Graphical LASSO Based Model Selection for Time Series
We propose a novel graphical model selection (GMS) scheme for high-dimensional stationary time series or discrete time process. The method is based on a natural generalization of the graphical LASSO (gLASSO), introduced originally for GMS based on i.i.d. samples, and estimates the conditional independence graph (CIG) of a time series from a finite length observation. The gLASSO for time series is defined as the solution of an l1-regularized maximum (approximate) likelihood problem. We solve this optimization problem using the alternating direction method of multipliers (ADMM). Our approach is nonparametric as we do not assume a finite dimensional (e.g., an autoregressive) parametric model for the observed process. Instead, we require the process to be sufficiently smooth in the spectral domain. For Gaussian processes, we characterize the performance of our method theoretically by deriving an upper bound on the probability that our algorithm fails to correctly identify the CIG. Numerical experiments demonstrate the ability of our method to recover the correct CIG from a limited amount of samples.
Code (0)
등록된 구현이 없습니다.
Tasks
Gaussian ProcessesModel SelectionTime SeriesTime Series AnalysisSimilar Papers 제목 키워드 기반
Sparse Graphical Linear Dynamical Systems
Time-series datasets are central in machine learning with applications in numerous fields of science and engineering, such as biomedicine, Earth observation, and network analysis. Extensive research exists on state-space…
Earth ObservationState Space ModelsTime SeriesOn Sparse High-Dimensional Graphical Model Learning For Dependent Time Series
We consider the problem of inferring the conditional independence graph (CIG) of a sparse, high-dimensional stationary multivariate Gaussian time series. A sparse-group lasso-based frequency-domain formulation of the pro…
Time SeriesTime Series AnalysisVocal Bursts Intensity PredictionMaximum likelihood thresholds of Gaussian graphical models and graphical lasso
Associated to each graph G is a Gaussian graphical model. Such models are often used in high-dimensional settings, i.e. where there are relatively few data points compared to the number of variables. The maximum likeliho…
The Cluster Graphical Lasso for improved estimation of Gaussian graphical models
We consider the task of estimating a Gaussian graphical model in the high-dimensional setting. The graphical lasso, which involves maximizing the Gaussian log likelihood subject to an l1 penalty, is a well-studied approa…
ClusteringModel SelectionOn Selecting Stable Predictors in Time Series Models
We extend the feature selection methodology to dependent data and propose a novel time series predictor selection scheme that accommodates statistical dependence in a more typical i.i.d sub-sampling based framework. Furt…
feature selectionTime SeriesTime Series Analysis