Alexej Gossmann

Jean Feng, Adarsh Subbaswamy, Alexej Gossmann et al.

After a machine learning (ML)-based system is deployed, monitoring its performance is important to ensure the safety and effectiveness of the algorithm over time. When an ML algorithm interacts with its environment, the algorithm can affect the data-generating mechanism and be a major source of bias when evaluating its standalone performance, an issue known as performativity. Although prior work has shown how to validate models in the presence of performativity using causal inference techniques, there has been little work on how to monitor models in the presence of performativity. Unlike the setting of model validation, there is much less agreement on which performance metrics to monitor. Different monitoring criteria impact how interpretable the resulting test statistic is, what assumptions are needed for identifiability, and the speed of detection. When this choice is further coupled with the decision to use observational versus interventional data, ML deployment teams are faced with a multitude of monitoring options. The aim of this work is to highlight the relatively under-appreciated complexity of designing a monitoring strategy and how causal reasoning can provide a systematic framework for choosing between these options. As a motivating example, we consider an ML-based risk prediction algorithm for predicting unplanned readmissions. Bringing together tools from causal inference and statistical process control, we consider six monitoring procedures (three candidate monitoring criteria and two data sources) and investigate their operating characteristics in simulation studies. Results from this case study emphasize the seemingly simple (and obvious) fact that not all monitoring systems are created equal, which has real-world impacts on the design and documentation of ML monitoring systems.

Jean Feng, Alexej Gossmann, Romain Pirracchio et al.

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.

Jean Feng, Gene Pennello, Nicholas Petrick et al.

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.

Jean Feng, Alexej Gossmann, Gene Pennello et al.

Performance monitoring 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. A simple approach is to ignore CMI and monitor only the untreated patients, whose outcomes remain unaltered. In general, ignoring CMI may inflate Type I error because (i) untreated patients disproportionally represent those with low predicted risk and (ii) evolution in both the model and clinician trust in the model can induce complex dependencies that violate standard assumptions. Nevertheless, we show that valid inference is still possible if one monitors conditional performance and if either conditional exchangeability or time-constant selection bias hold. Specifically, we develop a new score-based cumulative sum (CUSUM) monitoring procedure with dynamic control limits. Through simulations, we demonstrate the benefits of combining model updating with monitoring and investigate how over-trust in a prediction model may delay detection of performance deterioration. Finally, we illustrate how these monitoring methods can be used to detect calibration decay of an ML-based risk calculator for postoperative nausea and vomiting during the COVID-19 pandemic.

Xudong Sun, Carla Feistner, Alexej Gossmann et al.

Poor generalization performance caused by distribution shifts in unseen domains often hinders the trustworthy deployment of deep neural networks. Many domain generalization techniques address this problem by adding a domain invariant regularization loss terms during training. However, there is a lack of modular software that allows users to combine the advantages of different methods with minimal effort for reproducibility. DomainLab is a modular Python package for training user specified neural networks with composable regularization loss terms. Its decoupled design allows the separation of neural networks from regularization loss construction. Hierarchical combinations of neural networks, different domain generalization methods, and associated hyperparameters, can all be specified together with other experimental setup in a single configuration file. Hierarchical combinations of neural networks, different domain generalization methods, and associated hyperparameters, can all be specified together with other experimental setup in a single configuration file. In addition, DomainLab offers powerful benchmarking functionality to evaluate the generalization performance of neural networks in out-of-distribution data. The package supports running the specified benchmark on an HPC cluster or on a standalone machine. The package is well tested with over 95 percent coverage and well documented. From the user perspective, it is closed to modification but open to extension. The package is under the MIT license, and its source code, tutorial and documentation can be found at https://github.com/marrlab/DomainLab.

Jean Feng, Harvineet Singh, Fan Xia et al.

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.

Xudong Sun, Nutan Chen, Alexej Gossmann et al.

A probabilistic graphical model is proposed, modeling the joint model parameter and multiplier evolution, with a hypervolume based likelihood, promoting multi-objective descent in structural risk minimization. We address multi-objective model parameter optimization via a surrogate single objective penalty loss with time-varying multipliers, equivalent to online scheduling of loss landscape. The multi-objective descent goal is dispatched hierarchically into a series of constraint optimization sub-problems with shrinking bounds according to Pareto dominance. The bound serves as setpoint for the low-level multiplier controller to schedule loss landscapes via output feedback of each loss term. Our method forms closed loop of model parameter dynamic, circumvents excessive memory requirements and extra computational burden of existing multi-objective deep learning methods, and is robust against controller hyperparameter variation, demonstrated on domain generalization tasks with multi-dimensional regularization losses.

Harvineet Singh, Fan Xia, Alexej Gossmann et al.

Machine learning (ML) models frequently experience performance degradation when deployed in new contexts. Such degradation is rarely uniform: some subgroups may suffer large performance decay while others may not. Understanding where and how large differences in performance arise is critical for designing targeted corrective actions that mitigate decay for the most affected subgroups while minimizing any unintended effects. Current approaches do not provide such detailed insight, as they either (i) explain how average performance shifts arise or (ii) identify adversely affected subgroups without insight into how this occurred. To this end, we introduce a Subgroup-scanning Hierarchical Inference Framework for performance drifT (SHIFT). SHIFT first asks "Is there any subgroup with unacceptably large performance decay due to covariate/outcome shifts?" (Where?) and, if so, dives deeper to ask "Can we explain this using more detailed variable(subset)-specific shifts?" (How?). In real-world experiments, we find that SHIFT identifies interpretable subgroups affected by performance decay, and suggests targeted actions that effectively mitigate the decay.

Jean Feng, Alexej Gossmann, Berkman Sahiner et al.

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.

Xudong Sun, Alexej Gossmann, Yu Wang et al.

A novel variational inference based resampling framework is proposed to evaluate the robustness and generalization capability of deep learning models with respect to distribution shift. We use Auto Encoding Variational Bayes to find a latent representation of the data, on which a Variational Gaussian Mixture Model is applied to deliberately create distribution shift by dividing the dataset into different clusters. Wasserstein distance is used to characterize the extent of distribution shift between the generated data splits. We compare several popular Convolutional Neural Network (CNN) architectures and Bayesian CNN models for image classification on the Fashion-MNIST dataset, to assess their robustness and generalization behavior under the deliberately created distribution shift, as well as under random Cross Validation. Our method of creating artificial domain splits of a single dataset can also be used to establish novel model selection criteria and assessment tools in machine learning, as well as benchmark methods for domain adaptation and domain generalization approaches.

Peyman Hosseinzadeh Kassani, Alexej Gossmann, Yu-Ping Wang

The study of healthy brain development helps to better understand the brain transformation and brain connectivity patterns which happen during childhood to adulthood. This study presents a sparse machine learning solution across whole-brain functional connectivity (FC) measures of three sets of data, derived from resting state functional magnetic resonance imaging (rs-fMRI) and task fMRI data, including a working memory n-back task (nb-fMRI) and an emotion identification task (em-fMRI). These multi-modal image data are collected on a sample of adolescents from the Philadelphia Neurodevelopmental Cohort (PNC) for the prediction of brain ages. Due to extremely large variable-to-instance ratio of PNC data, a high dimensional matrix with several irrelevant and highly correlated features is generated and hence a pattern learning approach is necessary to extract significant features. We propose a sparse learner based on the residual errors along the estimation of an inverse problem for the extreme learning machine (ELM) neural network. The purpose of the approach is to overcome the overlearning problem through pruning of several redundant features and their corresponding output weights. The proposed multimodal sparse ELM classifier based on residual errors (RES-ELM) is highly competitive in terms of the classification accuracy compared to its counterparts such as conventional ELM, and sparse Bayesian learning ELM.

Alexej Gossmann, Pascal Zille, Vince Calhoun et al.

Reducing the number of false discoveries is presently one of the most pressing issues in the life sciences. It is of especially great importance for many applications in neuroimaging and genomics, where datasets are typically high-dimensional, which means that the number of explanatory variables exceeds the sample size. The false discovery rate (FDR) is a criterion that can be employed to address that issue. Thus it has gained great popularity as a tool for testing multiple hypotheses. Canonical correlation analysis (CCA) is a statistical technique that is used to make sense of the cross-correlation of two sets of measurements collected on the same set of samples (e.g., brain imaging and genomic data for the same mental illness patients), and sparse CCA extends the classical method to high-dimensional settings. Here we propose a way of applying the FDR concept to sparse CCA, and a method to control the FDR. The proposed FDR correction directly influences the sparsity of the solution, adapting it to the unknown true sparsity level. Theoretical derivation as well as simulation studies show that our procedure indeed keeps the FDR of the canonical vectors below a user-specified target level. We apply the proposed method to an imaging genomics dataset from the Philadelphia Neurodevelopmental Cohort. Our results link the brain connectivity profiles derived from brain activity during an emotion identification task, as measured by functional magnetic resonance imaging (fMRI), to the corresponding subjects' genomic data.