Geometric shrinkage priors for K\"ahlerian signal filters

We construct geometric shrinkage priors for K\"ahlerian signal filters. Based on the characteristics of K\"ahler manifolds, an efficient and robust algorithm for finding superharmonic priors which outperform the Jeffreys prior is introduced. Several ans\"atze for the Bayesian predictive priors are also suggested. In particular, the ans\"atze related to K\"ahler potential are geometrically intrinsic priors to the information manifold of which the geometry is derived from the potential. The implication of the algorithm to time series models is also provided.Comment: 10 pages, published versio

Application of K\"ahler manifold to signal processing and Bayesian inference

We review the information geometry of linear systems and its application to Bayesian inference, and the simplification available in the K\"ahler manifold case. We find conditions for the information geometry of linear systems to be K\"ahler, and the relation of the K\"ahler potential to information geometric quantities such as $\alpha$-divergence, information distance and the dual $\alpha$-connection structure. The K\"ahler structure simplifies the calculation of the metric tensor, connection, Ricci tensor and scalar curvature, and the $\alpha$-generalization of the geometric objects. The Laplace--Beltrami operator is also simplified in the K\"ahler geometry. One of the goals in information geometry is the construction of Bayesian priors outperforming the Jeffreys prior, which we use to demonstrate the utility of the K\"ahler structure.Comment: 8 pages, submitted to the Proceedings of MaxEnt 1

K\"ahlerian information geometry for signal processing

We prove the correspondence between the information geometry of a signal filter and a K\"ahler manifold. The information geometry of a minimum-phase linear system with a finite complex cepstrum norm is a K\"ahler manifold. The square of the complex cepstrum norm of the signal filter corresponds to the K\"ahler potential. The Hermitian structure of the K\"ahler manifold is explicitly emergent if and only if the impulse response function of the highest degree in $z$ is constant in model parameters. The K\"ahlerian information geometry takes advantage of more efficient calculation steps for the metric tensor and the Ricci tensor. Moreover, $\alpha$-generalization on the geometric tensors is linear in $\alpha$. It is also robust to find Bayesian predictive priors, such as superharmonic priors, because Laplace-Beltrami operators on K\"ahler manifolds are in much simpler forms than those of the non-K\"ahler manifolds. Several time series models are studied in the K\"ahlerian information geometry.Comment: 24 pages, published versio

Epidermal Growth Factor Gene Polymorphism and Risk of Hepatocellular Carcinoma: A Meta-Analysis

BACKGROUND: Hepatocarcinogenesis is a complex process that may be influenced by many factors, including polymorphism in the epidermal growth factor (EGF) gene. Previous work suggests an association between the EGF 61*A/G polymorphism (rs4444903) and susceptibility to hepatocellular carcinoma (HCC), but the results have been inconsistent. Therefore, we performed a meta-analysis of several studies covering a large population to address this controversy. METHODS: PubMed, EMBASE, Google Scholar and the Chinese National Knowledge Infrastructure databases were systematically searched to identify relevant studies. Data were abstracted independently by two reviewers. A meta-analysis was performed to examine the association between EGF 61*A/G polymorphism and susceptibility to HCC. Odds ratios (ORs) and 95% confidence intervals (95% CIs) were calculated. RESULTS: Eight studies were chosen in this meta-analysis, involving 1,304 HCC cases (1135 Chinese, 44 Caucasian and 125 mixed) and 2,613 controls (1638 Chinese, 77 Caucasian and 898 mixed). The EGF 61*G allele was significantly associated with increased risk of HCC based on allelic contrast (OR = 1.29, 95% CI = 1.16-1.44, p<0.001), homozygote comparison (OR = 1.79, 95% CI = 1.39-2.29, p<0.001) and a recessive genetic model (OR = 1.34, 95% CI = 1.16-1.54, p<0.001), while patients carrying the EGF 61*A/A genotype had significantly lower risk of HCC than those with the G/A or G/G genotype (A/A vs. G/A+G/G, OR = 0.66, 95% CI = 0.53-0.83, p<0.001). CONCLUSION: The 61*G polymorphism in EGF is a risk factor for hepatocarcinogenesis while the EGF 61*A allele is a protective factor. Further large and well-designed studies are needed to confirm this conclusion

Somatic mosaicism and common genetic variation contribute to the risk of very-early-onset inflammatory bowel disease

Abstract: Very-early-onset inflammatory bowel disease (VEO-IBD) is a heterogeneous phenotype associated with a spectrum of rare Mendelian disorders. Here, we perform whole-exome-sequencing and genome-wide genotyping in 145 patients (median age-at-diagnosis of 3.5 years), in whom no Mendelian disorders were clinically suspected. In five patients we detect a primary immunodeficiency or enteropathy, with clinical consequences (XIAP, CYBA, SH2D1A, PCSK1). We also present a case study of a VEO-IBD patient with a mosaic de novo, pathogenic allele in CYBB. The mutation is present in ~70% of phagocytes and sufficient to result in defective bacterial handling but not life-threatening infections. Finally, we show that VEO-IBD patients have, on average, higher IBD polygenic risk scores than population controls (99 patients and 18,780 controls; P < 4 × 10−10), and replicate this finding in an independent cohort of VEO-IBD cases and controls (117 patients and 2,603 controls; P < 5 × 10−10). This discovery indicates that a polygenic component operates in VEO-IBD pathogenesis

Fast Adaptive Identification of Stable Innovation Filters

The adaptive identification of the impulse response of an innovation filter is considered