From Bilinear Regression to Inductive Matrix Completion: A Quasi-Bayesian Analysis.

In this paper, we study the problem of bilinear regression, a type of statistical modeling that deals with multiple variables and multiple responses. One of the main difficulties that arise in this problem is the presence of missing data in the response matrix, a problem known as inductive matrix completion. To address these issues, we propose a novel approach that combines elements of Bayesian statistics with a quasi-likelihood method. Our proposed method starts by addressing the problem of bilinear regression using a quasi-Bayesian approach. The quasi-likelihood method that we employ in this step allows us to handle the complex relationships between the variables in a more robust way. Next, we adapt our approach to the context of inductive matrix completion. We make use of a low-rankness assumption and leverage the powerful PAC-Bayes bound technique to provide statistical properties for our proposed estimators and for the quasi-posteriors. To compute the estimators, we propose a Langevin Monte Carlo method to obtain approximate solutions to the problem of inductive matrix completion in a computationally efficient manner. To demonstrate the effectiveness of our proposed methods, we conduct a series of numerical studies. These studies allow us to evaluate the performance of our estimators under different conditions and provide a clear illustration of the strengths and limitations of our approach.

Evaluation of diagnostic factors used to refer children with constipation for rectal biopsies.

PURPOSE: Children with constipation and suspected Hirschsprung's disease are referred for rectal biopsy. Since this is an invasive procedure, appropriate indications should be applied to minimize the number of "unnecessary" biopsies. METHODS: We reviewed all constipated children who underwent a rectal biopsy to diagnose a possible Hirschsprung's disease at a tertiary referral hospital over a 6-year period (2013-2018). We registered clinical and demographic factors in these children and conducted correlation and multivariate regression analysis to evaluate the relation between these factors and a diagnosis of Hirschsprung's disease. RESULTS: We identified 225 children, aged 0-17 years. In total, Hirschsprung's disease was diagnosed in only 49/225 (22%). Among the 49 children with Hirschsprung's disease, 29 (59%) were diagnosed in the neonatal period. Among girls, HD was confirmed in only 10/101 (10%) children, and only 1 of these 10 girls was older than 6 months at the time of the biopsy. The following factors correlated significantly with Hirschsprung's disease diagnosis in children older than 1 month: "male sex", "failure to thrive", "gross abdominal distention plus vomiting" and "fulfils the Rome 4 criteria for functional constipation". CONCLUSION: In children referred for rectal biopsy, the factors most indicative of Hirschsprung's disease were "male sex", "failure to thrive", "gross abdominal distention plus vomiting" and "fulfils the Rome 4 criteria for functional constipation". Notably, the prevalence of Hirschsprung's disease decreased with the increasing age of the children. Girls referred for a biopsy rarely had Hirschsprung's disease, especially those older than 1 month.

Boosting heritability: estimating the genetic component of phenotypic variation with multiple sample splitting.

BACKGROUND: Heritability is a central measure in genetics quantifying how much of the variability observed in a trait is attributable to genetic differences. Existing methods for estimating heritability are most often based on random-effect models, typically for computational reasons. The alternative of using a fixed-effect model has received much more limited attention in the literature. RESULTS: In this paper, we propose a generic strategy for heritability inference, termed as "boosting heritability", by combining the advantageous features of different recent methods to produce an estimate of the heritability with a high-dimensional linear model. Boosting heritability uses in particular a multiple sample splitting strategy which leads in general to a stable and accurate estimate. We use both simulated data and real antibiotic resistance data from a major human pathogen, Sptreptococcus pneumoniae, to demonstrate the attractive features of our inference strategy. CONCLUSIONS: Boosting is shown to offer a reliable and practically useful tool for inference about heritability.