Abstract
Heart rate (HR) response to workout intensity reflects fitness and cardiorespiratory health. Physiological models have been developed to describe such heart rate dynamics and characterize ...cardiorespiratory fitness. However, these models have been limited to small studies in controlled lab environments and are challenging to apply to noisy—but ubiquitous—data from wearables. We propose a hybrid approach that combines a physiological model with flexible neural network components to learn a personalized, multidimensional representation of fitness. The physiological model describes the evolution of heart rate during exercise using ordinary differential equations (ODEs). ODE parameters are dynamically derived via a neural network connecting personalized representations to external environmental factors, from area topography to weather and instantaneous workout intensity. Our approach efficiently fits the hybrid model to a large set of 270,707 workouts collected from wearables of 7465 users from the Apple Heart and Movement Study. The resulting model produces fitness representations that accurately predict full HR response to exercise intensity in future workouts, with a per-workout median error of 6.1 BPM 4.4–8.8 IQR. We further demonstrate that the learned representations correlate with traditional metrics of cardiorespiratory fitness, such as VO
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max (explained variance 0.81 ± 0.003). Lastly, we illustrate how our model is naturally interpretable and explicitly describes the effects of environmental factors such as temperature and humidity on heart rate, e.g., high temperatures can increase heart rate by 10%. Combining physiological ODEs with flexible neural networks can yield interpretable, robust, and expressive models for health applications.
Nudges are interventions promoting healthy behavior without forbidding options or substantial incentives; the Apple Watch, for example, encourages users to stand by delivering a notification if they ...have been sitting for the first 50 minutes of an hour. On the basis of 76 billion minutes of observational standing data from 160,000 subjects in the public Apple Heart and Movement Study, we estimate the causal effect of this notification using a regression discontinuity design for time series data with time-varying treatment. We show that the nudge increases the probability of standing by up to 43.9% and remains effective with time. The nudge’s effectiveness increases with age and is independent of gender. Closing Apple Watch Activity Rings, a visualization of participants’ daily progress in Move, Exercise, and Stand, further increases the nudge’s impact. This work demonstrates the effectiveness of behavioral health interventions and introduces tools for investigating their causal effect from large-scale observations.
Observational causal inference tools applied to large data from the field demonstrate that health nudges can be very effective.
We introduce the unbounded depth neural network (UDN), an infinitely deep probabilistic model that adapts its complexity to the training data. The UDN contains an infinite sequence of hidden layers ...and places an unbounded prior on a truncation L, the layer from which it produces its data. Given a dataset of observations, the posterior UDN provides a conditional distribution of both the parameters of the infinite neural network and its truncation. We develop a novel variational inference algorithm to approximate this posterior, optimizing a distribution of the neural network weights and of the truncation depth L, and without any upper limit on L. To this end, the variational family has a special structure: it models neural network weights of arbitrary depth, and it dynamically creates or removes free variational parameters as its distribution of the truncation is optimized. (Unlike heuristic approaches to model search, it is solely through gradient-based optimization that this algorithm explores the space of truncations.) We study the UDN on real and synthetic data. We find that the UDN adapts its posterior depth to the dataset complexity; it outperforms standard neural networks of similar computational complexity; and it outperforms other approaches to infinite-depth neural networks.
The synthetic control (SC) method is a popular approach for estimating treatment effects from observational panel data. It rests on a crucial assumption that we can write the treated unit as a linear ...combination of the untreated units. This linearity assumption, however, can be unlikely to hold in practice and, when violated, the resulting SC estimates are incorrect. In this paper we examine two questions: (1) How large can the misspecification error be? (2) How can we limit it? First, we provide theoretical bounds to quantify the misspecification error. The bounds are comforting: small misspecifications induce small errors. With these bounds in hand, we then develop new SC estimators that are specially designed to minimize misspecification error. The estimators are based on additional data about each unit, which is used to produce the SC weights. (For example, if the units are countries then the additional data might be demographic information about each.) We study our estimators on synthetic data; we find they produce more accurate causal estimates than standard synthetic controls. We then re-analyze the California tobacco-program data of the original SC paper, now including additional data from the US census about per-state demographics. Our estimators show that the observations in the pre-treatment period lie within the bounds of misspecification error, and that the observations post-treatment lie outside of those bounds. This is evidence that our SC methods have uncovered a true effect.
Inferring causal relationships as directed acyclic graphs (DAGs) is an important but challenging problem. Differentiable Causal Discovery (DCD) is a promising approach to this problem, framing the ...search as a continuous optimization. But existing DCD methods are numerically unstable, with poor performance beyond tens of variables. In this paper, we propose Stable Differentiable Causal Discovery (SDCD), a new method that improves previous DCD methods in two ways: (1) It employs an alternative constraint for acyclicity; this constraint is more stable, both theoretically and empirically, and fast to compute. (2) It uses a training procedure tailored for sparse causal graphs, which are common in real-world scenarios. We first derive SDCD and prove its stability and correctness. We then evaluate it with both observational and interventional data and on both small-scale and large-scale settings. We find that SDCD outperforms existing methods in both convergence speed and accuracy and can scale to thousands of variables. We provide code at https://github.com/azizilab/sdcd.
Probabilistic prediction aims to compute predictive distributions rather than single-point predictions. These distributions enable practitioners to quantify uncertainty, compute risk, and detect ...outliers. However, most probabilistic methods assume parametric responses, such as Gaussian or Poisson distributions. When these assumptions fail, such models lead to bad predictions and poorly calibrated uncertainty. In this paper, we propose Treeffuser, an easy-to-use method for probabilistic prediction on tabular data. The idea is to learn a conditional diffusion model where the score function is estimated using gradient-boosted trees. The conditional diffusion model makes Treeffuser flexible and non-parametric, while the gradient-boosted trees make it robust and easy to train on CPUs. Treeffuser learns well-calibrated predictive distributions and can handle a wide range of regression tasks -- including those with multivariate, multimodal, and skewed responses. % , as well as categorical predictors and missing data We study Treeffuser on synthetic and real data and show that it outperforms existing methods, providing better-calibrated probabilistic predictions. We further demonstrate its versatility with an application to inventory allocation under uncertainty using sales data from Walmart. We implement Treeffuser in \href{https://github.com/blei-lab/treeffuser}{https://github.com/blei-lab/treeffuser}.
In drug discovery, mapping interactions between genes within cellular systems is a crucial early step. This helps formulate hypotheses regarding molecular mechanisms that could potentially be ...targeted by future medicines. The CausalBench Challenge was an initiative to invite the machine learning community to advance the state of the art in constructing gene-gene interaction networks. These networks, derived from large-scale, real-world datasets of single cells under various perturbations, are crucial for understanding the causal mechanisms underlying disease biology. Using the framework provided by the CausalBench benchmark, participants were tasked with enhancing the capacity of the state of the art methods to leverage large-scale genetic perturbation data. This report provides an analysis and summary of the methods submitted during the challenge to give a partial image of the state of the art at the time of the challenge. The winning solutions significantly improved performance compared to previous baselines, establishing a new state of the art for this critical task in biology and medicine.
Spatial studies of transcriptome provide biologists with gene expression maps of heterogeneous and complex tissues. However, most experimental protocols for spatial transcriptomics suffer from the ...need to select beforehand a small fraction of genes to be quantified over the entire transcriptome. Standard single-cell RNA sequencing (scRNA-seq) is more prevalent, easier to implement and can in principle capture any gene but cannot recover the spatial location of the cells. In this manuscript, we focus on the problem of imputation of missing genes in spatial transcriptomic data based on (unpaired) standard scRNA-seq data from the same biological tissue. Building upon domain adaptation work, we propose gimVI, a deep generative model for the integration of spatial transcriptomic data and scRNA-seq data that can be used to impute missing genes. After describing our generative model and an inference procedure for it, we compare gimVI to alternative methods from computational biology or domain adaptation on real datasets and outperform Seurat Anchors, Liger and CORAL to impute held-out genes.
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