ANOVA kernels and RKHS of zero mean functions for model-based sensitivity analysis

Given a reproducing kernel Hilbert space (H,〈.,.〉)(H,〈.,.〉) of real-valued functions and a suitable measure μμ over the source space D⊂RD⊂R, we decompose HH as the sum of a subspace of centered functions for μμ and its orthogonal in HH. This decomposition leads to a special case of ANOVA kernels, for which the functional ANOVA representation of the best predictor can be elegantly derived, either in an interpolation or regularization framework. The proposed kernels appear to be particularly convenient for analyzing the effect of each (group of) variable(s) and computing sensitivity indices without recursivity.

Kernel density correlation based non-rigid point set matching for statistical model-based 2D/3D reconstruction

This paper presents a kernel density correlation based nonrigid point set matching method and shows its application in statistical model based 2D/3D reconstruction of a scaled, patient-specific model from an un-calibrated x-ray radiograph. In this method, both the reference point set and the floating point set are first represented using kernel density estimates. A correlation measure between these two kernel density estimates is then optimized to find a displacement field such that the floating point set is moved to the reference point set. Regularizations based on the overall deformation energy and the motion smoothness energy are used to constraint the displacement field for a robust point set matching. Incorporating this non-rigid point set matching method into a statistical model based 2D/3D reconstruction framework, we can reconstruct a scaled, patient-specific model from noisy edge points that are extracted directly from the x-ray radiograph by an edge detector. Our experiment conducted on datasets of two patients and six cadavers demonstrates a mean reconstruction error of 1.9 mm

Chow–Liu trees are sufficient predictive models for reproducing key features of functional networks of periictal EEG time-series

Seizure freedom in patients suffering from pharmacoresistant epilepsies is still not achieved in 20–30% of all cases. Hence, current therapies need to be improved, based on a more complete understanding of ictogenesis. In this respect, the analysis of functional networks derived from intracranial electroencephalographic (iEEG) data has recently become a standard tool. Functional networks however are purely descriptive models and thus are conceptually unable to predict fundamental features of iEEG time-series, e.g., in the context of therapeutical brain stimulation. In this paper we present some first steps towards overcoming the limitations of functional network analysis, by showing that its results are implied by a simple predictive model of time-sliced iEEG time-series. More specifically, we learn distinct graphical models (so called Chow–Liu (CL) trees) as models for the spatial dependencies between iEEG signals. Bayesian inference is then applied to the CL trees, allowing for an analytic derivation/prediction of functional networks, based on thresholding of the absolute value Pearson correlation coefficient (CC) matrix. Using various measures, the thus obtained networks are then compared to those which were derived in the classical way from the empirical CC-matrix. In the high threshold limit we find (a) an excellent agreement between the two networks and (b) key features of periictal networks as they have previously been reported in the literature. Apart from functional networks, both matrices are also compared element-wise, showing that the CL approach leads to a sparse representation, by setting small correlations to values close to zero while preserving the larger ones. Overall, this paper shows the validity of CL-trees as simple, spatially predictive models for periictal iEEG data. Moreover, we suggest straightforward generalizations of the CL-approach for modeling also the temporal features of iEEG signals.

Postmortem magnetic resonance imaging: Reproducing typical autopsy heart measurements

PURPOSE The aim of this study was to evaluate the utility of cardiac postmortem magnetic resonance (PMMR) to perform routine measurements of the ventricular wall thicknesses and the heart valves and to assess if imaging measurements are consistent with traditional autopsy measurements. METHODS In this retrospective study, 25 cases with cardiac PMMR and subsequent autopsy were included. The thicknesses of the myocardial walls as well as the circumferences of all heart valves were measured on cardiac PMMR and compared to autopsy measurements. Paired samples T-test and the Wilcoxon-Signed rank test, were used to compare autopsy and cardiac PMMR measurements. For exploring correlations, the Pearson's Correlation coefficient and the Spearman's Rho test were used. RESULTS Cardiac PMMR measurements of the aortic and pulmonary valve circumferences showed no significant differences from autopsy measurements. The mitral and tricuspid valves circumferences differed significantly from autopsy measurements. Left myocardial and right myocardial wall thickness also differed significantly from autopsy measurements. Left and right myocardial wall thickness, and tricuspid valve circumference measurements on cardiac PMMR and autopsy, correlated strongly and significantly. CONCLUSION Several PMMR measurements of cardiac parameters differ significantly from corresponding autopsy measurements. However, there is a strong correlation between cardiac PMMR measurements and autopsy measurements in the majority of these parameters. It is important to note that myocardial walls are thicker when measured in situ on cardiac PMMR than when measured at autopsy. Investigators using post-mortem MR should be aware of these differences in order to avoid false diagnoses of cardiac pathology based on cardiac PMMR.

KDENS: Stata module for univariate kernel density estimation

kdens produces univariate kernel density estimates and graphs the result. kdens supplements official Stata's kdensity. Important additions are: adaptive (i.e. variable bandwidth) kernel density estimation, several automatic bandwidth selectors including the Sheather-Jones plug-in estimator, pointwise variability bands and confidence intervals, boundary correction for variables with bounded domain, fast binned approximation estimation. Note that the moremata package, also available from SSC, is required.