The Human Connectome Project: A data acquisition perspective

Network modelling methods for FMRI.

In recent years, several methods have been proposed for the discovery of causal structure from non-experimental data. Such methods make various assumptions on the data generating process to facilitate its identification from purely observational data. Continuing this line of research, we show how to discover the complete causal structure of continuous-valued data, under the assumptions that (a) the data generating process is linear, (b) there are no unobserved confounders, and (c) disturbance variables have non-Gaussian distributions of non-zero variances. The solution relies on the use of the statistical method known as independent component analysis, and does not require any pre-specified time-ordering of the variables. We provide a complete Matlab package for performing this LiNGAM analysis (short for Linear Non-Gaussian Acyclic Model), and demonstrate the effectiveness of the method using artificially generated data and real-world data.

/pdf/a-linear-non-gaussian-acyclic-model-for-causal-discovery-1shddymhg0.pdf

A Linear Non-Gaussian Acyclic Model for Causal Discovery

The discovery of causal relationships between a set of observed variables is a fundamental problem in science. For continuous-valued data linear acyclic causal models with additive noise are often used because these models are well understood and there are well-known methods to fit them to data. In reality, of course, many causal relationships are more or less nonlinear, raising some doubts as to the applicability and usefulness of purely linear methods. In this contribution we show that the basic linear framework can be generalized to nonlinear models. In this extended framework, nonlinearities in the data-generating process are in fact a blessing rather than a curse, as they typically provide information on the underlying causal system and allow more aspects of the true data-generating mechanisms to be identified. In addition to theoretical results we show simulations and some simple real data experiments illustrating the identification power provided by nonlinearities.

/pdf/nonlinear-causal-discovery-with-additive-noise-models-18njg9ychz.pdf

Nonlinear causal discovery with additive noise models

Resting-state functional magnetic resonance imaging has become a powerful tool for the study of functional networks in the brain. Even “at rest,” the brain's different functional networks spontaneously fluctuate in their activity level; each network's spatial extent can therefore be mapped by finding temporal correlations between its different subregions. Current correlation-based approaches measure the average functional connectivity between regions, but this average is less meaningful for regions that are part of multiple networks; one ideally wants a network model that explicitly allows overlap, for example, allowing a region's activity pattern to reflect one network's activity some of the time, and another network's activity at other times. However, even those approaches that do allow overlap have often maximized mutual spatial independence, which may be suboptimal if distinct networks have significant overlap. In this work, we identify functionally distinct networks by virtue of their temporal independence, taking advantage of the additional temporal richness available via improvements in functional magnetic resonance imaging sampling rate. We identify multiple “temporal functional modes,” including several that subdivide the default-mode network (and the regions anticorrelated with it) into several functionally distinct, spatially overlapping, networks, each with its own pattern of correlations and anticorrelations. These functionally distinct modes of spontaneous brain activity are, in general, quite different from resting-state networks previously reported, and may have greater biological interpretability.

https://www.pnas.org/content/pnas/109/8/3131.full.pdf

Temporally-independent functional modes of spontaneous brain activity

Estimation of causal effects using linear non-Gaussian causal models with hidden variables

The estimation of linear causal models (also known as structural equation models) from data is a well-known problem which has received much attention in the past Most previous work has, however, made an explicit or implicit assumption of gaussianity, limiting the identifiability of the models We have recently shown (Shimizu et al, 2005; Hoyer et al, 2006) that for non-gaussian distributions the full causal model can be estimated in the no hidden variables case In this contribution, we discuss the estimation of the model when confounding latent variables are present Although in this case uniqueness is no longer guaranteed, there is at most a finite set of models which can fit the data We develop an algorithm for estimating this set, and describe numerical simulations which confirm the theoretical arguments and demonstrate the practical viability of the approach Full Matlab code is provided for all simulations

Estimation of linear, non-gaussian causal models in the presence of confounding latent variables.

Independent component analysis (ICA) has been extensively studied since it was originated in the field of signal processing However, almost all the researches have focused on estimation and paid little attention to testing In this paper, we discuss testing significance of mixing and demixing coefficients in ICA We propose test statistics to examine significance of these coefficients statistically A simulation experiment implies the good performance of our testing procedure A real example in psychometrics, which is a new application area of ICA, is also presented

/pdf/testing-significance-of-mixing-and-demixing-coefficients-in-1wvnywh91y.pdf

Testing significance of mixing and demixing coefficients in ICA

The estimation of linear causal models (also known as structural equation models) from data is a well-known problem which has received much attention in the past. Most previous work has, however, made an explicit or implicit assumption of gaussianity, limiting the identifiability of the models. We have recently shown (Shimizu et al, 2005; Hoyer et al, 2006) that for non-gaussian distributions the full causal model can be estimated in the no hidden variables case. In this contribution, we discuss the estimation of the model when confounding latent variables are present. Although in this case uniqueness is no longer guaranteed, there is at most a finite set of models which can fit the data. We develop an algorithm for estimating this set, and describe numerical simulations which confirm the theoretical arguments and demonstrate the practical viability of the approach. Full Matlab code is provided for all simulations.

Antti J. Kerminen

Papers

A Linear Non-Gaussian Acyclic Model for Causal Discovery

Estimation of causal effects using linear non-Gaussian causal models with hidden variables

Estimation of linear, non-gaussian causal models in the presence of confounding latent variables.

Testing significance of mixing and demixing coefficients in ICA

Estimation of linear, non-gaussian causal models in the presence of confounding latent variables