Andrew C. Miller

Antoine Wehenkel, Laura Manduchi, Jens Behrmann et al. · apple-ml

Over the past decades, hemodynamics simulators have steadily evolved and have become tools of choice for studying cardiovascular systems in-silico. While such tools are routinely used to simulate whole-body hemodynamics from physiological parameters, solving the corresponding inverse problem of mapping waveforms back to plausible physiological parameters remains both promising and challenging. Motivated by advances in simulation-based inference (SBI), we cast this inverse problem as statistical inference. In contrast to alternative approaches, SBI provides \textit{posterior distributions} for the parameters of interest, providing a \textit{multi-dimensional} representation of uncertainty for \textit{individual} measurements. We showcase this ability by performing an in-silico uncertainty analysis of five biomarkers of clinical interest comparing several measurement modalities. Beyond the corroboration of known facts, such as the feasibility of estimating heart rate, our study highlights the potential of estimating new biomarkers from standard-of-care measurements. SBI reveals practically relevant findings that cannot be captured by standard sensitivity analyses, such as the existence of sub-populations for which parameter estimation exhibits distinct uncertainty regimes. Finally, we study the gap between in-vivo and in-silico with the MIMIC-III waveform database and critically discuss how cardiovascular simulations can inform real-world data analysis.

Sorawit Saengkyongam, Juan L. Gamella, Andrew C. Miller et al. · eth-zurich

The problem of domain generalization concerns learning predictive models that are robust to distribution shifts when deployed in new, previously unseen environments. Existing methods typically require labeled data from multiple training environments, limiting their applicability when labeled data are scarce. In this work, we study domain generalization in an anti-causal setting, where the outcome causes the observed covariates. Under this structure, environment perturbations that affect the covariates do not propagate to the outcome, which motivates regularizing the model's sensitivity to these perturbations. Crucially, estimating these perturbation directions does not require labels, enabling us to leverage unlabeled data from multiple environments. We propose two methods that penalize the model's sensitivity to variations in the mean and covariance of the covariates across environments, respectively, and prove that these methods have worst-case optimality guarantees under certain classes of environments. Finally, we demonstrate the empirical performance of our approach on a controlled physical system and a physiological signal dataset.

Salar Abbaspourazad, Oussama Elachqar, Andrew C. Miller et al.

Tracking biosignals is crucial for monitoring wellness and preempting the development of severe medical conditions. Today, wearable devices can conveniently record various biosignals, creating the opportunity to monitor health status without disruption to one's daily routine. Despite widespread use of wearable devices and existing digital biomarkers, the absence of curated data with annotated medical labels hinders the development of new biomarkers to measure common health conditions. In fact, medical datasets are usually small in comparison to other domains, which is an obstacle for developing neural network models for biosignals. To address this challenge, we have employed self-supervised learning using the unlabeled sensor data collected under informed consent from the large longitudinal Apple Heart and Movement Study (AHMS) to train foundation models for two common biosignals: photoplethysmography (PPG) and electrocardiogram (ECG) recorded on Apple Watch. We curated PPG and ECG datasets from AHMS that include data from ~141K participants spanning ~3 years. Our self-supervised learning framework includes participant level positive pair selection, stochastic augmentation module and a regularized contrastive loss optimized with momentum training, and generalizes well to both PPG and ECG modalities. We show that the pre-trained foundation models readily encode information regarding participants' demographics and health conditions. To the best of our knowledge, this is the first study that builds foundation models using large-scale PPG and ECG data collected via wearable consumer devices $\unicode{x2013}$ prior works have commonly used smaller-size datasets collected in clinical and experimental settings. We believe PPG and ECG foundation models can enhance future wearable devices by reducing the reliance on labeled data and hold the potential to help the users improve their health.

Salar Abbaspourazad, Anshuman Mishra, Joseph Futoma et al.

Modern wearable devices can conveniently record various biosignals in the many different environments of daily living, enabling a rich view of individual health. However, not all biosignals are the same: high-fidelity biosignals, such as photoplethysmogram (PPG), contain more physiological information, but require optical sensors with a high power footprint. Alternatively, a lower-fidelity biosignal such as accelerometry has a significantly smaller power footprint and is available in almost any wearable device. While accelerometry is widely used for activity recognition and fitness, it is less explored for health biomarkers and diagnosis. Here, we show that an accelerometry foundation model can predict a wide variety of health targets. To achieve improved performance, we distill representational knowledge from PPG encoders to accelerometery encoders using 20 million minutes of unlabeled data, collected from ~172K participants in the Apple Heart and Movement Study under informed consent. We observe strong cross-modal alignment on unseen data, e.g., 99.2% top-1 accuracy for retrieving PPG embeddings from accelerometry embeddings. We show that distilled accelerometry encoders have significantly more informative representations compared to self-supervised or supervised encoders trained directly on accelerometry data, observed by at least 23%-49% improved performance for predicting heart rate and heart rate variability. We also show that distilled accelerometry encoders are readily predictive of a wide array of downstream health targets, i.e., they are generalist foundation models. We believe accelerometry foundation models for health may unlock new opportunities for developing digital biomarkers from any wearable device.

Emanuele Palumbo, Sorawit Saengkyongam, Maria R. Cervera et al.

Continuous cardiovascular monitoring can play a key role in precision health. However, some fundamental cardiac biomarkers of interest, including stroke volume and cardiac output, require invasive measurements, e.g., arterial pressure waveforms (APW). As a non-invasive alternative, photoplethysmography (PPG) measurements are routinely collected in hospital settings. Unfortunately, the prediction of key cardiac biomarkers from PPG instead of APW remains an open challenge, further complicated by the scarcity of annotated PPG measurements. As a solution, we propose a hybrid approach that uses hemodynamic simulations and unlabeled clinical data to estimate cardiovascular biomarkers directly from PPG signals. Our hybrid model combines a conditional variational autoencoder trained on paired PPG-APW data with a conditional density estimator of cardiac biomarkers trained on labeled simulated APW segments. As a key result, our experiments demonstrate that the proposed approach can detect fluctuations of cardiac output and stroke volume and outperform a supervised baseline in monitoring temporal changes in these biomarkers.

Kyle Verrier, Achille Nazaret, Joseph Futoma et al.

Whether wearable photoplethysmography (PPG) contains dietary information remains unknown. We trained a language model on 1.1M meals to predict meal descriptions from PPG, aligning PPG to text. PPG nontrivially predicts meal content; predictability decreases for PPGs farther from meals. This transfers to dietary tasks: PPG increases AUC by 11% for intake and satiety across held-out and independent cohorts, with gains robust to text degradation. Wearable PPG may enable passive dietary monitoring.

Jens Behrmann, Maria R. Cervera, Antoine Wehenkel et al.

Smart wearables enable continuous tracking of established biomarkers such as heart rate, heart rate variability, and blood oxygen saturation via photoplethysmography (PPG). Beyond these metrics, PPG waveforms contain richer physiological information, as recent deep learning (DL) studies demonstrate. However, DL models often rely on features with unclear physiological meaning, creating a tension between predictive power, clinical interpretability, and sensor design. We address this gap by introducing PPGen, a biophysical model that relates PPG signals to interpretable physiological and optical parameters. Building on PPGen, we propose hybrid amortized inference (HAI), enabling fast, robust, and scalable estimation of relevant physiological parameters from PPG signals while correcting for model misspecification. In extensive in-silico experiments, we show that HAI can accurately infer physiological parameters under diverse noise and sensor conditions. Our results illustrate a path toward PPG models that retain the fidelity needed for DL-based features while supporting clinical interpretation and informed hardware design.

Mark Goldstein, Jörn-Henrik Jacobsen, Olina Chau et al.

Spurious correlations allow flexible models to predict well during training but poorly on related test distributions. Recent work has shown that models that satisfy particular independencies involving correlation-inducing \textit{nuisance} variables have guarantees on their test performance. Enforcing such independencies requires nuisances to be observed during training. However, nuisances, such as demographics or image background labels, are often missing. Enforcing independence on just the observed data does not imply independence on the entire population. Here we derive \acrshort{mmd} estimators used for invariance objectives under missing nuisances. On simulations and clinical data, optimizing through these estimates achieves test performance similar to using estimators that make use of the full data.

Andrew C. Miller, Leon A. Gatys, Joseph Futoma et al.

Machine learning models $-$ now commonly developed to screen, diagnose, or predict health conditions $-$ are evaluated with a variety of performance metrics. An important first step in assessing the practical utility of a model is to evaluate its average performance over an entire population of interest. In many settings, it is also critical that the model makes good predictions within predefined subpopulations. For instance, showing that a model is fair or equitable requires evaluating the model's performance in different demographic subgroups. However, subpopulation performance metrics are typically computed using only data from that subgroup, resulting in higher variance estimates for smaller groups. We devise a procedure to measure subpopulation performance that can be more sample-efficient than the typical subsample estimates. We propose using an evaluation model $-$ a model that describes the conditional distribution of the predictive model score $-$ to form model-based metric (MBM) estimates. Our procedure incorporates model checking and validation, and we propose a computationally efficient approximation of the traditional nonparametric bootstrap to form confidence intervals. We evaluate MBMs on two main tasks: a semi-synthetic setting where ground truth metrics are available and a real-world hospital readmission prediction task. We find that MBMs consistently produce more accurate and lower variance estimates of model performance for small subpopulations.

Andrew C. Miller, Nicholas J. Foti, Emily B. Fox

Breiman's classic paper casts data analysis as a choice between two cultures: data modelers and algorithmic modelers. Stated broadly, data modelers use simple, interpretable models with well-understood theoretical properties to analyze data. Algorithmic modelers prioritize predictive accuracy and use more flexible function approximations to analyze data. This dichotomy overlooks a third set of models $-$ mechanistic models derived from scientific theories (e.g., ODE/SDE simulators). Mechanistic models encode application-specific scientific knowledge about the data. And while these categories represent extreme points in model space, modern computational and algorithmic tools enable us to interpolate between these points, producing flexible, interpretable, and scientifically-informed hybrids that can enjoy accurate and robust predictions, and resolve issues with data analysis that Breiman describes, such as the Rashomon effect and Occam's dilemma. Challenges still remain in finding an appropriate point in model space, with many choices on how to compose model components and the degree to which each component informs inferences.

Jeffrey Chan, Andrew C. Miller, Emily B. Fox

Modern wearable devices are embedded with a range of noninvasive biomarker sensors that hold promise for improving detection and treatment of disease. One such sensor is the single-lead electrocardiogram (ECG) which measures electrical signals in the heart. The benefits of the sheer volume of ECG measurements with rich longitudinal structure made possible by wearables come at the price of potentially noisier measurements compared to clinical ECGs, e.g., due to movement. In this work, we develop a statistical model to simulate a structured noise process in ECGs derived from a wearable sensor, design a beat-to-beat representation that is conducive for analyzing variation, and devise a factor analysis-based method to denoise the ECG. We study synthetic data generated using a realistic ECG simulator and a structured noise model. At varying levels of signal-to-noise, we quantitatively measure an upper bound on performance and compare estimates from linear and non-linear models. Finally, we apply our method to a set of ECGs collected by wearables in a mobile health study.

Andrew C. Miller, Nicholas J. Foti, Emily Fox

We develop a new model of insulin-glucose dynamics for forecasting blood glucose in type 1 diabetics. We augment an existing biomedical model by introducing time-varying dynamics driven by a machine learning sequence model. Our model maintains a physiologically plausible inductive bias and clinically interpretable parameters -- e.g., insulin sensitivity -- while inheriting the flexibility of modern pattern recognition algorithms. Critical to modeling success are the flexible, but structured representations of subject variability with a sequence model. In contrast, less constrained models like the LSTM fail to provide reliable or physiologically plausible forecasts. We conduct an extensive empirical study. We show that allowing biomedical model dynamics to vary in time improves forecasting at long time horizons, up to six hours, and produces forecasts consistent with the physiological effects of insulin and carbohydrates.

Andrew C. Miller, Ziad Obermeyer, Sendhil Mullainathan

Databases of electronic health records (EHRs) are increasingly used to inform clinical decisions. Machine learning methods can find patterns in EHRs that are predictive of future adverse outcomes. However, statistical models may be built upon patterns of health-seeking behavior that vary across patient subpopulations, leading to poor predictive performance when training on one patient population and predicting on another. This note proposes two tests to better measure and understand model generalization. We use these tests to compare models derived from two data sources: (i) historical medical records, and (ii) electrocardiogram (EKG) waveforms. In a predictive task, we show that EKG-based models can be more stable than EHR-based models across different patient populations.

Andrew C. Miller, Ziad Obermeyer, David M. Blei et al.

An electrocardiogram (EKG) is a common, non-invasive test that measures the electrical activity of a patient's heart. EKGs contain useful diagnostic information about patient health that may be absent from other electronic health record (EHR) data. As multi-dimensional waveforms, they could be modeled using generic machine learning tools, such as a linear factor model or a variational autoencoder. We take a different approach:~we specify a model that directly represents the underlying electrophysiology of the heart and the EKG measurement process. We apply our model to two datasets, including a sample of emergency department EKG reports with missing data. We show that our model can more accurately reconstruct missing data (measured by test reconstruction error) than a standard baseline when there is significant missing data. More broadly, this physiological representation of heart function may be useful in a variety of settings, including prediction, causal analysis, and discovery.

Jeffrey Regier, Andrew C. Miller, David Schlegel et al.

We present a new, fully generative model for constructing astronomical catalogs from optical telescope image sets. Each pixel intensity is treated as a random variable with parameters that depend on the latent properties of stars and galaxies. These latent properties are themselves modeled as random. We compare two procedures for posterior inference. One procedure is based on Markov chain Monte Carlo (MCMC) while the other is based on variational inference (VI). The MCMC procedure excels at quantifying uncertainty, while the VI procedure is 1000 times faster. On a supercomputer, the VI procedure efficiently uses 665,000 CPU cores to construct an astronomical catalog from 50 terabytes of images in 14.6 minutes, demonstrating the scaling characteristics necessary to construct catalogs for upcoming astronomical surveys.

Yoon Kim, Sam Wiseman, Andrew C. Miller et al.

Amortized variational inference (AVI) replaces instance-specific local inference with a global inference network. While AVI has enabled efficient training of deep generative models such as variational autoencoders (VAE), recent empirical work suggests that inference networks can produce suboptimal variational parameters. We propose a hybrid approach, to use AVI to initialize the variational parameters and run stochastic variational inference (SVI) to refine them. Crucially, the local SVI procedure is itself differentiable, so the inference network and generative model can be trained end-to-end with gradient-based optimization. This semi-amortized approach enables the use of rich generative models without experiencing the posterior-collapse phenomenon common in training VAEs for problems like text generation. Experiments show this approach outperforms strong autoregressive and variational baselines on standard text and image datasets.

Andrew C. Miller, Nicholas J. Foti, Alexander D'Amour et al.

Optimization with noisy gradients has become ubiquitous in statistics and machine learning. Reparameterization gradients, or gradient estimates computed via the "reparameterization trick," represent a class of noisy gradients often used in Monte Carlo variational inference (MCVI). However, when these gradient estimators are too noisy, the optimization procedure can be slow or fail to converge. One way to reduce noise is to use more samples for the gradient estimate, but this can be computationally expensive. Instead, we view the noisy gradient as a random variable, and form an inexpensive approximation of the generating procedure for the gradient sample. This approximation has high correlation with the noisy gradient by construction, making it a useful control variate for variance reduction. We demonstrate our approach on non-conjugate multi-level hierarchical models and a Bayesian neural net where we observed gradient variance reductions of multiple orders of magnitude (20-2,000x).

Andrew C. Miller, Nicholas Foti, Ryan P. Adams

We propose a black-box variational inference method to approximate intractable distributions with an increasingly rich approximating class. Our method, termed variational boosting, iteratively refines an existing variational approximation by solving a sequence of optimization problems, allowing the practitioner to trade computation time for accuracy. We show how to expand the variational approximating class by incorporating additional covariance structure and by introducing new components to form a mixture. We apply variational boosting to synthetic and real statistical models, and show that resulting posterior inferences compare favorably to existing posterior approximation algorithms in both accuracy and efficiency.

Scott W. Linderman, Andrew C. Miller, Ryan P. Adams et al.

Many natural systems, such as neurons firing in the brain or basketball teams traversing a court, give rise to time series data with complex, nonlinear dynamics. We can gain insight into these systems by decomposing the data into segments that are each explained by simpler dynamic units. Building on switching linear dynamical systems (SLDS), we present a new model class that not only discovers these dynamical units, but also explains how their switching behavior depends on observations or continuous latent states. These "recurrent" switching linear dynamical systems provide further insight by discovering the conditions under which each unit is deployed, something that traditional SLDS models fail to do. We leverage recent algorithmic advances in approximate inference to make Bayesian inference in these models easy, fast, and scalable.