Related papers: The Locally Gaussian Partial Correlation
Conditional independence provides a way to understand causal relationships among the variables of interest. An underlying system may exhibit more fine-grained causal relationships especially between a variable and its parents, which will be…
Graphical models use graphs to represent conditional independence structure in the distribution of a random vector. In stochastic processes, graphs may represent so-called local independence or conditional Granger causality. Under some…
Measuring conditional dependencies among the variables of a network is of great interest to many disciplines. This paper studies some shortcomings of the existing dependency measures in detecting direct causal influences or their lack of…
We propose a novel extremal dependence measure called the partial tail-correlation coefficient (PTCC), in analogy to the partial correlation coefficient in classical multivariate analysis. The construction of our new coefficient is based on…
We consider the Granger causal structure learning problem from time series data. Granger causal algorithms predict a 'Granger causal effect' between two variables by testing if prediction error of one decreases significantly in the absence…
Independent component analysis (ICA) decomposes multivariate data into mutually independent components (ICs). The ICA model is subject to a constraint that at most one of these components is Gaussian, which is required for model…
Principal component analysis (PCA) is a well-established tool in machine learning and data processing. The principal axes in PCA were shown to be equivalent to the maximum marginal likelihood estimator of the factor loading matrix in a…
Granger causality is a statistical notion of causal influence based on prediction via vector autoregression. For Gaussian variables it is equivalent to transfer entropy, an information-theoretic measure of time-directed information transfer…
It is often useful in multivariate time series analysis to determine statistical causal relations between different time series. Granger causality is a fundamental measure for this purpose. Yet the traditional pairwise approach to Granger…
Standard likelihood penalties to learn Gaussian graphical models are based on regularising the off-diagonal entries of the precision matrix. Such methods, and their Bayesian counterparts, are not invariant to scalar multiplication of the…
It is of importance to investigate the significance of a subset of covariates $W$ for the response $Y$ given covariates $Z$ in regression modeling. To this end, we propose a significance test for the partial mean independence problem based…
We propose generalized conditional functional principal components analysis (GC-FPCA) for the joint modeling of the fixed and random effects of non-Gaussian functional outcomes. The method scales up to very large functional data sets by…
For a continuous random variable $Z$, testing conditional independence $X \perp\!\!\!\perp Y |Z$ is known to be a particularly hard problem. It constitutes a key ingredient of many constraint-based causal discovery algorithms. These…
There has been much interest in the nonparametric testing of conditional independence in the econometric and statistical literature, but the simplest and potentially most useful method, based on the sample partial correlation, seems to have…
This paper concerns the development of partial and semi-partial measures of spatial associations in the context of multivariate spatial lattice data which describe global or local associations among spatially aggregated measurements for…
We study the problem of learning multivariate dependencies in nonparametric and high-dimensional settings. This includes but is not limited to graphical models. Our approach effectively combines several features that are missing from…
Gaussian conditional random fields (GCRF) are a well-known used structured model for continuous outputs that uses multiple unstructured predictors to form its features and at the same time exploits dependence structure among outputs, which…
This paper presents a Gaussian process (GP) model for estimating piecewise continuous regression functions. In scientific and engineering applications of regression analysis, the underlying regression functions are piecewise continuous in…
Graphical models are widely used in scienti fic and engineering research to represent conditional independence structures between random variables. In many controlled experiments, environmental changes or external stimuli can often alter…
Inferring causal relationships from dynamical systems is the central interest of many scientific inquiries. Conditional local independence, which describes whether the evolution of one process is influenced by another process given…