Introduced more than a half-century ago, Granger causality has become a popular tool for
analyzing time series data in many application domains, from economics and finance to …

Vector autoregression (VAR) is a fundamental tool for modeling multivariate time series.
However, as the number of component series is increased, the VAR model becomes …

Granger causality has been used for the investigation of the inter-dependence structure of
the underlying systems of multivariate time series. In particular, the direct causal effects are …

Assuming stationarity is unrealistic in many time series applications. A more realistic
alternative is to assume piecewise stationarity, where the model can change at potentially …

The gene regulation network (GRN) is a high-dimensional complex system, which can be
represented by various mathematical or statistical models. The ordinary differential equation …

Probabilistic models are conceptually powerful tools for finding structure in data, but their
practical effectiveness is often limited by our ability to perform inference in them. Exact …

The task of estimating a Gaussian graphical model in the high-dimensional setting is
considered. The graphical lasso, which involves maximizing the Gaussian log likelihood …

Dynamical systems comprising of multiple components that can be partitioned into distinct
blocks originate in many scientific areas. A pertinent example is the interactions between …

Modern technological advances have enabled an unprecedented amount of structured data
with complex temporal dependence, urging the need for new methods to efficiently model …

As a special infinite-order vector autoregressive (VAR) model, the vector autoregressive
moving average (VARMA) model can capture much richer temporal patterns than the widely …