Estimation of Correlation Matrices from Limited time series Data using Machine Learning

Correlation matrices contain a wide variety of spatio-temp oral information about a dynamical system. Predicting correlation matrices from partial time series information of a few nodes characterizes the spatio-temporal dynamics of the entire underly ing system. This information can help to predict the underlying network structure, e.g., inferring neuronal connections from spiking data, deducing causal dependencies between genes from expression d ata, and discovering long spatial range influences in climate variations. Traditional methods of pr edicting correlation matrices utilize time series data of all the nodes of the underlying networks. Here, we use a supervised machine learning technique to predict the correlation matrix of entire syste ms from finite time series information of a few randomly selected nodes. The accuracy of the predict ion validates that only a limited time series of a subset of the entire system is enough to make g ood correlation matrix predictions. Furthermore, using an unsupervised learning algorithm, we furnish insights into the success of the predictions from our model. Finally, we employ the machine l earning model developed here to real-world data sets.