arXiv subjects

Jonathan Ish-Horowicz

Publications and source records attributed to Jonathan Ish-Horowicz.

4 recordsLinked to original sources

arXiv2022

Modelling phylogeny in 16S rRNA gene sequencing datasets using string-based kernels

The bacterial microbiome is increasingly being recognised as a key factor in human health, driven in large part by datasets collected using 16S rRNA (ribosomal ribonucleic acid) gene sequencing, which enable cost-effective quantification of the composition of an individual's bacterial community. One of the defining characteristics of 16S rRNA datasets is the evolutionary relationships that exist between taxa (phylogeny). Here, we demonstrate the utility of modelling these phylogenetic relationships in two statistical tasks (the two sample test and host trait prediction) and propose a novel family of kernels for analysing microbiome datasets by leveraging string kernels from the natural language processing literature. We show via simulation studies that a kernel two-sample test using the proposed kernel is sensitive to the phylogenetic scale of the difference between the two populations. In a second set of simulations we also show how Gaussian process modelling with string kernels can infer the distribution of bacterial-host effects across the phylogenetic tree \new{and apply this approach to a real host-trait prediction task.} The results in the paper can be reproduced by running the code at https://github.com/jonathanishhorowicz/modelling_phylogeny_in_16srrna_using_string_kernels.

stat.AP↗

arXiv2021

Epidemia: An R Package for Semi-Mechanistic Bayesian Modelling of Infectious Diseases using Point Processes

This article introduces epidemia, an R package for Bayesian, regression-oriented modeling of infectious diseases. The implemented models define a likelihood for all observed data while also explicitly modeling transmission dynamics: an approach often termed as semi-mechanistic. Infections are propagated over time using renewal equations. This approach is inspired by self-exciting, continuous-time point processes such as the Hawkes process. A variety of inferential tasks can be performed using the package. Key epidemiological quantities, including reproduction numbers and latent infections, may be estimated within the framework. The models may be used to evaluate the determinants of changes in transmission rates, including the effects of control measures. Epidemic dynamics may be simulated either from a fitted model or a prior model; allowing for prior/posterior predictive checks, experimentation, and forecasting.

stat.CO↗

arXiv2020

Interpreting Deep Neural Networks Through Variable Importance

While the success of deep neural networks (DNNs) is well-established across a variety of domains, our ability to explain and interpret these methods is limited. Unlike previously proposed local methods which try to explain particular classification decisions, we focus on global interpretability and ask a universally applicable question: given a trained model, which features are the most important? In the context of neural networks, a feature is rarely important on its own, so our strategy is specifically designed to leverage partial covariance structures and incorporate variable dependence into feature ranking. Our methodological contributions in this paper are two-fold. First, we propose an effect size analogue for DNNs that is appropriate for applications with highly collinear predictors (ubiquitous in computer vision). Second, we extend the recently proposed "RelATive cEntrality" (RATE) measure (Crawford et al., 2019) to the Bayesian deep learning setting. RATE applies an information theoretic criterion to the posterior distribution of effect sizes to assess feature significance. We apply our framework to three broad application areas: computer vision, natural language processing, and social science.

stat.ML↗

arXiv2017

Fully discrete finite element data assimilation method for the heat equation

We consider a finite element discretization for the reconstruction of the final state of the heat equation, when the initial data is unknown, but additional data is given in a sub domain in the space time. For the discretization in space we consider standard continuous affine finite element approximation, and the time derivative is discretized using a backward differentiation. We regularize the discrete system by adding a penalty of the $H^1$-semi-norm of the initial data, scaled with the mesh-parameter. The analysis of the method uses techniques developed in E. Burman and L. Oksanen, Data assimilation for the heat equation using stabilized finite element methods, arXiv, 2016, combining discrete stability of the numerical method with sharp Carleman estimates for the physical problem, to derive optimal error estimates for the approximate solution. For the natural space time energy norm, away from $t=0$, the convergence is the same as for the classical problem with known initial data, but contrary to the classical case, we do not obtain faster convergence for the $L^2$-norm at the final time.

math.NA↗