arXiv subjects

Cynthia Rudin

Publications and source records attributed to Cynthia Rudin.

At least 91 records · Page 5Linked to original sources

arXiv2022

Generalized and Scalable Optimal Sparse Decision Trees

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 a 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 orders of magnitude relative to the state-of-the art.

cs.LG↗

arXiv2022

Fast Sparse Classification for Generalized Linear and Additive Models

We present fast classification techniques for sparse generalized linear and additive models. These techniques can handle thousands of features and thousands of observations in minutes, even in the presence of many highly correlated features. For fast sparse logistic regression, our computational speed-up over other best-subset search techniques owes to linear and quadratic surrogate cuts for the logistic loss that allow us to efficiently screen features for elimination, as well as use of a priority queue that favors a more uniform exploration of features. As an alternative to the logistic loss, we propose the exponential loss, which permits an analytical solution to the line search at each iteration. Our algorithms are generally 2 to 5 times faster than previous approaches. They produce interpretable models that have accuracy comparable to black box models on challenging datasets.

cs.LG↗

arXiv2022

Exploring the Whole Rashomon Set of Sparse Decision Trees

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.

cs.LG↗

arXiv2022

Fast Optimization of Weighted Sparse Decision Trees for use in Optimal Treatment Regimes and Optimal Policy Design

Sparse decision trees are one of the most common forms of interpretable models. While recent advances have produced algorithms that fully optimize sparse decision trees for prediction, that work does not address policy design, because the algorithms cannot handle weighted data samples. Specifically, they rely on the discreteness of the loss function, which means that real-valued weights cannot be directly used. For example, none of the existing techniques produce policies that incorporate inverse propensity weighting on individual data points. We present three algorithms for efficient sparse weighted decision tree optimization. The first approach directly optimizes the weighted loss function; however, it tends to be computationally inefficient for large datasets. Our second approach, which scales more efficiently, transforms weights to integer values and uses data duplication to transform the weighted decision tree optimization problem into an unweighted (but larger) counterpart. Our third algorithm, which scales to much larger datasets, uses a randomized procedure that samples each data point with a probability proportional to its weight. We present theoretical bounds on the error of the two fast methods and show experimentally that these methods can be two orders of magnitude faster than the direct optimization of the weighted loss, without losing significant accuracy.

cs.LG↗

arXiv2022

FasterRisk: Fast and Accurate Interpretable Risk Scores

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.

cs.LG↗

arXiv2022

How to See Hidden Patterns in Metamaterials with Interpretable Machine Learning

Machine learning models can assist with metamaterials design by approximating computationally expensive simulators or solving inverse design problems. However, past work has usually relied on black box deep neural networks, whose reasoning processes are opaque and require enormous datasets that are expensive to obtain. In this work, we develop two novel machine learning approaches to metamaterials discovery that have neither of these disadvantages. These approaches, called shape-frequency features and unit-cell templates, can discover 2D metamaterials with user-specified frequency band gaps. Our approaches provide logical rule-based conditions on metamaterial unit-cells that allow for interpretable reasoning processes, and generalize well across design spaces of different resolutions. The templates also provide design flexibility where users can almost freely design the fine resolution features of a unit-cell without affecting the user's desired band gap.

cs.LG↗

arXiv2022

TimberTrek: Exploring and Curating Sparse Decision Trees with Interactive Visualization

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.

cs.HC↗

arXiv2022

A robust approach to quantifying uncertainty in matching problems of causal inference

Unquantified sources of uncertainty in observational causal analyses can break the integrity of the results. One would never want another analyst to repeat a calculation with the same dataset, using a seemingly identical procedure, only to find a different conclusion. However, as we show in this work, there is a typical source of uncertainty that is essentially never considered in observational causal studies: the choice of match assignment for matched groups, that is, which unit is matched to which other unit before a hypothesis test is conducted. The choice of match assignment is anything but innocuous, and can have a surprisingly large influence on the causal conclusions. Given that a vast number of causal inference studies test hypotheses on treatment effects after treatment cases are matched with similar control cases, we should find a way to quantify how much this extra source of uncertainty impacts results. What we would really like to be able to report is that \emph{no matter} which match assignment is made, as long as the match is sufficiently good, then the hypothesis test result still holds. In this paper, we provide methodology based on discrete optimization to create robust tests that explicitly account for this possibility. We formulate robust tests for binary and continuous data based on common test statistics as integer linear programs solvable with common methodologies. We study the finite-sample behavior of our test statistic in the discrete-data case. We apply our methods to simulated and real-world datasets and show that they can produce useful results in practical applied settings.

stat.ME↗

arXiv2022

Fast Sparse Decision Tree Optimization via Reference Ensembles

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 only been made on the problem 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. 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.

cs.LG↗

arXiv2022

There is no Accuracy-Interpretability Tradeoff in Reinforcement Learning for Mazes

Interpretability is an essential building block for trustworthiness in reinforcement learning systems. However, interpretability might come at the cost of deteriorated performance, leading many researchers to build complex models. Our goal is to analyze the cost of interpretability. We show that in certain cases, one can achieve policy interpretability while maintaining its optimality. We focus on a classical problem from reinforcement learning: mazes with $k$ obstacles in $\mathbb{R}^d$. We prove the existence of a small decision tree with a linear function at each inner node and depth $O(\log k + 2^d)$ that represents an optimal policy. Note that for the interesting case of a constant $d$, we have $O(\log k)$ depth. Thus, in this setting, there is no accuracy-interpretability tradeoff. To prove this result, we use a new "compressing" technique that might be useful in additional settings.

cs.LG↗

arXiv2022

On the Existence of Simpler Machine Learning Models

It is almost always easier to find an accurate-but-complex model than an accurate-yet-simple model. Finding optimal, sparse, accurate models of various forms (linear models with integer coefficients, decision sets, rule lists, decision trees) is generally NP-hard. We often do not know whether the search for a simpler model will be worthwhile, and thus we do not go to the trouble of searching for one. In this work, we ask an important practical question: can accurate-yet-simple models be proven to exist, or shown likely to exist, before explicitly searching for them? We hypothesize that there is an important reason that simple-yet-accurate models often do exist. This hypothesis is that the size of the Rashomon set is often large, where the Rashomon set is the set of almost-equally-accurate models from a function class. If the Rashomon set is large, it contains numerous accurate models, and perhaps at least one of them is the simple model we desire. In this work, we formally present the Rashomon ratio as a new gauge of simplicity for a learning problem, depending on a function class and a data set. The Rashomon ratio is the ratio of the volume of the set of accurate models to the volume of the hypothesis space, and it is different from standard complexity measures from statistical learning theory. Insight from studying the Rashomon ratio provides an easy way to check whether a simpler model might exist for a problem before finding it, namely whether several different machine learning methods achieve similar performance on the data. In that sense, the Rashomon ratio is a powerful tool for understanding why and when an accurate-yet-simple model might exist. If, as we hypothesize in this work, many real-world data sets admit large Rashomon sets, the implications are vast: it means that simple or interpretable models may often be used for high-stakes decisions without losing accuracy.

cs.LG↗

arXiv2022

SegDiscover: Visual Concept Discovery via Unsupervised Semantic Segmentation

Visual concept discovery has long been deemed important to improve interpretability of neural networks, because a bank of semantically meaningful concepts would provide us with a starting point for building machine learning models that exhibit intelligible reasoning process. Previous methods have disadvantages: either they rely on labelled support sets that incorporate human biases for objects that are "useful," or they fail to identify multiple concepts that occur within a single image. We reframe the concept discovery task as an unsupervised semantic segmentation problem, and present SegDiscover, a novel framework that discovers semantically meaningful visual concepts from imagery datasets with complex scenes without supervision. Our method contains three important pieces: generating concept primitives from raw images, discovering concepts by clustering in the latent space of a self-supervised pretrained encoder, and concept refinement via neural network smoothing. Experimental results provide evidence that our method can discover multiple concepts within a single image and outperforms state-of-the-art unsupervised methods on complex datasets such as Cityscapes and COCO-Stuff. Our method can be further used as a neural network explanation tool by comparing results obtained by different encoders.

cs.CV↗

arXiv2022

In Pursuit of Interpretable, Fair and Accurate Machine Learning for Criminal Recidivism Prediction

Objectives: We study interpretable recidivism prediction using machine learning (ML) models and analyze performance in terms of prediction ability, sparsity, and fairness. Unlike previous works, this study trains interpretable models that output probabilities rather than binary predictions, and uses quantitative fairness definitions to assess the models. This study also examines whether models can generalize across geographic locations. Methods: We generated black-box and interpretable ML models on two different criminal recidivism datasets from Florida and Kentucky. We compared predictive performance and fairness of these models against two methods that are currently used in the justice system to predict pretrial recidivism: the Arnold PSA and COMPAS. We evaluated predictive performance of all models on predicting six different types of crime over two time spans. Results: Several interpretable ML models can predict recidivism as well as black-box ML models and are more accurate than COMPAS or the Arnold PSA. These models are potentially useful in practice. Similar to the Arnold PSA, some of these interpretable models can be written down as a simple table. Others can be displayed using a set of visualizations. Our geographic analysis indicates that ML models should be trained separately for separate locations and updated over time. We also present a fairness analysis for the interpretable models. Conclusions: Interpretable machine learning models can perform just as well as non-interpretable methods and currently-used risk assessment scales, in terms of both prediction accuracy and fairness. Machine learning models might be more accurate when trained separately for distinct locations and kept up-to-date.

stat.ML↗

arXiv2022

BacHMMachine: An Interpretable and Scalable Model for Algorithmic Harmonization for Four-part Baroque Chorales

Algorithmic harmonization - the automated harmonization of a musical piece given its melodic line - is a challenging problem that has garnered much interest from both music theorists and computer scientists. One genre of particular interest is the four-part Baroque chorales of J.S. Bach. Methods for algorithmic chorale harmonization typically adopt a black-box, "data-driven" approach: they do not explicitly integrate principles from music theory but rely on a complex learning model trained with a large amount of chorale data. We propose instead a new harmonization model, called BacHMMachine, which employs a "theory-driven" framework guided by music composition principles, along with a "data-driven" model for learning compositional features within this framework. As its name suggests, BacHMMachine uses a novel Hidden Markov Model based on key and chord transitions, providing a probabilistic framework for learning key modulations and chordal progressions from a given melodic line. This allows for the generation of creative, yet musically coherent chorale harmonizations; integrating compositional principles allows for a much simpler model that results in vast decreases in computational burden and greater interpretability compared to state-of-the-art algorithmic harmonization methods, at no penalty to quality of harmonization or musicality. We demonstrate this improvement via comprehensive experiments and Turing tests comparing BacHMMachine to existing methods.

cs.SD↗

arXiv2021

Interpretable Mammographic Image Classification using Case-Based Reasoning and Deep Learning

When we deploy machine learning models in high-stakes medical settings, we must ensure these models make accurate predictions that are consistent with known medical science. Inherently interpretable networks address this need by explaining the rationale behind each decision while maintaining equal or higher accuracy compared to black-box models. In this work, we present a novel interpretable neural network algorithm that uses case-based reasoning for mammography. Designed to aid a radiologist in their decisions, our network presents both a prediction of malignancy and an explanation of that prediction using known medical features. In order to yield helpful explanations, the network is designed to mimic the reasoning processes of a radiologist: our network first detects the clinically relevant semantic features of each image by comparing each new image with a learned set of prototypical image parts from the training images, then uses those clinical features to predict malignancy. Compared to other methods, our model detects clinical features (mass margins) with equal or higher accuracy, provides a more detailed explanation of its prediction, and is better able to differentiate the classification-relevant parts of the image.

cs.CV↗

arXiv2021

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

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 lower-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.

cs.LG↗

arXiv2021

Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges

Interpretability in machine learning (ML) is crucial for high stakes decisions and troubleshooting. In this work, we provide fundamental principles for interpretable ML, and dispel common misunderstandings that dilute the importance of this crucial topic. We also identify 10 technical challenge areas in interpretable machine learning and provide history and background on each problem. Some of these problems are classically important, and some are recent problems that have arisen in the last few years. These problems are: (1) Optimizing sparse logical models such as decision trees; (2) Optimization of scoring systems; (3) Placing constraints into generalized additive models to encourage sparsity and better interpretability; (4) Modern case-based reasoning, including neural networks and matching for causal inference; (5) Complete supervised disentanglement of neural networks; (6) Complete or even partial unsupervised disentanglement of neural networks; (7) Dimensionality reduction for data visualization; (8) Machine learning models that can incorporate physics and other generative or causal constraints; (9) Characterization of the "Rashomon set" of good models; and (10) Interpretable reinforcement learning. This survey is suitable as a starting point for statisticians and computer scientists interested in working in interpretable machine learning.

cs.LG↗

arXiv2021

Multitask Learning for Citation Purpose Classification

We present our entry into the 2021 3C Shared Task Citation Context Classification based on Purpose competition. The goal of the competition is to classify a citation in a scientific article based on its purpose. This task is important because it could potentially lead to more comprehensive ways of summarizing the purpose and uses of scientific articles, but it is also difficult, mainly due to the limited amount of available training data in which the purposes of each citation have been hand-labeled, along with the subjectivity of these labels. Our entry in the competition is a multi-task model that combines multiple modules designed to handle the problem from different perspectives, including hand-generated linguistic features, TF-IDF features, and an LSTM-with-attention model. We also provide an ablation study and feature analysis whose insights could lead to future work.

cs.LG↗