Ensemble-Based Methods for Forecasting Census in Hospital Units

The ability to accurately forecast census counts in hospital departments has considerable implications for hospital resource allocation. In recent years several different methods have been proposed forecasting census counts, however many of these approaches do not use available patient-specific information. In this paper we present an ensemble-based methodology for forecasting the census under a framework that simultaneously incorporates both (i) arrival trends over time and (ii) patient-specific baseline and time-varying information. The proposed model for predicting census has three components, namely: current census count, number of daily arrivals and number of daily departures. To model the number of daily arrivals, we use a seasonality adjusted Poisson Autoregressive (PAR) model where the parameter estimates are obtained via conditional maximum likelihood. The number of daily departures is predicted by modeling the probability of departure from the census using logistic regression models that are adjusted for the amount of time spent in the census and incorporate both patient-specific baseline and time varying patient-specific covariate information. We illustrate our approach using neonatal intensive care unit (NICU) data collected at Women & Infants Hospital, Providence RI, which consists of 1001 consecutive NICU admissions between April 1st 2008 and March 31st 2009

Time-Varying Dispersion Integer-Valued GARCH Models

We propose a general class of INteger-valued Generalized AutoRegressive Conditionally Heteroskedastic (INGARCH) processes by allowing time-varying mean and dispersion parameters, which we call time-varying dispersion INGARCH (tv-DINGARCH) models. More specifically, we consider mixed Poisson INGARCH models and allow for a dynamic modeling of the dispersion parameter (as well as the mean), similarly to the spirit of the ordinary GARCH models. We derive conditions to obtain first and second order stationarity, and ergodicity as well. Estimation of the parameters is addressed and their associated asymptotic properties established as well. A restricted bootstrap procedure is proposed for testing constant dispersion against time-varying dispersion. Monte Carlo simulation studies are presented for checking point estimation, standard errors, and the performance of the restricted bootstrap approach. The inclusion of covariates is also addressed and applied to the daily number of deaths due to COVID-19 in Ireland. Insightful results were obtained in the data analysis, including a superior performance of the tv-DINGARCH processes over the ordinary INGARCH models.Comment: Paper submitted for publicatio

Dynamic Classification using Multivariate Locally Stationary Wavelet Processes

Methods for the supervised classification of signals generally aim to assign a signal to one class for its entire time span. In this paper we present an alternative formulation for multivariate signals where the class membership is permitted to change over time. Our aim therefore changes from classifying the signal as a whole to classifying the signal at each time point to one of a fixed number of known classes. We assume that each class is characterised by a different stationary generating process, the signal as a whole will however be nonstationary due to class switching. To capture this nonstationarity we use the recently proposed Multivariate Locally Stationary Wavelet model. To account for uncertainty in class membership at each time point our goal is not to assign a definite class membership but rather to calculate the probability of a signal belonging to a particular class. Under this framework we prove some asymptotic consistency results. This method is also shown to perform well when applied to both simulated and accelerometer data. In both cases our method is able to place a high probability on the correct class for the majority of time points

Graph-Regularized Manifold-Aware Conditional Wasserstein GAN for Brain Functional Connectivity Generation

Common measures of brain functional connectivity (FC) including covariance and correlation matrices are semi-positive definite (SPD) matrices residing on a cone-shape Riemannian manifold. Despite its remarkable success for Euclidean-valued data generation, use of standard generative adversarial networks (GANs) to generate manifold-valued FC data neglects its inherent SPD structure and hence the inter-relatedness of edges in real FC. We propose a novel graph-regularized manifold-aware conditional Wasserstein GAN (GR-SPD-GAN) for FC data generation on the SPD manifold that can preserve the global FC structure. Specifically, we optimize a generalized Wasserstein distance between the real and generated SPD data under an adversarial training, conditioned on the class labels. The resulting generator can synthesize new SPD-valued FC matrices associated with different classes of brain networks, e.g., brain disorder or healthy control. Furthermore, we introduce additional population graph-based regularization terms on both the SPD manifold and its tangent space to encourage the generator to respect the inter-subject similarity of FC patterns in the real data. This also helps in avoiding mode collapse and produces more stable GAN training. Evaluated on resting-state functional magnetic resonance imaging (fMRI) data of major depressive disorder (MDD), qualitative and quantitative results show that the proposed GR-SPD-GAN clearly outperforms several state-of-the-art GANs in generating more realistic fMRI-based FC samples. When applied to FC data augmentation for MDD identification, classification models trained on augmented data generated by our approach achieved the largest margin of improvement in classification accuracy among the competing GANs over baselines without data augmentation.Comment: 10 pages, 4 figure