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Register a new userA Probabilistic Model of Cardiac Physiology and Electrocardiograms
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An electrocardiogram (EKG) is a common, non-invasive test that measures the electrical activity of a patients 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.
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Patients resuscitated from cardiac arrest (CA) face a high risk of neurological disability and death, however pragmatic methods are lacking for accurate and reliable prognostication. The aim of this study was to build computational models to predict post-CA outcome by leveraging high-dimensional patient data available early after admission to the intensive care unit (ICU). We hypothesized that model performance could be enhanced by integrating physiological time series (PTS) data and by training machine learning (ML) classifiers. We compared three models integrating features extracted from the electronic health records (EHR) alone, features derived from PTS collected in the first 24hrs after ICU admission (PTS24), and models integrating PTS24 and EHR. Outcomes of interest were survival and neurological outcome at ICU discharge. Combined EHR-PTS24 models had higher discrimination (area under the receiver operating characteristic curve [AUC]) than models which used either EHR or PTS24 alone, for the prediction of survival (AUC 0.85, 0.80 and 0.68 respectively) and neurological outcome (0.87, 0.83 and 0.78). The best ML classifier achieved higher discrimination than the reference logistic regression model (APACHE III) for survival (AUC 0.85 vs 0.70) and neurological outcome prediction (AUC 0.87 vs 0.75). Feature analysis revealed previously unknown factors to be associated with post-CA recovery. Results attest to the effectiveness of ML models for post-CA predictive modeling and suggest that PTS recorded in very early phase after resuscitation encode short-term outcome probabilities.
We present a simple theoretical framework, and corresponding practical procedures, for comparing probabilistic models on real data in a traditional machine learning setting. This framework is based on the theory of proper scoring rules, but requires only basic algebra and probability theory to understand and verify. The theoretical concepts presented are well-studied, primarily in the statistics literature. The goal of this paper is to advocate their wider adoption for performance evaluation in empirical machine learning.
Opioid overdose rates have increased in the United States over the past decade and reflect a major public health crisis. Modeling and prediction of drug and opioid hotspots, where a high percentage of events fall in a small percentage of space-time, could help better focus limited social and health services. In this work we present a spatial-temporal point process model for drug overdose clustering. The data input into the model comes from two heterogeneous sources: 1) high volume emergency medical calls for service (EMS) records containing location and time, but no information on the type of non-fatal overdose and 2) fatal overdose toxicology reports from the coroner containing location and high-dimensional information from the toxicology screen on the drugs present at the time of death. We first use non-negative matrix factorization to cluster toxicology reports into drug overdose categories and we then develop an EM algorithm for integrating the two heterogeneous data sets, where the mark corresponding to overdose category is inferred for the EMS data and the high volume EMS data is used to more accurately predict drug overdose death hotspots. We apply the algorithm to drug overdose data from Indianapolis, showing that the point process defined on the integrated data outperforms point processes that use only homogeneous EMS (AUC improvement .72 to .8) or coroner data (AUC improvement .81 to .85).We also investigate the extent to which overdoses are contagious, as a function of the type of overdose, while controlling for exogenous fluctuations in the background rate that might also contribute to clustering. We find that drug and opioid overdose deaths exhibit significant excitation, with branching ratio ranging from .72 to .98.
We investigate a correspondence between two formalisms for discrete probabilistic modeling: probabilistic graphical models (PGMs) and tensor networks (TNs), a powerful modeling framework for simulating complex quantum systems. The graphical calculus of PGMs and TNs exhibits many similarities, with discrete undirected graphical models (UGMs) being a special case of TNs. However, more general probabilistic TN models such as Born machines (BMs) employ complex-valued hidden states to produce novel forms of correlation among the probabilities. While representing a new modeling resource for capturing structure in discrete probability distributions, this behavior also renders the direct application of standard PGM tools impossible. We aim to bridge this gap by introducing a hybrid PGM-TN formalism that integrates quantum-like correlations into PGM models in a principled manner, using the physically-motivated concept of decoherence. We first prove that applying decoherence to the entirety of a BM model converts it into a discrete UGM, and conversely, that any subgraph of a discrete UGM can be represented as a decohered BM. This method allows a broad family of probabilistic TN models to be encoded as partially decohered BMs, a fact we leverage to combine the representational strengths of both model families. We experimentally verify the performance of such hybrid models in a sequential modeling task, and identify promising uses of our method within the context of existing applications of graphical models.
We develop a probabilistic framework for deep learning based on the Deep Rendering Mixture Model (DRMM), a new generative probabilistic model that explicitly capture variations in data due to latent task nuisance variables. We demonstrate that max-sum inference in the DRMM yields an algorithm that exactly reproduces the operations in deep convolutional neural networks (DCNs), providing a first principles derivation. Our framework provides new insights into the successes and shortcomings of DCNs as well as a principled route to their improvement. DRMM training via the Expectation-Maximization (EM) algorithm is a powerful alternative to DCN back-propagation, and initial training results are promising. Classification based on the DRMM and other variants outperforms DCNs in supervised digit classification, training 2-3x faster while achieving similar accuracy. Moreover, the DRMM is applicable to semi-supervised and unsupervised learning tasks, achieving results that are state-of-the-art in several categories on the MNIST benchmark and comparable to state of the art on the CIFAR10 benchmark.
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