Low Rank and Structured Modeling of High-dimensional Vector Autoregressions

Abstract

Network modeling of high-dimensional time series data is a key learning task due to its widespread use in a number of application areas, including macroeconomics, finance and neuroscience. While the problem of sparse modeling based on vector autoregressive models (VAR) has been investigated in depth in the literature, more complex network structures that involve low rank and group sparse components have received considerably less attention, despite their presence in data. Failure to account for low-rank structures results in spurious connectivity among the observed time series, which may lead practitioners to draw incorrect conclusions about pertinent scientific or policy questions. In order to accurately estimate a network of Granger causal interactions after accounting for latent effects, we introduce a novel approach for estimating low-rank and structured sparse high-dimensional VAR models. We introduce a regularized framework involving a combination of nuclear norm and lasso (or group lasso) penalty. Further, and subsequently establish non-asymptotic upper bounds on the estimation error rates of the low-rank and the structured sparse components. We also introduce a fast estimation algorithm and finally demonstrate the performance of the proposed modeling framework over standard sparse VAR estimates through numerical experiments on synthetic and real data.

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• Joint Estimation and Inference for Data Integration Problems based on Multiple Multi-layered Gaussian Graphical Models
• Multi-linear Tensor Autoregressive Models
• Sparse Plus Low Rank Matrix Decomposition: A Discrete Optimization Approach
• Sparse Cholesky covariance parametrization for recovering latent structure in ordered data
• Low Rank Forecasting
• Streaming Linear System Identification with Reverse Experience Replay
• Identification of Low Rank Vector Processes
• Multiple Change Point Detection in Structured VAR Models: the VARDetect R Package
• Tight Risk Bound for High Dimensional Time Series Completion
• Factorization of a spectral density with smooth eigenvalues of a multidimensional stationary time series
• Smooth Online Parameter Estimation for time varying VAR models with application to rat's LFP data
• High-Dimensional Dynamic Systems Identification with Additional Constraints
• Change point detection in low-rank VAR processes
• A Sparsity Inducing Nuclear-Norm Estimator (SpINNEr) for Matrix-Variate Regression in Brain Connectivity Analysis