Learning short multivariate time series models through evolutionary and sparse matrix computation

Multivariate time series (MTS) data are widely available in different fields including medicine, finance, bioinformatics, science and engineering. Modelling MTS data accurately is important for many decision making activities. One area that has been largely overlooked so far is the particular type of time series where the data set consists of a large number of variables but with a small number of observations. In this paper we describe the development of a novel computational method based on Natural Computation and sparse matrices that bypasses the size restrictions of traditional statistical MTS methods, makes no distribution assumptions, and also locates the associated parameters. Extensive results are presented, where the proposed method is compared with both traditional statistical and heuristic search techniques and evaluated on a number of criteria. The results have implications for a wide range of applications involving the learning of short MTS models

Predicting glaucomatous visual field deterioration through short multivariate time series modelling

In bio-medical domains there are many applications involving the modelling of multivariate time series (MTS) data. One area that has been largely overlooked so far is the particular type of time series where the data set consists of a large number of variables but with a small number of observations. In this paper we describe the development of a novel computational method based on genetic algorithms that bypasses the size restrictions of traditional statistical MTS methods, makes no distribution assumptions, and also locates the order and associated parameters as a whole step. We apply this method to the prediction and modelling of glaucomatous visual field deterioration

Sparse Identification and Estimation of Large-Scale Vector AutoRegressive Moving Averages

The Vector AutoRegressive Moving Average (VARMA) model is fundamental to the theory of multivariate time series; however, in practice, identifiability issues have led many authors to abandon VARMA modeling in favor of the simpler Vector AutoRegressive (VAR) model. Such a practice is unfortunate since even very simple VARMA models can have quite complicated VAR representations. We narrow this gap with a new optimization-based approach to VARMA identification that is built upon the principle of parsimony. Among all equivalent data-generating models, we seek the parameterization that is "simplest" in a certain sense. A user-specified strongly convex penalty is used to measure model simplicity, and that same penalty is then used to define an estimator that can be efficiently computed. We show that our estimator converges to a parsimonious element in the set of all equivalent data-generating models, in a double asymptotic regime where the number of component time series is allowed to grow with sample size. Further, we derive non-asymptotic upper bounds on the estimation error of our method relative to our specially identified target. Novel theoretical machinery includes non-asymptotic analysis of infinite-order VAR, elastic net estimation under a singular covariance structure of regressors, and new concentration inequalities for quadratic forms of random variables from Gaussian time series. We illustrate the competitive performance of our methods in simulation and several application domains, including macro-economic forecasting, demand forecasting, and volatility forecasting

From Correlation to Causation: Estimation of Effective Connectivity from Continuous Brain Signals based on Zero-Lag Covariance

Knowing brain connectivity is of great importance both in basic research and for clinical applications. We are proposing a method to infer directed connectivity from zero-lag covariances of neuronal activity recorded at multiple sites. This allows us to identify causal relations that are reflected in neuronal population activity. To derive our strategy, we assume a generic linear model of interacting continuous variables, the components of which represent the activity of local neuronal populations. The suggested method for inferring connectivity from recorded signals exploits the fact that the covariance matrix derived from the observed activity contains information about the existence, the direction and the sign of connections. Assuming a sparsely coupled network, we disambiguate the underlying causal structure via $L^1$-minimization. In general, this method is suited to infer effective connectivity from resting state data of various types. We show that our method is applicable over a broad range of structural parameters regarding network size and connection probability of the network. We also explored parameters affecting its activity dynamics, like the eigenvalue spectrum. Also, based on the simulation of suitable Ornstein-Uhlenbeck processes to model BOLD dynamics, we show that with our method it is possible to estimate directed connectivity from zero-lag covariances derived from such signals. In this study, we consider measurement noise and unobserved nodes as additional confounding factors. Furthermore, we investigate the amount of data required for a reliable estimate. Additionally, we apply the proposed method on a fMRI dataset. The resulting network exhibits a tendency for close-by areas being connected as well as inter-hemispheric connections between corresponding areas. Also, we found that a large fraction of identified connections were inhibitory.Comment: 18 pages, 10 figure