When predictive models are used to support complex and important decisions, the ability to explain a model's reasoning can increase trust, expose hidden biases, and reduce vulnerability to adversarial attacks. However, attempts at interpreting models are often ad hoc and application-specific, and the concept of interpretability itself is not well-defined. We propose a general optimization framework to create explanations for linear models. Our methodology decomposes a linear model into a sequence of models of increasing complexity using coordinate updates on the coefficients. Computing this decomposition optimally is a difficult optimization problem for which we propose exact algorithms and scalable heuristics. By solving this problem, we can derive a parametrized family of interpretability metrics for linear models that generalizes typical proxies, and study the tradeoff between interpretability and predictive accuracy.
Many interpretable machine learning approaches involve optimizing some characteristics of the model as proxies for interpretability. Examples include sparsity for linear models @cite_14 , number of splits for decision trees @cite_29 , number of subspace features for case-based reasoning @cite_26 , or depth for rule lists @cite_1 @cite_5 . Some approaches optimize these proxies directly, while others fit auxiliary simple models to more complex black-box models @cite_4 @cite_6 @cite_7 @cite_17 @cite_27 @cite_24 .
@cite_14 @cite_26 @cite_4 @cite_7 @cite_29 @cite_1 @cite_6 @cite_24 @cite_27 @cite_5 @cite_17
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Discover New Methods for Dealing with High-Dimensional Data A sparse statistical model has only a small number of nonzero parameters or weights; therefore, it is much easier to estimate and interpret than a dense model. Statistical Learning with Sparsity: The Lasso and Generalizations presents methods that exploit sparsity to help recover the underlying signal in a set of data. Top experts in this rapidly evolving field, the authors describe the lasso for linear regression and a simple coordinate descent algorithm for its computation. They discuss the application of 1 penalties to generalized linear models and support vector machines, cover generalized penalties such as the elastic net and group lasso, and review numerical methods for optimization. They also present statistical inference methods for fitted (lasso) models, including the bootstrap, Bayesian methods, and recently developed approaches. In addition, the book examines matrix decomposition, sparse multivariate analysis, graphical models, and compressed sensing. It concludes with a survey of theoretical results for the lasso. In this age of big data, the number of features measured on a person or object can be large and might be larger than the number of observations. This book shows how the sparsity assumption allows us to tackle these problems and extract useful and reproducible patterns from big datasets. Data analysts, computer scientists, and theorists will appreciate this thorough and up-to-date treatment of sparse statistical modeling. 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. Despite widespread adoption, machine learning models remain mostly black boxes. Understanding the reasons behind predictions is, however, quite important in assessing trust, which is fundamental if one plans to take action based on a prediction, or when choosing whether to deploy a new model. Such understanding also provides insights into the model, which can be used to transform an untrustworthy model or prediction into a trustworthy one. In this work, we propose LIME, a novel explanation technique that explains the predictions of any classifier in an interpretable and faithful manner, by learning an interpretable model locally varound the prediction. We also propose a method to explain models by presenting representative individual predictions and their explanations in a non-redundant way, framing the task as a submodular optimization problem. We demonstrate the flexibility of these methods by explaining different models for text (e.g. random forests) and image classification (e.g. neural networks). We show the utility of explanations via novel experiments, both simulated and with human subjects, on various scenarios that require trust: deciding if one should trust a prediction, choosing between models, improving an untrustworthy classifier, and identifying why a classifier should not be trusted. Algorithmic systems that employ machine learning are often opaque—it is difficult to explain why a certain decision was made. We present a formal foundation to improve the transparency of such decision-making systems. Specifically, we introduce a family of Quantitative Input Influence (QII) measures that capture the degree of input influence on system outputs. These measures provide a foundation for the design of transparency reports that accompany system decisions (e.g., explaining a specific credit decision) and for testing tools useful for internal and external oversight (e.g., to detect algorithmic discrimination). Distinctively, our causal QII measures carefully account for correlated inputs while measuring influence. They support a general class of transparency queries and can, in particular, explain decisions about individuals and groups. Finally, since single inputs may not always have high influence, the QII measures also quantify the joint influence of a set of inputs (e.g., age and income) on outcomes (e.g. loan decisions) and the average marginal influence of individual inputs within such a set (e.g., income) using principled aggregation measures, such as the Shapley value, previously applied to measure influence in voting. Background. Introduction to Tree Classification. Right Sized Trees and Honest Estimates. Splitting Rules. Strengthening and Interpreting. Medical Diagnosis and Prognosis. Mass Spectra Classification. Regression Trees. Bayes Rules and Partitions. Optimal Pruning. Construction of Trees from a Learning Sample. Consistency. Bibliography. Notation Index. Subject Index. We aim to produce predictive models that are not only accurate, but are also interpretable to human experts. Our models are decision lists, which consist of a series of if...then... statements (for example, if high blood pressure, then stroke) that discretize a high-dimensional, multivariate feature space into a series of simple, readily interpretable decision statements. We introduce a generative model called Bayesian Rule Lists that yields a posterior distribution over possible decision lists. It employs a novel prior structure to encourage sparsity. Our experiments show that Bayesian Rule Lists has predictive accuracy on par with the current top algorithms for prediction in machine learning. Our method is motivated by recent developments in personalized medicine, and can be used to produce highly accurate and interpretable medical scoring systems. We demonstrate this by producing an alternative to the CHADS2 score, actively used in clinical practice for estimating the risk of stroke in patients that have atrial fibrillation. Our model is as interpretable as CHADS2, but more accurate. 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, with practical running times. The predictions in each leaf are probabilistic. Interpretability has become incredibly important as machine learning is increasingly used to inform consequential decisions. We propose to construct global explanations of complex, blackbox models in the form of a decision tree approximating the original model---as long as the decision tree is a good approximation, then it mirrors the computation performed by the blackbox model. We devise a novel algorithm for extracting decision tree explanations that actively samples new training points to avoid overfitting. We evaluate our algorithm on a random forest to predict diabetes risk and a learned controller for cart-pole. Compared to several baselines, our decision trees are both substantially more accurate and equally or more interpretable based on a user study. Finally, we describe several insights provided by our interpretations, including a causal issue validated by a physician.