scholarly journals The evaluation of COVID-19 prediction precision with a Lyapunov-like exponent

PLoS ONE ◽  
2021 ◽  
Vol 16 (5) ◽  
pp. e0252394
Author(s):  
Jiří Mazurek

In the field of machine learning, building models and measuring their performance are two equally important tasks. Currently, measures of precision of regression models’ predictions are usually based on the notion of mean error, where by error we mean a deviation of a prediction from an observation. However, these mean based measures of models’ performance have two drawbacks. Firstly, they ignore the length of the prediction, which is crucial when dealing with chaotic systems, where a small deviation at the beginning grows exponentially with time. Secondly, these measures are not suitable in situations where a prediction is made for a specific point in time (e.g. a date), since they average all errors from the start of the prediction to its end. Therefore, the aim of this paper is to propose a new measure of models’ prediction precision, a divergence exponent, based on the notion of the Lyapunov exponent which overcomes the aforementioned drawbacks. The proposed approach enables the measuring and comparison of models’ prediction precision for time series with unequal length and a given target date in the framework of chaotic phenomena. Application of the divergence exponent to the evaluation of models’ accuracy is demonstrated by two examples and then a set of selected predictions of COVID-19 spread from other studies is evaluated to show its potential.

2002 ◽  
Vol 7 (1) ◽  
pp. 41-52 ◽  
Author(s):  
A. M. López Jiménez ◽  
C. Camacho Martínez Vara de Rey ◽  
A. R. García Torres

The literature about non-linear dynamics offers a few recommendations, which sometimes are divergent, about the criteria to be used in order to select the optimal calculus parameters in the estimation of Lyapunov exponents by direct methods. These few recommendations are circumscribed to the analysis of chaotic systems. We have found no recommendation for the estimation ofλstarting from the time series of classic systems. The reason for this is the interest in distinguishing variability due to a chaotic behavior of determinist dynamic systems of variability caused by white noise or linear stochastic processes, and less in the identification of non-linear terms from the analysis of time series. In this study we have centered in the dependence of the Lyapunov exponent, obtained by means of direct estimation, of the initial distance and the time evolution. We have used generated series of chaotic systems and generated series of classic systems with varying complexity. To generate the series we have used the logistic map.


2021 ◽  
Vol 15 ◽  
Author(s):  
R S M Lakshmi Patibandla ◽  
B. Tarakeswara Rao ◽  
M. Ramakrishna Murty ◽  
V. Lakshman Narayana

: The extent of COVID-19 dataset within the entire ecosphere is dangerous for mankind. The possessions of a number of the most important financial practicality are anxious obligations to the massive impurity and transmissibility of this syndrome. To the rising extent of the cases and its ensuing hassle on the supervision and health authorities, approximately prediction systems would be vital to forecast the spread of cases within the imminent. In this paper, we've analyzed different regression models of machine learning for the forecasting of COVID-19, the prediction of varied constraints like a rise within the range of confirmed cases, amount of recovered cases and closed cases, etc. The levels attained by the recommended proposal are considered to predict the COVID-19 with the data supported statistic problems for day wise and week wise cases predictions.


2020 ◽  
Author(s):  
Pathikkumar Patel ◽  
Bhargav Lad ◽  
Jinan Fiaidhi

During the last few years, RNN models have been extensively used and they have proven to be better for sequence and text data. RNNs have achieved state-of-the-art performance levels in several applications such as text classification, sequence to sequence modelling and time series forecasting. In this article we will review different Machine Learning and Deep Learning based approaches for text data and look at the results obtained from these methods. This work also explores the use of transfer learning in NLP and how it affects the performance of models on a specific application of sentiment analysis.


2020 ◽  
Author(s):  
Hsiao-Ko Chang ◽  
Hui-Chih Wang ◽  
Chih-Fen Huang ◽  
Feipei Lai

BACKGROUND In most of Taiwan’s medical institutions, congestion is a serious problem for emergency departments. Due to a lack of beds, patients spend more time in emergency retention zones, which make it difficult to detect cardiac arrest (CA). OBJECTIVE We seek to develop a Drug Early Warning System Model (DEWSM), it included drug injections and vital signs as this research important features. We use it to predict cardiac arrest in emergency departments via drug classification and medical expert suggestion. METHODS We propose this new model for detecting cardiac arrest via drug classification and by using a sliding window; we apply learning-based algorithms to time-series data for a DEWSM. By treating drug features as a dynamic time-series factor for cardiopulmonary resuscitation (CPR) patients, we increase sensitivity, reduce false alarm rates and mortality, and increase the model’s accuracy. To evaluate the proposed model, we use the area under the receiver operating characteristic curve (AUROC). RESULTS Four important findings are as follows: (1) We identify the most important drug predictors: bits (intravenous therapy), and replenishers and regulators of water and electrolytes (fluid and electrolyte supplement). The best AUROC of bits is 85%, it means the medical expert suggest the drug features: bits, it will affect the vital signs, and then the evaluate this model correctly classified patients with CPR reach 85%; that of replenishers and regulators of water and electrolytes is 86%. These two features are the most influential of the drug features in the task. (2) We verify feature selection, in which accounting for drugs improve the accuracy: In Task 1, the best AUROC of vital signs is 77%, and that of all features is 86%. In Task 2, the best AUROC of all features is 85%, which demonstrates that thus accounting for the drugs significantly affects prediction. (3) We use a better model: For traditional machine learning, this study adds a new AI technology: the long short-term memory (LSTM) model with the best time-series accuracy, comparable to the traditional random forest (RF) model; the two AUROC measures are 85%. It can be seen that the use of new AI technology will achieve better results, currently comparable to the accuracy of traditional common RF, and the LSTM model can be adjusted in the future to obtain better results. (4) We determine whether the event can be predicted beforehand: The best classifier is still an RF model, in which the observational starting time is 4 hours before the CPR event. Although the accuracy is impaired, the predictive accuracy still reaches 70%. Therefore, we believe that CPR events can be predicted four hours before the event. CONCLUSIONS This paper uses a sliding window to account for dynamic time-series data consisting of the patient’s vital signs and drug injections. The National Early Warning Score (NEWS) only focuses on the score of vital signs, and does not include factors related to drug injections. In this study, the experimental results of adding the drug injections are better than only vital signs. In a comparison with NEWS, we improve predictive accuracy via feature selection, which includes drugs as features. In addition, we use traditional machine learning methods and deep learning (using LSTM method as the main processing time series data) as the basis for comparison of this research. The proposed DEWSM, which offers 4-hour predictions, is better than the NEWS in the literature. This also confirms that the doctor’s heuristic rules are consistent with the results found by machine learning algorithms.


2008 ◽  
Vol 18 (12) ◽  
pp. 3679-3687 ◽  
Author(s):  
AYDIN A. CECEN ◽  
CAHIT ERKAL

We present a critical remark on the pitfalls of calculating the correlation dimension and the largest Lyapunov exponent from time series data when trend and periodicity exist. We consider a special case where a time series Zi can be expressed as the sum of two subsystems so that Zi = Xi + Yi and at least one of the subsystems is deterministic. We show that if the trend and periodicity are not properly removed, correlation dimension and Lyapunov exponent estimations yield misleading results, which can severely compromise the results of diagnostic tests and model identification. We also establish an analytic relationship between the largest Lyapunov exponents of the subsystems and that of the whole system. In addition, the impact of a periodic parameter perturbation on the Lyapunov exponent for the logistic map and the Lorenz system is discussed.


2012 ◽  
Vol 197 ◽  
pp. 271-277
Author(s):  
Zhu Ping Gong

Small data set approach is used for the estimation of Largest Lyapunov Exponent (LLE). Primarily, the mean period drawback of Small data set was corrected. On this base, the LLEs of daily qualified rate time series of HZ, an electronic manufacturing enterprise, were estimated and all positive LLEs were taken which indicate that this time series is a chaotic time series and the corresponding produce process is a chaotic process. The variance of the LLEs revealed the struggle between the divergence nature of quality system and quality control effort. LLEs showed sharp increase in getting worse quality level coincide with the company shutdown. HZ’s daily qualified rate, a chaotic time series, shows us the predictable nature of quality system in a short-run.


Sign in / Sign up

Export Citation Format

Share Document