Estimation of Correlation Matrices from Limited time series Data using Machine Learning
This addresses the challenge of inferring network structures in fields like neuroscience and climate science, but it is incremental as it builds on existing machine learning techniques for correlation estimation.
The paper tackles the problem of predicting correlation matrices from limited time series data of a few nodes, using supervised machine learning to achieve accurate predictions, validated by the model's performance on real-world datasets.
Correlation matrices contain a wide variety of spatio-temporal 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 underlying 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 data, and discovering long spatial range influences in climate variations. Traditional methods of predicting 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 systems from finite time series information of a few randomly selected nodes. The accuracy of the prediction validates that only a limited time series of a subset of the entire system is enough to make good 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 learning model developed here to real-world data sets.