Online Bayesian Modeling and Prediction of Nonlinear Systems

2007 ◽  
Vol 46 (02) ◽  
pp. 96-101 ◽  
Author(s):  
T. Matsumoto
Keyword(s):  
Time Series ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Posterior Distribution ◽  
Sequential Monte Carlo ◽  
Time Series Data ◽  
Series Data ◽  
Target System ◽  
Sequential Monte Carlo Method ◽  
Online Prediction

Summary Objectives : Given time-series data from an unknown target system, one often wants to build a model for the system behind the data and make predictions. If the target system can be assumed to be linear, there are means of modeling and predicting the target system in question. If, however, one cannot assume the system is linear, various linear theories have natural limitations in terms of modeling and predictive capabilities. This paper attempts to construct a model from time-series data and make an online prediction when the linear assumption is not valid. Methods : The problem is formulated within a Bayesian framework implemented by the Sequential Monte Carlo method. Online Bayesian learning/prediction requires computation of a posterior distribution in a sequential manner as each datum arrives. The Sequential Monte Carlo method computes the importance weight in order to draw sample from the posterior distribution. The scheme is tested against time-series data from a noisy Rossler system. Results : The test time-series data is the x-coordinate of the trajectory generated by a noisy Roessler system. Attempts are made with regard to online reconstruction of the attractor and online prediction of the time-series data. Conclusions : The proposed algorithm appears to be functional. The algorithm should be tested against real world data.

scholarly journals Monte Carlo Filtering Objectives

2021 ◽  
Author(s):  
Shuangshuang Chen ◽  
Sihao Ding ◽  
Yiannis Karayiannidis ◽  
Mårten Björkman
Keyword(s):  
Time Series ◽  
Monte Carlo ◽  
Sequential Monte Carlo ◽  
Time Series Data ◽  
Generative Models ◽  
Gradient Estimates ◽  
Series Data ◽  
Stable Model ◽  
Model Learning ◽  
Marginal Likelihoods

Learning generative models and inferring latent trajectories have shown to be challenging for time series due to the intractable marginal likelihoods of flexible generative models. It can be addressed by surrogate objectives for optimization. We propose Monte Carlo filtering objectives (MCFOs), a family of variational objectives for jointly learning parametric generative models and amortized adaptive importance proposals of time series. MCFOs extend the choices of likelihood estimators beyond Sequential Monte Carlo in state-of-the-art objectives, possess important properties revealing the factors for the tightness of objectives, and allow for less biased and variant gradient estimates. We demonstrate that the proposed MCFOs and gradient estimations lead to efficient and stable model learning, and learned generative models well explain data and importance proposals are more sample efficient on various kinds of time series data.

scholarly journals Ranking Information Extracted from Uncertainty Quantification of the Prediction of a Deep Learning Model on Medical Time Series Data

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1078
Author(s):  
Ruxandra Stoean ◽  
Catalin Stoean ◽  
Miguel Atencia ◽  
Roberto Rodríguez-Labrada ◽  
Gonzalo Joya
Keyword(s):  
Time Series ◽  
Monte Carlo ◽  
Deep Learning ◽  
Uncertainty Quantification ◽  
Time Series Data ◽  
Short Term Memory ◽  
Learning Model ◽  
Series Data ◽  
Real World Problem ◽  
Uncertainty Estimates

Uncertainty quantification in deep learning models is especially important for the medical applications of this complex and successful type of neural architectures. One popular technique is Monte Carlo dropout that gives a sample output for a record, which can be measured statistically in terms of average probability and variance for each diagnostic class of the problem. The current paper puts forward a convolutional–long short-term memory network model with a Monte Carlo dropout layer for obtaining information regarding the model uncertainty for saccadic records of all patients. These are next used in assessing the uncertainty of the learning model at the higher level of sets of multiple records (i.e., registers) that are gathered for one patient case by the examining physician towards an accurate diagnosis. Means and standard deviations are additionally calculated for the Monte Carlo uncertainty estimates of groups of predictions. These serve as a new collection where a random forest model can perform both classification and ranking of variable importance. The approach is validated on a real-world problem of classifying electrooculography time series for an early detection of spinocerebellar ataxia 2 and reaches an accuracy of 88.59% in distinguishing between the three classes of patients.

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