1,721,176 research outputs found
An invariance property of predictors in kernel-induced hypothesis spaces
No full textWe consider kernel-based learning methods for regression and analyze
what happens to the risk minimizer when new variables, statistically
independent of input and target variables, are added to the set of input
variables. This problem arises, for example, in the detection of causality
relations between two time series. We find that the risk minimizer
remains unchanged if we constrain the risk minimization to hypothesis
spaces induced by suitable kernel functions. We show that not all
kernel-induced hypothesis spaces enjoy this property. We present sufficient
conditions ensuring that the risk minimizer does not change and
show that they hold for inhomogeneous polynomial and gaussian radial
basis function kernels. We also provide examples of kernel-induced hypothesis
spaces whose risk minimizer changes if independent variables
are added as input.We consider kernel-based learning methods for regression and analyze what happens to the risk minimizer when new variables, statistically independent of input and target variables, are added to the set of input variables. This problem arises, for example, in the detection of causality relations between two time series. We find that the risk minimizer remains unchanged if we constrain the risk minimization to hypothesis spaces induced by suitable kernel functions. We show that not all kernel-induced hypothesis spaces enjoy this property. We present sufficient conditions ensuring that the risk minimizer does not change and show that they hold for inhomogeneous polynomial and gaussian radial basis function kernels. We also provide examples of kernel-induced hypothesis spaces whose risk minimizer changes if independent variables are added as input. © 2006 Massachusetts Institute of Technology
Finding an hidden common partition in duplex structure-function brain networks
No full textWe investigate the intricate relationship between human brain structure and function from a complex networks perspective. Indeed, several works in neuroimaging data analysis indicate the presence of robust partitions in both structural and functional networks, thus confirming that these two networks are interdependent. The function acts on the structure in virtue of the mechanism of neural plasticity, and conversely the structure acts on the function by means of topological constraints. In the attempt to understand this relation, we focus on groups of nodes making a comparison among structural and functional neural networks by exploiting their hierarchical modular organization. With respect to traditional methods in the community detection framework, we have developed a novel approach which allow us to figure out a common skeleton shared by structure and function in brain network. Using this, a new, and optimal common partition, can be extracted from duplex structure-function networks. Specifically, an algorithm, based on a probabilistic network model, has been developed to design an unsupervised multi-layer community detection. Hence, a numerical implementation has been rooted on the Expectation-Maximization technique (EM) to perform statistical inference on real brain data. We tested our algorithm on structural connectivity (SC) and resting state functional connectivity networks (rsFC) extracted from 12 healthy patients. Furthermore, we define a novel network measure called Cross-Modularity X, suitable to quantify the grade of similarity between two layers partitions. Finally, in order to validate our clustering algorithm, we use this quantity to make a comparison with classical single-layer community detection methods. As main result we obtain that the correlations between structural and functional networks are improved when the comparison has been made at the level of our extracted partition
Information-Theoretic Framework for Measuring Brain--Heart Causal Interactions in Healthy Subjects and Patients with Sleep Disorders
No full text
Decomposition of the transfer entropy: Partial conditioning and informative clustering
No full textWe propose a formal expansion of the transfer entropy to address the problem or partial conditioning evaluating information flow in multivariate datasets. This approach will then be adapted to put in evidence irreducible sets of variables which provide information for the future state of each assigned target. Multiplets characterized by an high value will be associated to informational circuits present in the system, with an informational character (synergetic or redundant) which can be associated to the sign of the contribution. These methods are then applied to the analysis of fMRI data
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