Noise-cleaning the precision matrix of fMRI time series

by   Miguel Ibáñez-Berganza, et al.

We present a comparison between various algorithms of inference of covariance and precision matrices in small datasets of real vectors, of the typical length and dimension of human brain activity time series retrieved by functional Magnetic Resonance Imaging (fMRI). Assuming a Gaussian model underlying the neural activity, the problem consists in denoising the empirically observed matrices in order to obtain a better estimator of the true precision and covariance matrices. We consider several standard noise-cleaning algorithms and compare them on two types of datasets. The first type are time series of fMRI brain activity of human subjects at rest. The second type are synthetic time series sampled from a generative Gaussian model of which we can vary the fraction of dimensions per sample q = N/T and the strength of off-diagonal correlations. The reliability of each algorithm is assessed in terms of test-set likelihood and, in the case of synthetic data, of the distance from the true precision matrix. We observe that the so called Optimal Rotationally Invariant Estimator, based on Random Matrix Theory, leads to a significantly lower distance from the true precision matrix in synthetic data, and higher test likelihood in natural fMRI data. We propose a variant of the Optimal Rotationally Invariant Estimator in which one of its parameters is optimised by cross-validation. In the severe undersampling regime (large q) typical of fMRI series, it outperforms all the other estimators. We furthermore propose a simple algorithm based on an iterative likelihood gradient ascent, providing an accurate estimation for weakly correlated datasets.


page 1

page 2

page 3

page 4


Detecting changes in the covariance structure of functional time series with application to fMRI data

Functional magnetic resonance imaging (fMRI) data provides information c...

Joint Nonparametric Precision Matrix Estimation with Confounding

We consider the problem of precision matrix estimation where, due to ext...

Large Non-Stationary Noisy Covariance Matrices: A Cross-Validation Approach

We introduce a novel covariance estimator that exploits the heteroscedas...

Regularization of covariance matrices on Riemannian manifolds using linear systems

We propose an approach to use the state covariance of linear systems to ...

Locally Linear Embedding and fMRI feature selection in psychiatric classification

Background: Functional magnetic resonance imaging (fMRI) provides non-in...

Low Dimensional Embedding of fMRI datasets

We propose a novel method to embed a functional magnetic resonance imagi...

Biases in Inverse Ising Estimates of Near-Critical Behaviour

Inverse Ising inference allows pairwise interactions of complex binary s...

Please sign up or login with your details

Forgot password? Click here to reset