arXiv subjects

Yair Daon

Publications and source records attributed to Yair Daon.

4 recordsLinked to original sources

arXiv2021

DOPE: D-Optimal Pooling Experimental design with application for SARS-CoV-2 screening

Testing individuals for the presence of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the pathogen causing the coronavirus disease 2019 (COVID-19), is crucial for curtailing transmission chains. Moreover, rapidly testing many potentially infected individuals is often a limiting factor in controlling COVID-19 outbreaks. Hence, pooling strategies, wherein individuals are grouped and tested simultaneously, are employed. We present a novel pooling strategy that implements D-Optimal Pooling Experimental design (DOPE). DOPE defines optimal pooled tests as those maximizing the mutual information between data and infection states. We estimate said mutual information via Monte-Carlo sampling and employ a discrete optimization heuristic for maximizing it. DOPE outperforms common pooling strategies both in terms of lower error rates and fewer tests utilized. DOPE holds several additional advantages: it provides posterior distributions of the probability of infection, rather than only binary classification outcomes; it naturally incorporates prior information of infection probabilities and test error rates; and finally, it can be easily extended to include other, newly discovered information regarding COVID-19. Hence, we believe that implementation of Bayesian D-optimal experimental design holds a great promise for the efforts of combating COVID-19 and other future pandemics.

stat.AP↗

arXiv2020

Clusterization in D-optimal designs: the case against linearization

Estimation of parameters in physical processes often demands costly measurements, prompting the pursuit of an optimal measurement strategy. Finding such strategy is termed the problem of optimal experimental design, abbreviated as optimal design. Remarkably, optimal designs can yield tightly clustered measurement locations, leading researchers to fundamentally revise the design problem just to circumvent this issue. Some authors introduce error correlation among error terms that are initially independent, while others restrict measurement locations to a finite set of locations. While both approaches may prevent clusterization, they also fundamentally alter the optimal design problem. In this study, we consider Bayesian D-optimal designs, i.e.~designs that maximize the expected Kullback-Leibler divergence between posterior and prior. We propose an analytically tractable model for D-optimal designs over Hilbert spaces. In this framework, we make several key contributions: (a) We establish that measurement clusterization is a generic trait of D-optimal designs for linear inverse problems with independent Gaussian measurement errors and a Gaussian prior. (b) We prove that introducing correlations among measurement error terms mitigates clusterization. (c) We characterize D-optimal designs as reducing uncertainty across a subset of prior covariance eigenvectors. (d) We leverage this characterization to argue that measurement clusterization arises as a consequence of the pigeonhole principle: when more measurements are taken than there are locations where the select eigenvectors are large and others are small -- clusterization occurs. Finally, we use our analysis to argue against the use of Gaussian priors with linearized physical models when seeking a D-optimal design.

math.ST↗

arXiv2017

Mitigating the Influence of the Boundary on PDE-based Covariance Operators

Gaussian random fields over infinite-dimensional Hilbert spaces require the definition of appropriate covariance operators. The use of elliptic PDE operators to construct covariance operators allows to build on fast PDE solvers for manipulations with the resulting covariance and precision operators. However, PDE operators require a choice of boundary conditions, and this choice can have a strong and usually undesired influence on the Gaussian random field. We propose two techniques that allow to ameliorate these boundary effects for large-scale problems. The first approach combines the elliptic PDE operator with a Robin boundary condition, where a varying Robin coefficient is computed from an optimization problem. The second approach normalizes the pointwise variance by rescaling the covariance operator. These approaches can be used individually or can be combined. We study properties of these approaches, and discuss their computational complexity. The performance of our approaches is studied for random fields defined over simple and complex two- and three-dimensional domains.

stat.ME↗

arXiv2012

Bernoullicity of equilibrium measures on countable Markov shifts

We study the equilibrium behaviour of a two-sided topological Markov shift with a countable number of states. We assume the potential associated with this shift is Walters with finite first variation and that the shift is topologically transitive. We show the equilibrium measure of the system is Bernoulli up to a period. In the process we generalize several theorems on countable Markov shifts. We prove a variational principle and the uniqueness of equilibrium measures. A key step is to show that functions with Walters property on a two-sided shift are cohomologous to one-sided functions with the Walters property. Then we turn to show that functions with summable variations on two-sided CMS are cohomologous to one-sided functions, also with summable variations.

math.DS↗