Related papers: Granger Causality Maps for Langevin Systems
This is a comment to the paper 'A study of problems encountered in Granger causality analysis from a neuroscience perspective'. We agree that interpretation issues of Granger Causality in Neuroscience exist (partially due to the historical…
Mapping with uncertainty representation is required in many research domains, especially for localization. Although there are many investigations regarding the uncertainty of the pose estimation of an ego-robot with map information, the…
We develop a framework for derivative Gaussian process latent variable models (DGP-LVMs) that can handle multi-dimensional output data using modified derivative covariance functions. The modifications account for complexities in the…
In systems of multiple agents, identifying the cause of observed agent dynamics is challenging. Often, these agents operate in diverse, non-stationary environments, where models rely on hand-crafted environment-specific features to infer…
In this work, we investigate a range of time series, including Gaussian noises (white, pink, and blue), stochastic processes (Ornstein-Uhlenbeck, fractional Brownian motion, and Levy flights), and chaotic systems (the logistic map), using…
Gaussian Processes (GPs) are a versatile method that enables different approaches towards learning for dynamics and control. Gaussianity assumptions appear in two dimensions in GPs: The positive semi-definite kernel of the underlying…
Granger-causality in the frequency domain is an emerging tool to analyze the causal relationship between two time series. We propose a bootstrap test on unconditional and conditional Granger-causality spectra, as well as on their…
Granger causality is among the widely used data-driven approaches for causal analysis of time series data with applications in various areas including economics, molecular biology, and neuroscience. Two of the main challenges of this…
The generalized Langevin equation is used as a model for various coarse-grained physical processes, e.g., the time evolution of the velocity of a given larger particle in an implicitly represented solvent, when the relevant time scales of…
Gaussian processes (GPs) with derivatives are useful in many applications, including Bayesian optimization, implicit surface reconstruction, and terrain reconstruction. Fitting a GP to function values and derivatives at $n$ points in $d$…
For a wide range of phenomena, current computational ability does not always allow for fully atomistic simulations of high-dimensional molecular systems to reach time scales of interest. Coarse-graining (CG) is an established approach to…
Despite their promise and ubiquity, Gaussian processes (GPs) can be difficult to use in practice due to the computational impediments of fitting and sampling from them. Here we discuss a short R package for efficient multivariate normal…
This paper proposes a novel method (GLS Granger test) to determine causal relationships between time series based on the estimation of the autocovariance matrix and generalized least squares. We show the effectiveness of proposed…
Identifying directed interactions between species from time series of their population densities has many uses in ecology. This key statistical task is equivalent to causal time series inference, which connects to the Granger causality (GC)…
We present a new method for forecasting systems of multiple interrelated time series. The method learns the forecast models together with discovering leading indicators from within the system that serve as good predictors improving the…
Most of the metrics used for detecting a causal relationship among multiple time series ignore the effects of practical measurement impairments, such as finite sample effects, undersampling and measurement noise. It has been shown that…
Gaussian process (GP) models are widely used to analyze spatially referenced data and to predict values at locations without observations. In contrast to many algorithmic procedures, GP models are based on a statistical framework, which…
This paper studies multi-horizon Granger causality using high-dimensional local projections in sparse Vector Autoregressive (VAR) systems. Since local projection coefficients are nonlinear transformations of the underlying VAR parameters,…
Reconstructing complete 3D shapes from incomplete or noisy observations is a fundamentally ill-posed problem that requires balancing measurement consistency with shape plausibility. Existing methods for shape reconstruction can achieve…
Kernel-based methods are used in the context of Granger Causality to enable the identification of nonlinear causal relationships between time series variables. In this paper, we show that two state of the art kernel-based Granger Causality…