a c statistic of 0.82 (95% CI, 0.80-0.84), the CHADS2 index was the most accurate predictor of stroke. The stroke rate per 100 patient-years without antithrombotic therapy increased by a factor of 1.5 (95% CI, 1.3-1.7) for each 1-point increase in the CHADS2 score: 1.9 (95% CI, 1.2-3.0) for a score of 0; 2.8 (95% CI, 2.0-3.8) for 1; 4.0 (95% CI, 3.1-5.1) for 2; 5.9 (95% CI, 4.6-7.3) for 3; 8.5 (95% CI, 6.3-11.1) for 4; 12.5 (95% CI, 8.2-17.5) for 5; and 18.2 (95% CI, 10.5-27.4) for 6. Conclusion The 2 existing classification schemes and especially a new stroke risk index, CHADS2, can quantify risk of stroke for patients who have AF and may aid in selection of antithrombotic therapy.

Validation of clinical classification schemes for predicting stroke: results from the national registry of atrial fibrillation☆

The interpretation of deep learning models is a challenge due to their size, complexity, and often opaque internal state. In addition, many systems, such as image classifiers, operate on low-level features rather than high-level concepts. To address these challenges, we introduce Concept Activation Vectors (CAVs), which provide an interpretation of a neural net's internal state in terms of human-friendly concepts. The key idea is to view the high-dimensional internal state of a neural net as an aid, not an obstacle. We show how to use CAVs as part of a technique, Testing with CAVs (TCAV), that uses directional derivatives to quantify the degree to which a user-defined concept is important to a classification result--for example, how sensitive a prediction of "zebra" is to the presence of stripes. Using the domain of image classification as a testing ground, we describe how CAVs may be used to explore hypotheses and generate insights for a standard image classification network as well as a medical application.

Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)

Algorithmic systems that employ machine learning play an increasing role in making substantive decisions in modern society, ranging from online personalization to insurance and credit decisions to predictive policing. But their decision-making processes are often opaque -- it is difficult to explain why a certain decision was made. We develop 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 influence of inputs on outputs of systems. 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 (e.g., a loan decision) and groups (e.g., disparate impact based on gender). 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 marginal influence of individual inputs within such a set (e.g., income). Since a single input may be part of multiple influential sets, the average marginal influence of the input is computed using principled aggregation measures, such as the Shapley value, previously applied to measure influence in voting. Further, since transparency reports could compromise privacy, we explore the transparency-privacy tradeoff and prove that a number of useful transparency reports can be made differentially private with very little addition of noise. Our empirical validation with standard machine learning algorithms demonstrates that QII measures are a useful transparency mechanism when black box access to the learning system is available. In particular, they provide better explanations than standard associative measures for a host of scenarios that we consider. Further, we show that in the situations we consider, QII is efficiently approximable and can be made differentially private while preserving accuracy.

/pdf/algorithmic-transparency-via-quantitative-input-influence-109zh4gbpl.pdf

Algorithmic Transparency via Quantitative Input Influence: Theory and Experiments with Learning Systems

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.

Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges

Data-trained predictive models see widespread use, but for the most part they are used as black boxes which output a prediction or score. It is therefore hard to acquire a deeper understanding of model behavior and in particular how different features influence the model prediction. This is important when interpreting the behavior of complex models or asserting that certain problematic attributes (such as race or gender) are not unduly influencing decisions. In this paper, we present a technique for auditing black-box models, which lets us study the extent to which existing models take advantage of particular features in the data set, without knowing how the models work. Our work focuses on the problem of indirect influence: how some features might indirectly influence outcomes via other, related features. As a result, we can find attribute influences even in cases where, upon further direct examination of the model, the attribute is not referred to by the model at all. Our approach does not require the black-box model to be retrained. This is important if, for example, the model is only accessible via an API, and contrasts our work with other methods that investigate feature influence such as feature selection. We present experimental evidence for the effectiveness of our procedure using a variety of publicly available data sets and models. We also validate our procedure using techniques from interpretable learning and feature selection, as well as against other black-box auditing procedures. To further demonstrate the effectiveness of this technique, we use it to audit a black-box recidivism prediction algorithm.

/pdf/auditing-black-box-models-for-indirect-influence-41nm8jmpg4.pdf

Auditing black-box models for indirect influence

Scoring systems are classification models that only require users to add, subtract and multiply a few meaningful numbers to make a prediction. These models are often used because they are practical and interpretable. In this paper, we introduce an off-the-shelf tool to create scoring systems that both accurate and interpretable, known as a Supersparse Linear Integer Model (SLIM). SLIM is a discrete optimization problem that minimizes the 0-1 loss to encourage a high level of accuracy, regularizes the L0-norm to encourage a high level of sparsity, and constrains coefficients to a set of interpretable values. We illustrate the practical and interpretable nature of SLIM scoring systems through applications in medicine and criminology, and show that they are are accurate and sparse in comparison to state-of-the-art classification models using numerical experiments.

pdf/supersparse-linear-integer-models-for-interpretable-57k6xk8wxq.pdf

Supersparse Linear Integer Models for Interpretable Classification

We introduce Supersparse Linear Integer Models (SLIM) as a tool to create scoring systems for binary classification. We derive theoretical bounds on the true risk of SLIM scoring systems, and present experimental results to show that SLIM scoring systems are accurate, sparse, and interpretable classification models.

pdf/supersparse-linear-integer-models-for-predictive-scoring-4mdslblhoi.pdf

Supersparse Linear Integer Models for Predictive Scoring Systems

Scoring systems are classification models that make predictions using a sparse linear combination of variables with integer coefficients Such systems are frequently used in medicine because they are interpretable; that is, they only require users to add, subtract and multiply a few meaningful numbers in order to make a prediction See, for instance, these commonly used scoring systems: (Gage et al 2001; Le Gall et al 1984; Le Gall, Lemeshow, and Saulnier 1993; Knaus et al 1985) Scoring systems strike a delicate balance between accuracy and interpretability that is difficult to replicate with existing machine learning algorithms

Current linear methods such as the lasso, elastic net and LARS are not designed to create scoring systems, since regularization is primarily used to improve accuracy as opposed to sparsity and interpretability (Tibshirani 1996; Zou and Hastie 2005; Efron et al 2004) These methods can produce very sparse models through heavy regularization or feature selection methods (Guyon and Elisseeff 2003); however, feature selection often relies on greedy optimization and cannot guarantee an optimal balance between sparsity and accuracy Moreover, the interpretability of scoring systems requires integer coefficients, which these methods do not produce Existing approaches to interpretable modeling include decision trees and lists (Ruping 2006; Quinlan 1986; Rivest 1987; Letham et al 2013)

We introduce a formal approach for creating scoring systems, called Supersparse Linear Integer Models (SLIM) SLIM produces scoring systems that are accurate and interpretable using a mixed-integer program (MIP) whose objective penalizes the training error, L0-norm and L1-norm of its coefficients SLIM can create scoring systems for datasets with thousands of training examples and tens to hundreds of features - larger than the sizes of most studies in medicine, where scoring systems are often used

/pdf/supersparse-linear-integer-models-for-predictive-scoring-4gi72fvd6i.pdf

Supersparse linear integer models for predictive scoring systems

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 visitors 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 in the UCB and {\epsilon}-greedy methods and we introduce a new policy called the variable arm pool method. 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.

Regulating Greed Over Time.

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.

/pdf/reducing-exploration-of-dying-arms-in-mortal-bandits-2469lblr63.pdf

Reducing Exploration of Dying Arms in Mortal Bandits

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