NARMAX model as a sparse, interpretable and transparent machine learning approach for big medical and healthcare data analysis

Influenza and influenza-like illnesses are one of the leading causes of death in the world, resulting in heavy losses to individual families and nations. Accurate and timely forecasts of seasonal influenza would therefore crucially important to inform and facilitate public health decision-making for presenting and intervening influenza epidemics. System identification and data-driven modelling approaches play an indispensable role in analyzing and understanding complex processes including medical, healthcare and environmental time series. This paper aims to present a type of sparse, interpretable and transparent (SIT) model, which cannot only be used for future behavior prediction but more importantly for understanding the dependent relationship between the response variables of a system on potential independent variables (also known as input variables or predictors). An ideal candidate for such a SIT representation is the well-known NARMAX (nonlinear autoregressive moving average with exogenous inputs) model, which can be established based on input and output data of the system of interest, and the final refined model is usually simple, parsimonious and easy to interpret. The general framework of the NARMAX model is presented, and the state-of-the-art algorithms for such a SIT model estimation are described. Two case studies are provided to illustrate how well the SIT-NARMAX model can work for medical, healthcare and related data

Identification of continuous-time models for nonlinear dynamic systems from discrete data

A new iOFR-MF (iterative orthogonal forward regression--modulating function) algorithm is proposed to identify continuous-time models from noisy data by combining the MF method and the iOFR algorithm. In the new method, a set of candidate terms, which describe different dynamic relationships among the system states or between the input and output, are first constructed. These terms are then modulated using the MF method to generate the data matrix. The iOFR algorithm is next applied to build the relationships between these modulated terms, which include detecting the model structure and estimating the associated parameters. The relationships between the original variables are finally recovered from the model of the modulated terms. Both nonlinear state-space models and a class of higher order nonlinear input–output models are considered. The new direct method is compared with the traditional finite difference method and results show that the new method performs much better than the finite difference method. The new method works well even when the measurements are severely corrupted by noise. The selection of appropriate MFs is also discussed

Modelling and Prediction of Global Magnetic Disturbance in Near-Earth Space: a Case Study for Kp Index using NARX Models

Severe geomagnetic disturbances can be hazardous for mod-ern technological systems. The reliable forecast of parameters related to thestate of the magnetosphere can facilitate the mitigation of adverse effects ofspace weather. This study is devoted to the modeling and forecasting of theevolution of the Kp index related to global geomagnetic disturbances. Through-out this work the Nonlinear AutoRegressive with eXogenous inputs (NARX)methodology is applied. Two approaches are presented: i) a recursive slid-ing window approach, and ii) a direct approach. These two approaches arestudied separately and are then compared to evaluate their performances.It is shown that the direct approach outperforms the recursive approach, butboth tend to produce predictions slightly biased from the true values for lowand high disturbances

A New Proxy Measurement Algorithm with Application to the Estimation of Vertical Ground Reaction Forces Using Wearable Sensors

Measurement of the ground reaction forces (GRF) during walking is typically limited to laboratory settings, and only short observations using wearable pressure insoles have been reported so far. In this study, a new proxy measurement method is proposed to estimate the vertical component of the GRF (vGRF) from wearable accelerometer signals. The accelerations are used as the proxy variable. An orthogonal forward regression algorithm (OFR) is employed to identify the dynamic relationships between the proxy variables and the measured vGRF using pressure-sensing insoles. The obtained model, which represents the connection between the proxy variable and the vGRF, is then used to predict the latter. The results have been validated using pressure insoles data collected from nine healthy individuals under two outdoor walking tasks in non-laboratory settings. The results show that the vGRFs can be reconstructed with high accuracy (with an average prediction error of less than 5.0%) using only one wearable sensor mounted at the waist (L5, fifth lumbar vertebra). Proxy measures with different sensor positions are also discussed. Results show that the waist acceleration-based proxy measurement is more stable with less inter-task and inter-subject variability than the proxy measures based on forehead level accelerations. The proposed proxy measure provides a promising low-cost method for monitoring ground reaction forces in real-life settings and introduces a novel generic approach for replacing the direct determination of difficult to measure variables in many applications

Ultra-Orthogonal Forward Regression Algorithms for the Identification of Non-Linear Dynamic Systems

A new ultra-least squares (ULS) criterion is introduced for system identification. Unlike the standard least squares criterion which is based on the Euclidean norm of the residuals, the new ULS criterion is derived from the Sobolev space norm. The new criterion measures not only the discrepancy between the observed signals and the model prediction but also the discrepancy between the associated weak derivatives of the observed and the model signals. The new ULS criterion possesses a clear physical interpretation and is easy to implement. Based on this, a new Ultra-Orthogonal Forward Regression (UOFR) algorithm is introduced for nonlinear system identification, which includes converting a least squares regression problem into the associated ultra-least squares problem and solving the ultra-least squares problem using the orthogonal forward regression method. Numerical simulations show that the new UOFR algorithm can significantly improve the performance of the classic OFR algorithm

The variability of the Atlantic meridional circulation since 1980, as hindcast by a data-driven nonlinear systems model

The Atlantic meridional overturning circulation (AMOC), an important component of the climate system, has only been directly measured since the RAPID array’s installation across the Atlantic at 26°N in 2004. This has shown that the AMOC strength is highly variable on monthly timescales; however, after an abrupt, short-lived, halving of the strength of the AMOC early in 2010, its mean has remained ~ 15% below its pre-2010 level. To attempt to understand the reasons for this variability, we use a control systems identification approach to model the AMOC, with the RAPID data of 2004–2017 providing a trial and test data set. After testing to find the environmental variables, and systems model, that allow us to best match the RAPID observations, we reconstruct AMOC variation back to 1980. Our reconstruction suggests that there is inter-decadal variability in the strength of the AMOC, with periods of both weaker flow than recently, and flow strengths similar to the late 2000s, since 1980. Recent signs of weakening may therefore not reflect the beginning of a sustained decline. It is also shown that there may be predictive power for AMOC variability of around 6 months, as ocean density contrasts between the source and sink regions for the North Atlantic Drift, with lags up to 6 months, are found to be important components of the systems model

Electron flux models for different energies at geostationary orbit

Forecast models were derived for energetic electrons at all energy ranges sampled by the third-generation Geostationary Operational Environmental Satellites (GOES). These models were based on Multi-Input Single-Output Nonlinear Autoregressive Moving Average with Exogenous inputs methodologies. The model inputs include the solar wind velocity, density and pressure, the fraction of time that the interplanetary magnetic field (IMF) was southward, the IMF contribution of a solar wind-magnetosphere coupling function proposed by Boynton et al. (2011b), and the Dst index. As such, this study has deduced five new 1 h resolution models for the low-energy electrons measured by GOES (30–50 keV, 50–100 keV, 100–200 keV, 200–350 keV, and 350–600 keV) and extended the existing >800 keV and >2 MeV Geostationary Earth Orbit electron fluxes models to forecast at a 1 h resolution. All of these models were shown to provide accurate forecasts, with prediction efficiencies ranging between 66.9% and 82.3%