6,075 research outputs found
Decorrelation of Neutral Vector Variables: Theory and Applications
In this paper, we propose novel strategies for neutral vector variable
decorrelation. Two fundamental invertible transformations, namely serial
nonlinear transformation and parallel nonlinear transformation, are proposed to
carry out the decorrelation. For a neutral vector variable, which is not
multivariate Gaussian distributed, the conventional principal component
analysis (PCA) cannot yield mutually independent scalar variables. With the two
proposed transformations, a highly negatively correlated neutral vector can be
transformed to a set of mutually independent scalar variables with the same
degrees of freedom. We also evaluate the decorrelation performances for the
vectors generated from a single Dirichlet distribution and a mixture of
Dirichlet distributions. The mutual independence is verified with the distance
correlation measurement. The advantages of the proposed decorrelation
strategies are intensively studied and demonstrated with synthesized data and
practical application evaluations
Tensor Analysis and Fusion of Multimodal Brain Images
Current high-throughput data acquisition technologies probe dynamical systems
with different imaging modalities, generating massive data sets at different
spatial and temporal resolutions posing challenging problems in multimodal data
fusion. A case in point is the attempt to parse out the brain structures and
networks that underpin human cognitive processes by analysis of different
neuroimaging modalities (functional MRI, EEG, NIRS etc.). We emphasize that the
multimodal, multi-scale nature of neuroimaging data is well reflected by a
multi-way (tensor) structure where the underlying processes can be summarized
by a relatively small number of components or "atoms". We introduce
Markov-Penrose diagrams - an integration of Bayesian DAG and tensor network
notation in order to analyze these models. These diagrams not only clarify
matrix and tensor EEG and fMRI time/frequency analysis and inverse problems,
but also help understand multimodal fusion via Multiway Partial Least Squares
and Coupled Matrix-Tensor Factorization. We show here, for the first time, that
Granger causal analysis of brain networks is a tensor regression problem, thus
allowing the atomic decomposition of brain networks. Analysis of EEG and fMRI
recordings shows the potential of the methods and suggests their use in other
scientific domains.Comment: 23 pages, 15 figures, submitted to Proceedings of the IEE
Towards a Multi-Subject Analysis of Neural Connectivity
Directed acyclic graphs (DAGs) and associated probability models are widely
used to model neural connectivity and communication channels. In many
experiments, data are collected from multiple subjects whose connectivities may
differ but are likely to share many features. In such circumstances it is
natural to leverage similarity between subjects to improve statistical
efficiency. The first exact algorithm for estimation of multiple related DAGs
was recently proposed by Oates et al. 2014; in this letter we present examples
and discuss implications of the methodology as applied to the analysis of fMRI
data from a multi-subject experiment. Elicitation of tuning parameters requires
care and we illustrate how this may proceed retrospectively based on technical
replicate data. In addition to joint learning of subject-specific connectivity,
we allow for heterogeneous collections of subjects and simultaneously estimate
relationships between the subjects themselves. This letter aims to highlight
the potential for exact estimation in the multi-subject setting.Comment: to appear in Neural Computation 27:1-2
Likelihood Non-Gaussianity in Large-Scale Structure Analyses
Standard present day large-scale structure (LSS) analyses make a major
assumption in their Bayesian parameter inference --- that the likelihood has a
Gaussian form. For summary statistics currently used in LSS, this assumption,
even if the underlying density field is Gaussian, cannot be correct in detail.
We investigate the impact of this assumption on two recent LSS analyses: the
Beutler et al. (2017) power spectrum multipole () analysis and the
Sinha et al. (2017) group multiplicity function () analysis. Using
non-parametric divergence estimators on mock catalogs originally constructed
for covariance matrix estimation, we identify significant non-Gaussianity in
both the and likelihoods. We then use Gaussian mixture density
estimation and Independent Component Analysis on the same mocks to construct
likelihood estimates that approximate the true likelihood better than the
Gaussian -likelihood. Using these likelihood estimates, we accurately
estimate the true posterior probability distribution of the Beutler et al.
(2017) and Sinha et al. (2017) parameters. Likelihood non-Gaussianity shifts
the constraint by , but otherwise, does not
significantly impact the overall parameter constraints of Beutler et al.
(2017). For the analysis, using the pseudo-likelihood significantly
underestimates the uncertainties and biases the constraints of Sinha et al.
(2017) halo occupation parameters. For and , the posteriors
are shifted by and and broadened by and
, respectively. The divergence and likelihood estimation methods we
present provide a straightforward framework for quantifying the impact of
likelihood non-Gaussianity and deriving more accurate parameter constraints.Comment: 33 pages, 7 figure
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