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.

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.

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

Identifying mechanisms of treatment effects and recovery in rehabilitation of schizophrenia: longitudinal analytic methods

The longitudinal dimension of schizophrenia and related severe mental illness is a key component of theoretical models of recovery. However, empirical longitudinal investigations have been underrepresented in the psychopathology of schizophrenia. Similarly, traditional approaches to longitudinal analysis of psychopathological data have had serious limitations. The utilization of modern longitudinal methods is necessary to capture the complexity of biopsychosocial models of treatment and recovery in schizophrenia. The present paper summarizes empirical data from traditional longitudinal research investigating recovery in symptoms, neurocognition, and social functioning. Studies conducted under treatment as usual conditions are compared to psychosocial intervention studies and potential treatment mechanisms of psychosocial interventions are discussed. Investigations of rehabilitation for schizophrenia using the longitudinal analytic strategies of growth curve and time series analysis are demonstrated. The respective advantages and disadvantages of these modern methods are highlighted. Their potential use for future research of treatment effects and recovery in schizophrenia is also discussed.