Graph Kernels

We present a unified framework to study graph kernels, special cases of which include the random walk (Gärtner et al., 2003; Borgwardt et al., 2005) and marginalized (Kashima et al., 2003, 2004; Mahé et al., 2004) graph kernels. Through reduction to a Sylvester equation we improve the time complexity of kernel computation between unlabeled graphs with n vertices from O(n^6) to O(n^3). We find a spectral decomposition approach even more efficient when computing entire kernel matrices. For labeled graphs we develop conjugate gradient and fixed-point methods that take O(dn^3) time per iteration, where d is the size of the label set. By extending the necessary linear algebra to Reproducing Kernel Hilbert Spaces (RKHS) we obtain the same result for d-dimensional edge kernels, and O(n^4) in the infinite-dimensional case; on sparse graphs these algorithms only take O(n^2) time per iteration in all cases. Experiments on graphs from bioinformatics and other application domains show that these techniques can speed up computation of the kernel by an order of magnitude or more. We also show that certain rational kernels (Cortes et al., 2002, 2003, 2004) when specialized to graphs reduce to our random walk graph kernel. Finally, we relate our framework to R-convolution kernels (Haussler, 1999) and provide a kernel that is close to the optimal assignment kernel of Fröhlich et al. (2006) yet provably positive semi-definite

Generalized Shortest Path Kernel on Graphs

We consider the problem of classifying graphs using graph kernels. We define a new graph kernel, called the generalized shortest path kernel, based on the number and length of shortest paths between nodes. For our example classification problem, we consider the task of classifying random graphs from two well-known families, by the number of clusters they contain. We verify empirically that the generalized shortest path kernel outperforms the original shortest path kernel on a number of datasets. We give a theoretical analysis for explaining our experimental results. In particular, we estimate distributions of the expected feature vectors for the shortest path kernel and the generalized shortest path kernel, and we show some evidence explaining why our graph kernel outperforms the shortest path kernel for our graph classification problem.Comment: Short version presented at Discovery Science 2015 in Banf

Preferential query answering in the semantic web with possibilistic networks

In this paper, we explore how ontological knowledge expressed via existential rules can be combined with possibilistic networks (i) to represent qualitative preferences along with domain knowledge, and (ii) to realize preference-based answering of conjunctive queries (CQs). We call these combinations ontological possibilistic networks (OP-nets). We define skyline and k-rank answers to CQs under preferences and provide complexity (including data tractability) results for deciding consistency and CQ skyline membership for OP-nets. We show that our formalism has a lower complexity than a similar existing formalism

Increased Belief Instability in Psychotic Disorders Predicts Treatment Response to Metacognitive Training

BACKGROUND AND HYPOTHESIS: In a complex world, gathering information and adjusting our beliefs about the world is of paramount importance. The literature suggests that patients with psychotic disorders display a tendency to draw early conclusions based on limited evidence, referred to as the jumping-to-conclusions bias, but few studies have examined the computational mechanisms underlying this and related belief-updating biases. Here, we employ a computational approach to understand the relationship between jumping-to-conclusions, psychotic disorders, and delusions. STUDY DESIGN: We modeled probabilistic reasoning of 261 patients with psychotic disorders and 56 healthy controls during an information sampling task-the fish task-with the Hierarchical Gaussian Filter. Subsequently, we examined the clinical utility of this computational approach by testing whether computational parameters, obtained from fitting the model to each individual's behavior, could predict treatment response to Metacognitive Training using machine learning. STUDY RESULTS: We observed differences in probabilistic reasoning between patients with psychotic disorders and healthy controls, participants with and without jumping-to-conclusions bias, but not between patients with low and high current delusions. The computational analysis suggested that belief instability was increased in patients with psychotic disorders. Jumping-to-conclusions was associated with both increased belief instability and greater prior uncertainty. Lastly, belief instability predicted treatment response to Metacognitive Training at the individual level. CONCLUSIONS: Our results point towards increased belief instability as a key computational mechanism underlying probabilistic reasoning in psychotic disorders. We provide a proof-of-concept that this computational approach may be useful to help identify suitable treatments for individual patients with psychotic disorders

Personalized Estimates of Brain Structural Variability in Individuals With Early Psychosis

Early psychosis in first-episode psychosis (FEP) and clinical high-risk (CHR) individuals has been associated with alterations in mean regional measures of brain morphology. Examination of variability in brain morphology could assist in quantifying the degree of brain structural heterogeneity in clinical relative to healthy control (HC) samples.; Structural magnetic resonance imaging data were obtained from CHR (n = 71), FEP (n = 72), and HC individuals (n = 55). Regional brain variability in cortical thickness (CT), surface area (SA), and subcortical volume (SV) was assessed with the coefficient of variation (CV). Furthermore, the person-based similarity index (PBSI) was employed to quantify the similarity of CT, SA, and SV profile of each individual to others within the same diagnostic group. Normative modeling of the PBSI-CT, PBSI-SA, and PBSI-SV was used to identify CHR and FEP individuals whose scores deviated markedly from those of the healthy individuals.; There was no effect of diagnosis on the CV for any regional measure (P > .38). CHR and FEP individuals differed significantly from the HC group in terms of PBSI-CT (P < .0001), PBSI-SA (P < .0001), and PBSI-SV (P = .01). In the clinical groups, normative modeling identified 32 (22%) individuals with deviant PBSI-CT, 12 (8.4%) with deviant PBSI-SA, and 21 (15%) with deviant PBSI-SV; differences of small effect size indicated that individuals with deviant PBSI scores had lower IQ and higher psychopathology.; Examination of brain structural variability in early psychosis indicated heterogeneity at the level of individual profiles and encourages further large-scale examination to identify individuals that deviate markedly from normative reference data

Acute effects of LSD on amygdala activity during processing of fearful stimuli in healthy subjects

Lysergic acid diethylamide (LSD) induces profound changes in various mental domains, including perception, self-awareness and emotions. We used functional magnetic resonance imaging (fMRI) to investigate the acute effects of LSD on the neural substrate of emotional processing in humans. Using a double-blind, randomised, cross-over study design, placebo or 100 μg LSD were orally administered to 20 healthy subjects before the fMRI scan, taking into account the subjective and pharmacological peak effects of LSD. The plasma levels of LSD were determined immediately before and after the scan. The study (including the a priori-defined study end point) was registered at ClinicalTrials.gov before study start (NCT02308969). The administration of LSD reduced reactivity of the left amygdala and the right medial prefrontal cortex relative to placebo during the presentation of fearful faces (P&lt;0.05, family-wise error). Notably, there was a significant negative correlation between LSD-induced amygdala response to fearful stimuli and the LSD-induced subjective drug effects (P&lt;0.05). These data suggest that acute administration of LSD modulates the engagement of brain regions that mediate emotional processing