arXiv subjects

Katherine Heller

Publications and source records attributed to Katherine Heller.

46 records · Page 3Linked to original sources

arXiv2017

An Improved Multi-Output Gaussian Process RNN with Real-Time Validation for Early Sepsis Detection

Sepsis is a poorly understood and potentially life-threatening complication that can occur as a result of infection. Early detection and treatment improves patient outcomes, and as such it poses an important challenge in medicine. In this work, we develop a flexible classifier that leverages streaming lab results, vitals, and medications to predict sepsis before it occurs. We model patient clinical time series with multi-output Gaussian processes, maintaining uncertainty about the physiological state of a patient while also imputing missing values. The mean function takes into account the effects of medications administered on the trajectories of the physiological variables. Latent function values from the Gaussian process are then fed into a deep recurrent neural network to classify patient encounters as septic or not, and the overall model is trained end-to-end using back-propagation. We train and validate our model on a large dataset of 18 months of heterogeneous inpatient stays from the Duke University Health System, and develop a new "real-time" validation scheme for simulating the performance of our model as it will actually be used. Our proposed method substantially outperforms clinical baselines, and improves on a previous related model for detecting sepsis. Our model's predictions will be displayed in a real-time analytics dashboard to be used by a sepsis rapid response team to help detect and improve treatment of sepsis.

stat.ML↗

arXiv2017

Predictive Hierarchical Clustering: Learning clusters of CPT codes for improving surgical outcomes

We develop a novel algorithm, Predictive Hierarchical Clustering (PHC), for agglomerative hierarchical clustering of current procedural terminology (CPT) codes. Our predictive hierarchical clustering aims to cluster subgroups, not individual observations, found within our data, such that the clusters discovered result in optimal performance of a classification model. Therefore, merges are chosen based on a Bayesian hypothesis test, which chooses pairings of the subgroups that result in the best model fit, as measured by held out predictive likelihoods. We place a Dirichlet prior on the probability of merging clusters, allowing us to adjust the size and sparsity of clusters. The motivation is to predict patient-specific surgical outcomes using data from ACS NSQIP (American College of Surgeon's National Surgical Quality Improvement Program). An important predictor of surgical outcomes is the actual surgical procedure performed as described by a CPT code. We use PHC to cluster CPT codes, represented as subgroups, together in a way that enables us to better predict patient-specific outcomes compared to currently used clusters based on clinical judgment.

stat.ME↗

arXiv2017

Learning to Detect Sepsis with a Multitask Gaussian Process RNN Classifier

We present a scalable end-to-end classifier that uses streaming physiological and medication data to accurately predict the onset of sepsis, a life-threatening complication from infections that has high mortality and morbidity. Our proposed framework models the multivariate trajectories of continuous-valued physiological time series using multitask Gaussian processes, seamlessly accounting for the high uncertainty, frequent missingness, and irregular sampling rates typically associated with real clinical data. The Gaussian process is directly connected to a black-box classifier that predicts whether a patient will become septic, chosen in our case to be a recurrent neural network to account for the extreme variability in the length of patient encounters. We show how to scale the computations associated with the Gaussian process in a manner so that the entire system can be discriminatively trained end-to-end using backpropagation. In a large cohort of heterogeneous inpatient encounters at our university health system we find that it outperforms several baselines at predicting sepsis, and yields 19.4% and 55.5% improved areas under the Receiver Operating Characteristic and Precision Recall curves as compared to the NEWS score currently used by our hospital.

stat.ML↗

arXiv2017

Fast Second-Order Stochastic Backpropagation for Variational Inference

We propose a second-order (Hessian or Hessian-free) based optimization method for variational inference inspired by Gaussian backpropagation, and argue that quasi-Newton optimization can be developed as well. This is accomplished by generalizing the gradient computation in stochastic backpropagation via a reparametrization trick with lower complexity. As an illustrative example, we apply this approach to the problems of Bayesian logistic regression and variational auto-encoder (VAE). Additionally, we compute bounds on the estimator variance of intractable expectations for the family of Lipschitz continuous function. Our method is practical, scalable and model free. We demonstrate our method on several real-world datasets and provide comparisons with other stochastic gradient methods to show substantial enhancement in convergence rates.

stat.ML↗

arXiv2016

Scalable Modeling of Multivariate Longitudinal Data for Prediction of Chronic Kidney Disease Progression

Prediction of the future trajectory of a disease is an important challenge for personalized medicine and population health management. However, many complex chronic diseases exhibit large degrees of heterogeneity, and furthermore there is not always a single readily available biomarker to quantify disease severity. Even when such a clinical variable exists, there are often additional related biomarkers routinely measured for patients that may better inform the predictions of their future disease state. To this end, we propose a novel probabilistic generative model for multivariate longitudinal data that captures dependencies between multivariate trajectories. We use a Gaussian process based regression model for each individual trajectory, and build off ideas from latent class models to induce dependence between their mean functions. We fit our method using a scalable variational inference algorithm to a large dataset of longitudinal electronic patient health records, and find that it improves dynamic predictions compared to a recent state of the art method. Our local accountable care organization then uses the model predictions during chart reviews of high risk patients with chronic kidney disease.

stat.ML↗

arXiv2015

$k$-means: Fighting against Degeneracy in Sequential Monte Carlo with an Application to Tracking

For regular particle filter algorithm or Sequential Monte Carlo (SMC) methods, the initial weights are traditionally dependent on the proposed distribution, the posterior distribution at the current timestamp in the sampled sequence, and the target is the posterior distribution of the previous timestamp. This is technically correct, but leads to algorithms which usually have practical issues with degeneracy, where all particles eventually collapse onto a single particle. In this paper, we propose and evaluate using $k$ means clustering to attack and even take advantage of this degeneracy. Specifically, we propose a Stochastic SMC algorithm which initializes the set of $k$ means, providing the initial centers chosen from the collapsed particles. To fight against degeneracy, we adjust the regular SMC weights, mediated by cluster proportions, and then correct them to retain the same expectation as before. We experimentally demonstrate that our approach has better performance than vanilla algorithms.

stat.ML↗

arXiv2015

The Bayesian Echo Chamber: Modeling Social Influence via Linguistic Accommodation

We present the Bayesian Echo Chamber, a new Bayesian generative model for social interaction data. By modeling the evolution of people's language usage over time, this model discovers latent influence relationships between them. Unlike previous work on inferring influence, which has primarily focused on simple temporal dynamics evidenced via turn-taking behavior, our model captures more nuanced influence relationships, evidenced via linguistic accommodation patterns in interaction content. The model, which is based on a discrete analog of the multivariate Hawkes process, permits a fully Bayesian inference algorithm. We validate our model's ability to discover latent influence patterns using transcripts of arguments heard by the US Supreme Court and the movie "12 Angry Men." We showcase our model's capabilities by using it to infer latent influence patterns from Federal Open Market Committee meeting transcripts, demonstrating state-of-the-art performance at uncovering social dynamics in group discussions.

stat.ML↗

arXiv2013

Ranking relations using analogies in biological and information networks

Analogical reasoning depends fundamentally on the ability to learn and generalize about relations between objects. We develop an approach to relational learning which, given a set of pairs of objects $\mathbf{S}=\{A^{(1)}:B^{(1)},A^{(2)}:B^{(2)},\ldots,A^{(N)}:B ^{(N)}\}$, measures how well other pairs A:B fit in with the set $\mathbf{S}$. Our work addresses the following question: is the relation between objects A and B analogous to those relations found in $\mathbf{S}$? Such questions are particularly relevant in information retrieval, where an investigator might want to search for analogous pairs of objects that match the query set of interest. There are many ways in which objects can be related, making the task of measuring analogies very challenging. Our approach combines a similarity measure on function spaces with Bayesian analysis to produce a ranking. It requires data containing features of the objects of interest and a link matrix specifying which relationships exist; no further attributes of such relationships are necessary. We illustrate the potential of our method on text analysis and information networks. An application on discovering functional interactions between pairs of proteins is discussed in detail, where we show that our approach can work in practice even if a small set of protein pairs is provided.

stat.ME↗

arXiv2012

Bayesian and L1 Approaches to Sparse Unsupervised Learning

The use of L1 regularisation for sparse learning has generated immense research interest, with successful application in such diverse areas as signal acquisition, image coding, genomics and collaborative filtering. While existing work highlights the many advantages of L1 methods, in this paper we find that L1 regularisation often dramatically underperforms in terms of predictive performance when compared with other methods for inferring sparsity. We focus on unsupervised latent variable models, and develop L1 minimising factor models, Bayesian variants of "L1", and Bayesian models with a stronger L0-like sparsity induced through spike-and-slab distributions. These spike-and-slab Bayesian factor models encourage sparsity while accounting for uncertainty in a principled manner and avoiding unnecessary shrinkage of non-zero values. We demonstrate on a number of data sets that in practice spike-and-slab Bayesian methods outperform L1 minimisation, even on a computational budget. We thus highlight the need to re-assess the wide use of L1 methods in sparsity-reliant applications, particularly when we care about generalising to previously unseen data, and provide an alternative that, over many varying conditions, provides improved generalisation performance.

cs.LG↗

arXiv2010

Compact differences of composition operators

When $φ$ and $ψ$ are linear-fractional self-maps of the unit ball $B_N$ in ${\mathbb C}^N$, $N\geq 1$, we show that the difference $C_φ-C_ψ$ cannot be non-trivially compact on either the Hardy space $H^2(B_N)$ or any weighted Bergman space $A^2_α(B_N)$. Our arguments emphasize geometrical properties of the inducing maps $φ$ and $ψ$.

math.FA↗