Bayesian Concept Bottleneck Models with LLM Priors

Concept Bottleneck Models (CBMs) have been proposed as a compromise between white-box and black-box models, aiming to achieve interpretability without sacrificing accuracy. The standard training procedure for CBMs is to predefine a candidate set of human-interpretable concepts, extract their values from the training data, and identify a sparse subset as inputs to a transparent prediction model. However, such approaches are often hampered by the tradeoff between enumerating a sufficiently large set of concepts to include those that are truly relevant versus controlling the cost of obtaining concept extractions. This work investigates a novel approach that sidesteps these challenges: BC-LLM iteratively searches over a potentially infinite set of concepts within a Bayesian framework, in which Large Language Models (LLMs) serve as both a concept extraction mechanism and prior. BC-LLM is broadly applicable and multi-modal. Despite imperfections in LLMs, we prove that BC-LLM can provide rigorous statistical inference and uncertainty quantification. In experiments, it outperforms comparator methods including black-box models, converges more rapidly towards relevant concepts and away from spuriously correlated ones, and is more robust to out-of-distribution samples.

A hierarchical decomposition for explaining ML performance discrepancies

Machine learning (ML) algorithms can often differ in performance across domains. Understanding $\textit{why}$ their performance differs is crucial for determining what types of interventions (e.g., algorithmic or operational) are most effective at closing the performance gaps. Existing methods focus on $\textit{aggregate decompositions}$ of the total performance gap into the impact of a shift in the distribution of features $p(X)$ versus the impact of a shift in the conditional distribution of the outcome $p(Y|X)$; however, such coarse explanations offer only a few options for how one can close the performance gap. $\textit{Detailed variable-level decompositions}$ that quantify the importance of each variable to each term in the aggregate decomposition can provide a much deeper understanding and suggest much more targeted interventions. However, existing methods assume knowledge of the full causal graph or make strong parametric assumptions. We introduce a nonparametric hierarchical framework that provides both aggregate and detailed decompositions for explaining why the performance of an ML algorithm differs across domains, without requiring causal knowledge. We derive debiased, computationally-efficient estimators, and statistical inference procedures for asymptotically valid confidence intervals.

A Brief Tutorial on Sample Size Calculations for Fairness Audits

In fairness audits, a standard objective is to detect whether a given algorithm performs substantially differently between subgroups. Properly powering the statistical analysis of such audits is crucial for obtaining informative fairness assessments, as it ensures a high probability of detecting unfairness when it exists. However, limited guidance is available on the amount of data necessary for a fairness audit, lacking directly applicable results concerning commonly used fairness metrics. Additionally, the consideration of unequal subgroup sample sizes is also missing. In this tutorial, we address these issues by providing guidance on how to determine the required subgroup sample sizes to maximize the statistical power of hypothesis tests for detecting unfairness. Our findings are applicable to audits of binary classification models and multiple fairness metrics derived as summaries of the confusion matrix. Furthermore, we discuss other aspects of audit study designs that can increase the reliability of audit results.

Towards a Post-Market Monitoring Framework for Machine Learning-based Medical Devices: A case study

After a machine learning (ML)-based system is deployed in clinical practice, performance monitoring is important to ensure the safety and effectiveness of the algorithm over time. The goal of this work is to highlight the complexity of designing a monitoring strategy and the need for a systematic framework that compares the multitude of monitoring options. One of the main decisions is choosing between using real-world (observational) versus interventional data. Although the former is the most convenient source of monitoring data, it exhibits well-known biases, such as confounding, selection, and missingness. In fact, when the ML algorithm interacts with its environment, the algorithm itself may be a primary source of bias. On the other hand, a carefully designed interventional study that randomizes individuals can explicitly eliminate such biases, but the ethics, feasibility, and cost of such an approach must be carefully considered. Beyond the decision of the data source, monitoring strategies vary in the performance criteria they track, the interpretability of the test statistics, the strength of their assumptions, and their speed at detecting performance decay. As a first step towards developing a framework that compares the various monitoring options, we consider a case study of an ML-based risk prediction algorithm for postoperative nausea and vomiting (PONV). Bringing together tools from causal inference and statistical process control, we walk through the basic steps of defining candidate monitoring criteria, describing potential sources of bias and the causal model, and specifying and comparing candidate monitoring procedures. We hypothesize that these steps can be applied more generally, as causal inference can address other sources of biases as well.

Is this model reliable for everyone? Testing for strong calibration

In a well-calibrated risk prediction model, the average predicted probability is close to the true event rate for any given subgroup. Such models are reliable across heterogeneous populations and satisfy strong notions of algorithmic fairness. However, the task of auditing a model for strong calibration is well-known to be difficult -- particularly for machine learning (ML) algorithms -- due to the sheer number of potential subgroups. As such, common practice is to only assess calibration with respect to a few predefined subgroups. Recent developments in goodness-of-fit testing offer potential solutions but are not designed for settings with weak signal or where the poorly calibrated subgroup is small, as they either overly subdivide the data or fail to divide the data at all. We introduce a new testing procedure based on the following insight: if we can reorder observations by their expected residuals, there should be a change in the association between the predicted and observed residuals along this sequence if a poorly calibrated subgroup exists. This lets us reframe the problem of calibration testing into one of changepoint detection, for which powerful methods already exist. We begin with introducing a sample-splitting procedure where a portion of the data is used to train a suite of candidate models for predicting the residual, and the remaining data are used to perform a score-based cumulative sum (CUSUM) test. To further improve power, we then extend this adaptive CUSUM test to incorporate cross-validation, while maintaining Type I error control under minimal assumptions. Compared to existing methods, the proposed procedure consistently achieved higher power in simulation studies and more than doubled the power when auditing a mortality risk prediction model.

Monitoring machine learning (ML)-based risk prediction algorithms in the presence of confounding medical interventions

Monitoring the performance of machine learning (ML)-based risk prediction models in healthcare is complicated by the issue of confounding medical interventions (CMI): when an algorithm predicts a patient to be at high risk for an adverse event, clinicians are more likely to administer prophylactic treatment and alter the very target that the algorithm aims to predict. Ignoring CMI by monitoring only the untreated patients--whose outcomes remain unaltered--can inflate false alarm rates, because the evolution of both the model and clinician-ML interactions can induce complex dependencies in the data that violate standard assumptions. A more sophisticated approach is to explicitly account for CMI by modeling treatment propensities, but its time-varying nature makes accurate estimation difficult. Given the many sources of complexity in the data, it is important to determine situations in which a simple procedure that ignores CMI provides valid inference. Here we describe the special case of monitoring model calibration, under either the assumption of conditional exchangeability or time-constant selection bias. We introduce a new score-based cumulative sum (CUSUM) chart for monitoring in a frequentist framework and review an alternative approach using Bayesian inference. Through simulations, we investigate the benefits of combining model updating with monitoring and study when over-trust in a prediction model does (or does not) delay detection. Finally, we simulate monitoring an ML-based postoperative nausea and vomiting risk calculator during the COVID-19 pandemic.

Sequential algorithmic modification with test data reuse

After initial release of a machine learning algorithm, the model can be fine-tuned by retraining on subsequently gathered data, adding newly discovered features, or more. Each modification introduces a risk of deteriorating performance and must be validated on a test dataset. It may not always be practical to assemble a new dataset for testing each modification, especially when most modifications are minor or are implemented in rapid succession. Recent works have shown how one can repeatedly test modifications on the same dataset and protect against overfitting by (i) discretizing test results along a grid and (ii) applying a Bonferroni correction to adjust for the total number of modifications considered by an adaptive developer. However, the standard Bonferroni correction is overly conservative when most modifications are beneficial and/or highly correlated. This work investigates more powerful approaches using alpha-recycling and sequentially-rejective graphical procedures (SRGPs). We introduce novel extensions that account for correlation between adaptively chosen algorithmic modifications. In empirical analyses, the SRGPs control the error rate of approving unacceptable modifications and approve a substantially higher number of beneficial modifications than previous approaches.

Bayesian logistic regression for online recalibration and revision of risk prediction models with performance guarantees

After deploying a clinical prediction model, subsequently collected data can be used to fine-tune its predictions and adapt to temporal shifts. Because model updating carries risks of over-updating/fitting, we study online methods with performance guarantees. We introduce two procedures for continual recalibration or revision of an underlying prediction model: Bayesian logistic regression (BLR) and a Markov variant that explicitly models distribution shifts (MarBLR). We perform empirical evaluation via simulations and a real-world study predicting COPD risk. We derive "Type I and II" regret bounds, which guarantee the procedures are non-inferior to a static model and competitive with an oracle logistic reviser in terms of the average loss. Both procedures consistently outperformed the static model and other online logistic revision methods. In simulations, the average estimated calibration index (aECI) of the original model was 0.828 (95%CI 0.818-0.938). Online recalibration using BLR and MarBLR improved the aECI, attaining 0.265 (95%CI 0.230-0.300) and 0.241 (95%CI 0.216-0.266), respectively. When performing more extensive logistic model revisions, BLR and MarBLR increased the average AUC (aAUC) from 0.767 (95%CI 0.765-0.769) to 0.800 (95%CI 0.798-0.802) and 0.799 (95%CI 0.797-0.801), respectively, in stationary settings and protected against substantial model decay. In the COPD study, BLR and MarBLR dynamically combined the original model with a continually-refitted gradient boosted tree to achieve aAUCs of 0.924 (95%CI 0.913-0.935) and 0.925 (95%CI 0.914-0.935), compared to the static model's aAUC of 0.904 (95%CI 0.892-0.916). Despite its simplicity, BLR is highly competitive with MarBLR. MarBLR outperforms BLR when its prior better reflects the data. BLR and MarBLR can improve the transportability of clinical prediction models and maintain their performance over time.

Learning how to approve updates to machine learning algorithms in non-stationary settings

Machine learning algorithms in healthcare have the potential to continually learn from real-world data generated during healthcare delivery and adapt to dataset shifts. As such, the FDA is looking to design policies that can autonomously approve modifications to machine learning algorithms while maintaining or improving the safety and effectiveness of the deployed models. However, selecting a fixed approval strategy, a priori, can be difficult because its performance depends on the stationarity of the data and the quality of the proposed modifications. To this end, we investigate a learning-to-approve approach (L2A) that uses accumulating monitoring data to learn how to approve modifications. L2A defines a family of strategies that vary in their "optimism''---where more optimistic policies have faster approval rates---and searches over this family using an exponentially weighted average forecaster. To control the cumulative risk of the deployed model, we give L2A the option to abstain from making a prediction and incur some fixed abstention cost instead. We derive bounds on the average risk of the model deployed by L2A, assuming the distributional shifts are smooth. In simulation studies and empirical analyses, L2A tailors the level of optimism for each problem-setting: It learns to abstain when performance drops are common and approve beneficial modifications quickly when the distribution is stable.

Efficient nonparametric statistical inference on population feature importance using Shapley values

The true population-level importance of a variable in a prediction task provides useful knowledge about the underlying data-generating mechanism and can help in deciding which measurements to collect in subsequent experiments. Valid statistical inference on this importance is a key component in understanding the population of interest. We present a computationally efficient procedure for estimating and obtaining valid statistical inference on the Shapley Population Variable Importance Measure (SPVIM). Although the computational complexity of the true SPVIM scales exponentially with the number of variables, we propose an estimator based on randomly sampling only $\Theta(n)$ feature subsets given $n$ observations. We prove that our estimator converges at an asymptotically optimal rate. Moreover, by deriving the asymptotic distribution of our estimator, we construct valid confidence intervals and hypothesis tests. Our procedure has good finite-sample performance in simulations, and for an in-hospital mortality prediction task produces similar variable importance estimates when different machine learning algorithms are applied.