Gaussian approximation for high dimensional time series

Modeling High Dimensional Time Series

This paper investigates the effectiveness of the recently proposed Gaussian Process Dynamical Model (GPDM) on high dimensional chaotic time series. The GPDM takes a Bayesian approach to modeling high-dimensional time series data, using the Gaussian process Latent Variable model (GPLVM) for nonlinear dimensionality reduction combined with a nonlinear dynamical model in latent space. The GPDM is ...

Linear Time Clustering for High Dimensional Mixtures of Gaussian Clouds

Clustering mixtures of Gaussian distributions is a fundamental and challenging problem that is ubiquitous in various high-dimensional data processing tasks. While state-of-the-art work on learning Gaussian mixture models has focused primarily on improving separation bounds and their generalization to arbitrary classes of mixture models, less emphasis has been paid to practical computational eff...

Compact modeling of high-dimensional time-series

Symbolic Analysis of High-Dimensional Time Series

In order to extract and to visualize qualitative information from a highdimensional time series, we apply ideas from symbolic dynamics. Counting certain ordinal patterns in the given series, we obtain a series of matrices whose entries are symbol frequencies. This matrix series is explored by simple methods from nominal statistics and information theory. The method is applied to detect and to v...

Temporal Regularized Matrix Factorization for High-dimensional Time Series Prediction

Time series prediction problems are becoming increasingly high-dimensional in modern applications, such as climatology and demand forecasting. For example, in the latter problem, the number of items for which demand needs to be forecast might be as large as 50,000. In addition, the data is generally noisy and full of missing values. Thus, modern applications require methods that are highly scal...