we show that our framework accurately estimates the true importance of a variable for the underlying data distribution. We provide theoretical guarantees on the consistency and finite sample error rates for our estimator. Finally, we demonstrate its utility with a real-world case study exploring which genes are important for predicting HIV load in persons with HIV, highlighting an important gene that has not previously been studied in connection with HIV.

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NeurIPS Conference 2023 Conference Paper

This Looks Like Those: Illuminating Prototypical Concepts Using Multiple Visualizations

  • Chiyu Ma
  • Brandon Zhao
  • Chaofan Chen
  • Cynthia Rudin

We present ProtoConcepts, a method for interpretable image classification combining deep learning and case-based reasoning using prototypical parts. Existing work in prototype-based image classification uses a "this looks like that'' reasoning process, which dissects a test image by finding prototypical parts and combining evidence from these prototypes to make a final classification. However, all of the existing prototypical part-based image classifiers provide only one-to-one comparisons, where a single training image patch serves as a prototype to compare with a part of our test image. With these single-image comparisons, it can often be difficult to identify the underlying concept being compared (e. g. , "is it comparing the color or the shape? ''). Our proposed method modifies the architecture of prototype-based networks to instead learn prototypical concepts which are visualized using multiple image patches. Having multiple visualizations of the same prototype allows us to more easily identify the concept captured by that prototype (e. g. , "the test image and the related training patches are all the same shade of blue''), and allows our model to create richer, more interpretable visual explanations. Our experiments show that our ``this looks like those'' reasoning process can be applied as a modification to a wide range of existing prototypical image classification networks while achieving comparable accuracy on benchmark datasets.

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UAI Conference 2023 Conference Paper

Variable importance matching for causal inference

  • Quinn Lanners
  • Harsh Parikh
  • Alexander Volfovsky
  • Cynthia Rudin
  • David Page

Our goal is to produce methods for observational causal inference that are auditable, easy to troubleshoot, yield accurate treatment effect estimates, and scalable to high-dimensional data. We describe a general framework called Model-to-Match that achieves these goals by (i) learning a distance metric via outcome modeling, (ii) creating matched groups using the distance metric, and (iii) using the matched groups to estimate treatment effects. Model-to-Match uses variable importance measurements to construct a distance metric, making it a flexible framework that can be adapted to various applications. Concentrating on the scalability of the problem in the number of potential confounders, we operationalize the Model-to-Match framework with LASSO. We derive performance guarantees for settings where LASSO outcome modeling consistently identifies all confounders (importantly without requiring the linear model to be correctly specified). We also provide experimental results demonstrating the auditability of matches, as well as extensions to more general nonparametric outcome modeling.

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UAI Conference 2022 Conference Paper

Data poisoning attacks on off-policy policy evaluation methods

  • Elita A. Lobo
  • Harvineet Singh
  • Marek Petrik
  • Cynthia Rudin
  • Himabindu Lakkaraju

Off-policy Evaluation (OPE) methods are a crucial tool for evaluating policies in high-stakes domains such as healthcare, where exploration is often infeasible, unethical, or expensive. However, the extent to which such methods can be trusted under adversarial threats to data quality is largely unexplored. In this work, we make the first attempt at investigating the sensitivity of OPE methods to marginal adversarial perturbations to the data. We design a generic data poisoning attack framework leveraging influence functions from robust statistics to carefully construct perturbations that maximize error in the policy value estimates. We carry out extensive experimentation with multiple healthcare and control datasets. Our results demonstrate that many existing OPE methods are highly prone to generating value estimates with large errors when subject to data poisoning attacks, even for small adversarial perturbations. These findings question the reliability of policy values derived using OPE methods and motivate the need for developing OPE methods that are statistically robust to train-time data poisoning attacks.

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NeurIPS Conference 2022 Conference Paper

Exploring the Whole Rashomon Set of Sparse Decision Trees

  • Rui Xin
  • Chudi Zhong
  • Zhi Chen
  • Takuya Takagi
  • Margo Seltzer
  • Cynthia Rudin

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.

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AAAI Conference 2022 Conference Paper

Fast Sparse Decision Tree Optimization via Reference Ensembles

  • Hayden McTavish
  • Chudi Zhong
  • Reto Achermann
  • Ilias Karimalis
  • Jacques Chen
  • Cynthia Rudin
  • Margo Seltzer

Sparse decision tree optimization has been one of the most fundamental problems in AI since its inception and is a challenge at the core of interpretable machine learning. Sparse decision tree optimization is computationally hard, and despite steady effort since the 1960’s, breakthroughs have been made on the problem only within the past few years, primarily on the problem of finding optimal sparse decision trees. However, current state-of-the-art algorithms often require impractical amounts of computation time and memory to find optimal or near-optimal trees for some real-world datasets, particularly those having several continuous-valued features. Given that the search spaces of these decision tree optimization problems are massive, can we practically hope to find a sparse decision tree that competes in accuracy with a black box machine learning model? We address this problem via smart guessing strategies that can be applied to any optimal branch-and-bound-based decision tree algorithm. The guesses come from knowledge gleaned from black box models. We show that by using these guesses, we can reduce the run time by multiple orders of magnitude while providing bounds on how far the resulting trees can deviate from the black box’s accuracy and expressive power. Our approach enables guesses about how to bin continuous features, the size of the tree, and lower bounds on the error for the optimal decision tree. Our experiments show that in many cases we can rapidly construct sparse decision trees that match the accuracy of black box models. To summarize: when you are having trouble optimizing, just guess.

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NeurIPS Conference 2022 Conference Paper

FasterRisk: Fast and Accurate Interpretable Risk Scores

  • Jiachang Liu
  • Chudi Zhong
  • Boxuan Li
  • Margo Seltzer
  • Cynthia Rudin

Over the last century, risk scores have been the most popular form of predictive model used in healthcare and criminal justice. Risk scores are sparse linear models with integer coefficients; often these models can be memorized or placed on an index card. Typically, risk scores have been created either without data or by rounding logistic regression coefficients, but these methods do not reliably produce high-quality risk scores. Recent work used mathematical programming, which is computationally slow. We introduce an approach for efficiently producing a collection of high-quality risk scores learned from data. Specifically, our approach produces a pool of almost-optimal sparse continuous solutions, each with a different support set, using a beam-search algorithm. Each of these continuous solutions is transformed into a separate risk score through a "star ray" search, where a range of multipliers are considered before rounding the coefficients sequentially to maintain low logistic loss. Our algorithm returns all of these high-quality risk scores for the user to consider. This method completes within minutes and can be valuable in a broad variety of applications.

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JMLR Journal 2022 Journal Article

MALTS: Matching After Learning to Stretch

  • Harsh Parikh
  • Cynthia Rudin
  • Alexander Volfovsky

We introduce a flexible framework that produces high-quality almost-exact matches for causal inference. Most prior work in matching uses ad-hoc distance metrics, often leading to poor quality matches, particularly when there are irrelevant covariates. In this work, we learn an interpretable distance metric for matching, which leads to substantially higher quality matches. The learned distance metric stretches the covariate space according to each covariate's contribution to outcome prediction: this stretching means that mismatches on important covariates carry a larger penalty than mismatches on irrelevant covariates. Our ability to learn flexible distance metrics leads to matches that are interpretable and useful for the estimation of conditional average treatment effects. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2022. ( edit, beta )

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JMLR Journal 2022 Journal Article

Rethinking Nonlinear Instrumental Variable Models through Prediction Validity

  • Chunxiao Li
  • Cynthia Rudin
  • Tyler H. McCormick

Instrumental variables (IV) are widely used in the social and health sciences in situations where a researcher would like to measure a causal effect but cannot perform an experiment. For valid causal inference in an IV model, there must be external (exogenous) variation that (i) has a sufficiently large impact on the variable of interest (called the relevance assumption) and where (ii) the only pathway through which the external variation impacts the outcome is via the variable of interest (called the exclusion restriction). For statistical inference, researchers must also make assumptions about the functional form of the relationship between the three variables. Current practice assumes (i) and (ii) are met, then postulates a functional form with limited input from the data. In this paper, we describe a framework that leverages machine learning to validate these typically unchecked but consequential assumptions in the IV framework, providing the researcher empirical evidence about the quality of the instrument given the data at hand. Central to the proposed approach is the idea of prediction validity. Prediction validity checks that error terms -- which should be independent from the instrument -- cannot be modeled with machine learning any better than a model that is identically zero. We use prediction validity to develop both one-stage and two-stage approaches for IV, and demonstrate their performance on an example relevant to climate change policy. [abs] [ pdf ][ bib ] &copy JMLR 2022. ( edit, beta )

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JMLR Journal 2021 Journal Article

FLAME: A Fast Large-scale Almost Matching Exactly Approach to Causal Inference

  • Tianyu Wang
  • Marco Morucci
  • M. Usaid Awan
  • Yameng Liu
  • Sudeepa Roy
  • Cynthia Rudin
  • Alexander Volfovsky

A classical problem in causal inference is that of matching, where treatment units need to be matched to control units based on covariate information. In this work, we propose a method that computes high quality almost-exact matches for high-dimensional categorical datasets. This method, called FLAME (Fast Large-scale Almost Matching Exactly), learns a distance metric for matching using a hold-out training data set. In order to perform matching efficiently for large datasets, FLAME leverages techniques that are natural for query processing in the area of database management, and two implementations of FLAME are provided: the first uses SQL queries and the second uses bit-vector techniques. The algorithm starts by constructing matches of the highest quality (exact matches on all covariates), and successively eliminates variables in order to match exactly on as many variables as possible, while still maintaining interpretable high-quality matches and balance between treatment and control groups. We leverage these high quality matches to estimate conditional average treatment effects (CATEs). Our experiments show that FLAME scales to huge datasets with millions of observations where existing state-of-the-art methods fail, and that it achieves significantly better performance than other matching methods. [abs] [ pdf ][ bib ] [ website ] &copy JMLR 2021. ( edit, beta )

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JAIR Journal 2021 Journal Article

Playing Codenames with Language Graphs and Word Embeddings

  • Divya Koyyalagunta
  • Anna Sun
  • Rachel Lea Draelos
  • Cynthia Rudin

Although board games and video games have been studied for decades in artificial intelligence research, challenging word games remain relatively unexplored. Word games are not as constrained as games like chess or poker. Instead, word game strategy is defined by the players’ understanding of the way words relate to each other. The word game Codenames provides a unique opportunity to investigate common sense understanding of relationships between words, an important open challenge. We propose an algorithm that can generate Codenames clues from the language graph BabelNet or from any of several embedding methods – word2vec, GloVe, fastText or BERT. We introduce a new scoring function that measures the quality of clues, and we propose a weighting term called DETECT that incorporates dictionary-based word representations and document frequency to improve clue selection. We develop BabelNet-Word Selection Framework (BabelNet-WSF) to improve BabelNet clue quality and overcome the computational barriers that previously prevented leveraging language graphs for Codenames. Extensive experiments with human evaluators demonstrate that our proposed innovations yield state-of-the-art performance, with up to 102.8% improvement in precision@2 in some cases. Overall, this work advances the formal study of word games and approaches for common sense language understanding.

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JMLR Journal 2021 Journal Article

Regulating Greed Over Time in Multi-Armed Bandits

  • Stefano Tracà
  • Cynthia Rudin
  • Weiyu Yan

In retail, there are predictable yet dramatic time-dependent patterns in customer behavior, such as periodic changes in the number of visitors, or increases in customers just before major holidays. The current paradigm of multi-armed bandit analysis does not take these known patterns into account. This means that for applications in retail, where prices are fixed for periods of time, current bandit algorithms will not suffice. This work provides a remedy that takes the time-dependent patterns into account, and we show how this remedy is implemented for the UCB, $\varepsilon$-greedy, and UCB-L algorithms, and also through a new policy called the variable arm pool algorithm. In the corrected methods, exploitation (greed) is regulated over time, so that more exploitation occurs during higher reward periods, and more exploration occurs in periods of low reward. In order to understand why regret is reduced with the corrected methods, we present a set of bounds that provide insight into why we would want to exploit during periods of high reward, and discuss the impact on regret. Our proposed methods perform well in experiments, and were inspired by a high-scoring entry in the Exploration and Exploitation 3 contest using data from Yahoo$!$ Front Page. That entry heavily used time-series methods to regulate greed over time, which was substantially more effective than other contextual bandit methods. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2021. ( edit, beta )

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JMLR Journal 2021 Journal Article

Understanding How Dimension Reduction Tools Work: An Empirical Approach to Deciphering t-SNE, UMAP, TriMap, and PaCMAP for Data Visualization

  • Yingfan Wang
  • Haiyang Huang
  • Cynthia Rudin
  • Yaron Shaposhnik

Dimension reduction (DR) techniques such as t-SNE, UMAP, and TriMap have demonstrated impressive visualization performance on many real-world datasets. One tension that has always faced these methods is the trade-off between preservation of global structure and preservation of local structure: these methods can either handle one or the other, but not both. In this work, our main goal is to understand what aspects of DR methods are important for preserving both local and global structure: it is difficult to design a better method without a true understanding of the choices we make in our algorithms and their empirical impact on the low-dimensional embeddings they produce. Towards the goal of local structure preservation, we provide several useful design principles for DR loss functions based on our new understanding of the mechanisms behind successful DR methods. Towards the goal of global structure preservation, our analysis illuminates that the choice of which components to preserve is important. We leverage these insights to design a new algorithm for DR, called Pairwise Controlled Manifold Approximation Projection (PaCMAP), which preserves both local and global structure. Our work provides several unexpected insights into what design choices both to make and avoid when constructing DR algorithms. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2021. ( edit, beta )

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UAI Conference 2020 Conference Paper

Adaptive Hyper-box Matching for Interpretable Individualized Treatment Effect Estimation

  • Marco Morucci
  • Vittorio Orlandi
  • Sudeepa Roy 0001
  • Cynthia Rudin
  • Alexander Volfovsky

We propose a matching method for observational data that matches units with others in unit-specific, hyper-box-shaped regions of the covariate space. These regions are large enough that many matches are created for each unit and small enough that the treatment effect is roughly constant throughout. The regions are found as either the solution to a mixed integer program, or using a (fast) approximation algorithm. The result is an interpretable and tailored estimate of the causal effect for each unit.

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ICML Conference 2020 Conference Paper

Bandits for BMO Functions

  • Tianyu Wang 0008
  • Cynthia Rudin

We study the bandit problem where the underlying expected reward is a Bounded Mean Oscillation (BMO) function. BMO functions are allowed to be discontinuous and unbounded, and are useful in modeling signals with singularities in the domain. We develop a toolset for BMO bandits, and provide an algorithm that can achieve poly-log $\delta$-regret – a regret measured against an arm that is optimal after removing a $\delta$-sized portion of the arm space.

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ICML Conference 2020 Conference Paper

Generalized and Scalable Optimal Sparse Decision Trees

  • Jimmy Lin
  • Chudi Zhong
  • Diane Hu
  • Cynthia Rudin
  • Margo I. Seltzer

Decision tree optimization is notoriously difficult from a computational perspective but essential for the field of interpretable machine learning. Despite efforts over the past 40 years, only recently have optimization breakthroughs been made that have allowed practical algorithms to find optimal decision trees. These new techniques have the potential to trigger a paradigm shift, where, it is possible to construct sparse decision trees to efficiently optimize a variety of objective functions, without relying on greedy splitting and pruning heuristics that often lead to suboptimal solutions. The contribution in this work is to provide a general framework for decision tree optimization that addresses the two significant open problems in the area: treatment of imbalanced data and fully optimizing over continuous variables. We present techniques that produce optimal decision trees over variety of objectives including F-score, AUC, and partial area under the ROC convex hull. We also introduce a scalable algorithm that produces provably optimal results in the presence of continuous variables and speeds up decision tree construction by several order of magnitude relative to the state-of-the art.

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JMLR Journal 2019 Journal Article

All Models are Wrong, but Many are Useful: Learning a Variable's Importance by Studying an Entire Class of Prediction Models Simultaneously

  • Aaron Fisher
  • Cynthia Rudin
  • Francesca Dominici

Variable importance (VI) tools describe how much covariates contribute to a prediction model's accuracy. However, important variables for one well-performing model (for example, a linear model $f(\mathbf{x})=\mathbf{x}^{T}\beta$ with a fixed coefficient vector $\beta$) may be unimportant for another model. In this paper, we propose model class reliance (MCR) as the range of VI values across all well-performing model in a prespecified class. Thus, MCR gives a more comprehensive description of importance by accounting for the fact that many prediction models, possibly of different parametric forms, may fit the data well. In the process of deriving MCR, we show several informative results for permutation-based VI estimates, based on the VI measures used in Random Forests. Specifically, we derive connections between permutation importance estimates for a single prediction model, U-statistics, conditional variable importance, conditional causal effects, and linear model coefficients. We then give probabilistic bounds for MCR, using a novel, generalizable technique. We apply MCR to a public data set of Broward County criminal records to study the reliance of recidivism prediction models on sex and race. In this application, MCR can be used to help inform VI for unknown, proprietary models. [abs] [ pdf ][ bib ] &copy JMLR 2019. ( edit, beta )

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UAI Conference 2019 Conference Paper

Interpretable Almost Matching Exactly With Instrumental Variables

  • M. Usaid Awan
  • Yameng Liu
  • Marco Morucci
  • Sudeepa Roy 0001
  • Cynthia Rudin
  • Alexander Volfovsky

Uncertainty in the estimation of the causal effect in observational studies is often due to unmeasured confounding, i. e. , the presence of unobserved covariates linking treatments and outcomes. Instrumental Variables (IV) are commonly used to reduce the effects of unmeasured confounding. Existing methods for IV estimation either require strong parametric assumptions, use arbitrary distance metrics, or do not scale well to large datasets. We propose a matching framework for IV in the presence of observed categorical confounders that addresses these weaknesses. Our method first matches units exactly, and then consecutively drops variables to approximately match the remaining units on as many variables as possible. We show that our algorithm constructs better matches than other existing methods on simulated datasets, and we produce interesting results in an application to political canvassing.

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JMLR Journal 2019 Journal Article

Learning Optimized Risk Scores

  • Berk Ustun
  • Cynthia Rudin

Risk scores are simple classification models that let users make quick risk predictions by adding and subtracting a few small numbers. These models are widely used in medicine and criminal justice, but are difficult to learn from data because they need to be calibrated, sparse, use small integer coefficients, and obey application-specific constraints. In this paper, we introduce a machine learning method to learn risk scores. We formulate the risk score problem as a mixed integer nonlinear program, and present a cutting plane algorithm to recover its optimal solution. We improve our algorithm with specialized techniques that generate feasible solutions, narrow the optimality gap, and reduce data-related computation. Our algorithm can train risk scores in a way that scales linearly in the number of samples in a dataset, and that allows practitioners to address application-specific constraints without parameter tuning or post-processing. We benchmark the performance of different methods to learn risk scores on publicly available datasets, comparing risk scores produced by our method to risk scores built using methods that are used in practice. We also discuss the practical benefits of our method through a real-world application where we build a customized risk score for ICU seizure prediction in collaboration with the Massachusetts General Hospital. [abs] [ pdf ][ bib ] &copy JMLR 2019. ( edit, beta )

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NeurIPS Conference 2019 Conference Paper

Optimal Sparse Decision Trees

  • Xiyang Hu
  • Cynthia Rudin
  • Margo Seltzer

Decision tree algorithms have been among the most popular algorithms for interpretable (transparent) machine learning since the early 1980's. The problem that has plagued decision tree algorithms since their inception is their lack of optimality, or lack of guarantees of closeness to optimality: decision tree algorithms are often greedy or myopic, and sometimes produce unquestionably suboptimal models. Hardness of decision tree optimization is both a theoretical and practical obstacle, and even careful mathematical programming approaches have not been able to solve these problems efficiently. This work introduces the first practical algorithm for optimal decision trees for binary variables. The algorithm is a co-design of analytical bounds that reduce the search space and modern systems techniques, including data structures and a custom bit-vector library. We highlight possible steps to improving the scalability and speed of future generations of this algorithm based on insights from our theory and experiments.

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UAI Conference 2019 Conference Paper

Reducing Exploration of Dying Arms in Mortal Bandits

  • Stefano Tracà
  • Weiyu Yan
  • Cynthia Rudin

Mortal bandits have proven to be extremely useful for providing news article recommendations, running automated online advertising campaigns, and for other applications where the set of available options changes over time. Previous work on this problem showed how to regulate exploration of new arms when they have recently appeared, but they do not adapt when the arms are about to disappear. Since in most applications we can determine either exactly or approximately when arms will disappear, we can leverage this information to improve performance: we should not be exploring arms that are about to disappear. We provide adaptations of algorithms, regret bounds, and experiments for this study, showing a clear benefit from regulating greed (exploration/exploitation) for arms that will soon disappear. We illustrate numerical performance on the Yahoo! Front Page Today Module User Click Log Dataset.

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NeurIPS Conference 2019 Conference Paper

This Looks Like That: Deep Learning for Interpretable Image Recognition

  • Chaofan Chen
  • Oscar Li
  • Daniel Tao
  • Alina Barnett
  • Cynthia Rudin
  • Jonathan Su

When we are faced with challenging image classification tasks, we often explain our reasoning by dissecting the image, and pointing out prototypical aspects of one class or another. The mounting evidence for each of the classes helps us make our final decision. In this work, we introduce a deep network architecture -- prototypical part network (ProtoPNet), that reasons in a similar way: the network dissects the image by finding prototypical parts, and combines evidence from the prototypes to make a final classification. The model thus reasons in a way that is qualitatively similar to the way ornithologists, physicians, and others would explain to people on how to solve challenging image classification tasks. The network uses only image-level labels for training without any annotations for parts of images. We demonstrate our method on the CUB-200-2011 dataset and the Stanford Cars dataset. Our experiments show that ProtoPNet can achieve comparable accuracy with its analogous non-interpretable counterpart, and when several ProtoPNets are combined into a larger network, it can achieve an accuracy that is on par with some of the best-performing deep models. Moreover, ProtoPNet provides a level of interpretability that is absent in other interpretable deep models.

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AAAI Conference 2018 Conference Paper

Deep Learning for Case-Based Reasoning Through Prototypes: A Neural Network That Explains Its Predictions

  • Oscar Li
  • Hao Liu
  • Chaofan Chen
  • Cynthia Rudin

Deep neural networks are widely used for classification. These deep models often suffer from a lack of interpretability – they are particularly difficult to understand because of their non-linear nature. As a result, neural networks are often treated as “black box” models, and in the past, have been trained purely to optimize the accuracy of predictions. In this work, we create a novel network architecture for deep learning that naturally explains its own reasoning for each prediction. This architecture contains an autoencoder and a special prototype layer, where each unit of that layer stores a weight vector that resembles an encoded training input. The encoder of the autoencoder allows us to do comparisons within the latent space, while the decoder allows us to visualize the learned prototypes. The training objective has four terms: an accuracy term, a term that encourages every prototype to be similar to at least one encoded input, a term that encourages every encoded input to be close to at least one prototype, and a term that encourages faithful reconstruction by the autoencoder. The distances computed in the prototype layer are used as part of the classification process. Since the prototypes are learned during training, the learned network naturally comes with explanations for each prediction, and the explanations are loyal to what the network actually computes.

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JMLR Journal 2018 Journal Article

Learning Certifiably Optimal Rule Lists for Categorical Data

  • Elaine Angelino
  • Nicholas Larus-Stone
  • Daniel Alabi
  • Margo Seltzer
  • Cynthia Rudin

We present the design and implementation of a custom discrete optimization technique for building rule lists over a categorical feature space. Our algorithm produces rule lists with optimal training performance, according to the regularized empirical risk, with a certificate of optimality. By leveraging algorithmic bounds, efficient data structures, and computational reuse, we achieve several orders of magnitude speedup in time and a massive reduction of memory consumption. We demonstrate that our approach produces optimal rule lists on practical problems in seconds. Our results indicate that it is possible to construct optimal sparse rule lists that are approximately as accurate as the COMPAS proprietary risk prediction tool on data from Broward County, Florida, but that are completely interpretable. This framework is a novel alternative to CART and other decision tree methods for interpretable modeling. [abs] [ pdf ][ bib ] &copy JMLR 2018. ( edit, beta )

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JMLR Journal 2017 Journal Article

A Bayesian Framework for Learning Rule Sets for Interpretable Classification

  • Tong Wang
  • Cynthia Rudin
  • Finale Doshi-Velez
  • Yimin Liu
  • Erica Klampfl
  • Perry MacNeille

We present a machine learning algorithm for building classifiers that are comprised of a small number of short rules. These are restricted disjunctive normal form models. An example of a classifier of this form is as follows: If $X$ satisfies (condition $A$ AND condition $B$) OR (condition $C$) OR $\cdots$, then $Y=1$. Models of this form have the advantage of being interpretable to human experts since they produce a set of rules that concisely describe a specific class. We present two probabilistic models with prior parameters that the user can set to encourage the model to have a desired size and shape, to conform with a domain-specific definition of interpretability. We provide a scalable MAP inference approach and develop theoretical bounds to reduce computation by iteratively pruning the search space. We apply our method (Bayesian Rule Sets -- BRS ) to characterize and predict user behavior with respect to in-vehicle context-aware personalized recommender systems. Our method has a major advantage over classical associative classification methods and decision trees in that it does not greedily grow the model. [abs] [ pdf ][ bib ] &copy JMLR 2017. ( edit, beta )

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ICML Conference 2017 Conference Paper

Scalable Bayesian Rule Lists

  • Hongyu Yang
  • Cynthia Rudin
  • Margo I. Seltzer

We present an algorithm for building probabilistic rule lists that is two orders of magnitude faster than previous work. Rule list algorithms are competitors for decision tree algorithms. They are associative classifiers, in that they are built from pre-mined association rules. They have a logical structure that is a sequence of IF-THEN rules, identical to a decision list or one-sided decision tree. Instead of using greedy splitting and pruning like decision tree algorithms, we aim to fully optimize over rule lists, striking a practical balance between accuracy, interpretability, and computational speed. The algorithm presented here uses a mixture of theoretical bounds (tight enough to have practical implications as a screening or bounding procedure), computational reuse, and highly tuned language libraries to achieve computational efficiency. Currently, for many practical problems, this method achieves better accuracy and sparsity than decision trees. In many cases, the computational time is practical and often less than that of decision trees.

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JMLR Journal 2016 Journal Article

The Factorized Self-Controlled Case Series Method: An Approach for Estimating the Effects of Many Drugs on Many Outcomes

  • Ramin Moghaddass
  • Cynthia Rudin
  • David Madigan

We provide a hierarchical Bayesian model for estimating the effects of transient drug exposures on a collection of health outcomes, where the effects of all drugs on all outcomes are estimated simultaneously. The method possesses properties that allow it to handle important challenges of dealing with large- scale longitudinal observational databases. In particular, this model is a generalization of the self-controlled case series (SCCS) method, meaning that certain patient specific baseline rates never need to be estimated. Further, this model is formulated with layers of latent factors, which substantially reduces the number of parameters and helps with interpretability by illuminating latent classes of drugs and outcomes. We believe our work is the first to consider multivariate SCCS (in the sense of multiple outcomes) and is the first to couple latent factor analysis with SCCS. We demonstrate the approach by estimating the effects of various time-sensitive insulin treatments for diabetes. [abs] [ pdf ][ bib ] &copy JMLR 2016. ( edit, beta )

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NeurIPS Conference 2014 Conference Paper

The Bayesian Case Model: A Generative Approach for Case-Based Reasoning and Prototype Classification

  • Been Kim
  • Cynthia Rudin
  • Julie Shah

We present the Bayesian Case Model (BCM), a general framework for Bayesian case-based reasoning (CBR) and prototype classification and clustering. BCM brings the intuitive power of CBR to a Bayesian generative framework. The BCM learns prototypes, the ``quintessential observations that best represent clusters in a dataset, by performing joint inference on cluster labels, prototypes and important features. Simultaneously, BCM pursues sparsity by learning subspaces, the sets of features that play important roles in the characterization of the prototypes. The prototype and subspace representation provides quantitative benefits in interpretability while preserving classification accuracy. Human subject experiments verify statistically significant improvements to participants' understanding when using explanations produced by BCM, compared to those given by prior art. "

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JMLR Journal 2013 Journal Article

Learning Theory Analysis for Association Rules and Sequential Event Prediction

  • Cynthia Rudin
  • Benjamin Letham
  • David Madigan

We present a theoretical analysis for prediction algorithms based on association rules. As part of this analysis, we introduce a problem for which rules are particularly natural, called “sequential event prediction." In sequential event prediction, events in a sequence are revealed one by one, and the goal is to determine which event will next be revealed. The training set is a collection of past sequences of events. An example application is to predict which item will next be placed into a customer's online shopping cart, given his/her past purchases. In the context of this problem, algorithms based on association rules have distinct advantages over classical statistical and machine learning methods: they look at correlations based on subsets of co-occurring past events (items a and b imply item c), they can be applied to the sequential event prediction problem in a natural way, they can potentially handle the “cold start" problem where the training set is small, and they yield interpretable predictions. In this work, we present two algorithms that incorporate association rules. These algorithms can be used both for sequential event prediction and for supervised classification, and they are simple enough that they can possibly be understood by users, customers, patients, managers, etc. We provide generalization guarantees on these algorithms based on algorithmic stability analysis from statistical learning theory. We include a discussion of the strict minimum support threshold often used in association rule mining, and introduce an “adjusted confidence" measure that provides a weaker minimum support condition that has advantages over the strict minimum support. The paper brings together ideas from statistical learning theory, association rule mining and Bayesian analysis. [abs] [ pdf ][ bib ] &copy JMLR 2013. ( edit, beta )

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JMLR Journal 2013 Journal Article

Machine Learning with Operational Costs

  • Theja Tulabandhula
  • Cynthia Rudin

This work proposes a way to align statistical modeling with decision making. We provide a method that propagates the uncertainty in predictive modeling to the uncertainty in operational cost, where operational cost is the amount spent by the practitioner in solving the problem. The method allows us to explore the range of operational costs associated with the set of reasonable statistical models, so as to provide a useful way for practitioners to understand uncertainty. To do this, the operational cost is cast as a regularization term in a learning algorithm's objective function, allowing either an optimistic or pessimistic view of possible costs, depending on the regularization parameter. From another perspective, if we have prior knowledge about the operational cost, for instance that it should be low, this knowledge can help to restrict the hypothesis space, and can help with generalization. We provide a theoretical generalization bound for this scenario. We also show that learning with operational costs is related to robust optimization. [abs] [ pdf ][ bib ] &copy JMLR 2013. ( edit, beta )

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JMLR Journal 2013 Journal Article

The Rate of Convergence of AdaBoost

  • Indraneel Mukherjee
  • Cynthia Rudin
  • Robert E. Schapire

The AdaBoost algorithm was designed to combine many “weak” hypotheses that perform slightly better than random guessing into a “strong” hypothesis that has very low error. We study the rate at which AdaBoost iteratively converges to the minimum of the “exponential loss”. Unlike previous work, our proofs do not require a weak-learning assumption, nor do they require that minimizers of the exponential loss are finite. Our first result shows that the exponential loss of AdaBoost's computed parameter vector will be at most $\varepsilon$ more than that of any parameter vector of $\ell_1$-norm bounded by $B$ in a number of rounds that is at most a polynomial in $B$ and $1/\varepsilon$. We also provide lower bounds showing that a polynomial dependence is necessary. Our second result is that within $C/\varepsilon$ iterations, AdaBoost achieves a value of the exponential loss that is at most $\varepsilon$ more than the best possible value, where $C$ depends on the data set. We show that this dependence of the rate on $\varepsilon$ is optimal up to constant factors, that is, at least $\Omega(1/\varepsilon)$ rounds are necessary to achieve within $\varepsilon$ of the optimal exponential loss. [abs] [ pdf ][ bib ] &copy JMLR 2013. ( edit, beta )

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JMLR Journal 2011 Journal Article

On Equivalence Relationships Between Classification and Ranking Algorithms

  • Şeyda Ertekin
  • Cynthia Rudin

We demonstrate that there are machine learning algorithms that can achieve success for two separate tasks simultaneously, namely the tasks of classification and bipartite ranking. This means that advantages gained from solving one task can be carried over to the other task, such as the ability to obtain conditional density estimates, and an order-of-magnitude reduction in computational time for training the algorithm. It also means that some algorithms are robust to the choice of evaluation metric used; they can theoretically perform well when performance is measured either by a misclassification error or by a statistic of the ROC curve (such as the area under the curve). Specifically, we provide such an equivalence relationship between a generalization of Freund et al.'s RankBoost algorithm, called the "P-Norm Push," and a particular cost-sensitive classification algorithm that generalizes AdaBoost, which we call "P-Classification." We discuss and validate the potential benefits of this equivalence relationship, and perform controlled experiments to understand P-Classification's empirical performance. There is no established equivalence relationship for logistic regression and its ranking counterpart, so we introduce a logistic-regression-style algorithm that aims in between classification and ranking, and has promising experimental performance with respect to both tasks. [abs] [ pdf ][ bib ] &copy JMLR 2011. ( edit, beta )

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JMLR Journal 2009 Journal Article

Margin-based Ranking and an Equivalence between AdaBoost and RankBoost

  • Cynthia Rudin
  • Robert E. Schapire

We study boosting algorithms for learning to rank. We give a general margin-based bound for ranking based on covering numbers for the hypothesis space. Our bound suggests that algorithms that maximize the ranking margin will generalize well. We then describe a new algorithm, smooth margin ranking, that precisely converges to a maximum ranking-margin solution. The algorithm is a modification of RankBoost, analogous to "approximate coordinate ascent boosting." Finally, we prove that AdaBoost and RankBoost are equally good for the problems of bipartite ranking and classification in terms of their asymptotic behavior on the training set. Under natural conditions, AdaBoost achieves an area under the ROC curve that is equally as good as RankBoost's; furthermore, RankBoost, when given a specific intercept, achieves a misclassification error that is as good as AdaBoost's. This may help to explain the empirical observations made by Cortes and Mohri, and Caruana and Niculescu-Mizil, about the excellent performance of AdaBoost as a bipartite ranking algorithm, as measured by the area under the ROC curve. [abs] [ pdf ][ bib ] &copy JMLR 2009. ( edit, beta )

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JMLR Journal 2009 Journal Article

The P-Norm Push: A Simple Convex Ranking Algorithm that Concentrates at the Top of the List

  • Cynthia Rudin

We are interested in supervised ranking algorithms that perform especially well near the top of the ranked list, and are only required to perform sufficiently well on the rest of the list. In this work, we provide a general form of convex objective that gives high-scoring examples more importance. This "push" near the top of the list can be chosen arbitrarily large or small, based on the preference of the user. We choose l p -norms to provide a specific type of push; if the user sets p larger, the objective concentrates harder on the top of the list. We derive a generalization bound based on the p -norm objective, working around the natural asymmetry of the problem. We then derive a boosting-style algorithm for the problem of ranking with a push at the top. The usefulness of the algorithm is illustrated through experiments on repository data. We prove that the minimizer of the algorithm's objective is unique in a specific sense. Furthermore, we illustrate how our objective is related to quality measurements for information retrieval. [abs] [ pdf ][ bib ] &copy JMLR 2009. ( edit, beta )

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JMLR Journal 2004 Journal Article

The Dynamics of AdaBoost: Cyclic Behavior and Convergence of Margins

  • Cynthia Rudin
  • Ingrid Daubechies
  • Robert E. Schapire

In order to study the convergence properties of the AdaBoost algorithm, we reduce AdaBoost to a nonlinear iterated map and study the evolution of its weight vectors. This dynamical systems approach allows us to understand AdaBoost's convergence properties completely in certain cases; for these cases we find stable cycles, allowing us to explicitly solve for AdaBoost's output. Using this unusual technique, we are able to show that AdaBoost does not always converge to a maximum margin combined classifier, answering an open question. In addition, we show that "non-optimal" AdaBoost (where the weak learning algorithm does not necessarily choose the best weak classifier at each iteration) may fail to converge to a maximum margin classifier, even if "optimal" AdaBoost produces a maximum margin. Also, we show that if AdaBoost cycles, it cycles among "support vectors", i.e., examples that achieve the same smallest margin. [abs] [ pdf ]

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NeurIPS Conference 2003 Conference Paper

On the Dynamics of Boosting

  • Cynthia Rudin
  • Ingrid Daubechies
  • Robert Schapire

In order to understand AdaBoost’s dynamics, especially its ability to maximize margins, we derive an associated simplified nonlinear iterated map and analyze its behavior in low-dimensional cases. We find stable cycles for these cases, which can explicitly be used to solve for Ada- Boost’s output. By considering AdaBoost as a dynamical system, we are able to prove R¨atsch and Warmuth’s conjecture that AdaBoost may fail to converge to a maximal-margin combined classifier when given a ‘non- optimal’ weak learning algorithm. AdaBoost is known to be a coordinate descent method, but other known algorithms that explicitly aim to max- imize the margin (such as AdaBoost⁄ and arc-gv) are not. We consider a differentiable function for which coordinate ascent will yield a maxi- mum margin solution. We then make a simple approximation to derive a new boosting algorithm whose updates are slightly more aggressive than those of arc-gv.

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