Robustness against data loss with Algebraic Statistics

TL;DR

This paper introduces an algorithm that constructs nested robust experimental designs by systematically removing runs, enhancing resilience to data loss and aiding flexible experimental planning.

Contribution

The paper presents a novel algorithm using algebraic statistics to generate nested robust designs from any initial design, improving experimental robustness and flexibility.

Findings

Algorithm effectively creates nested robust designs.

Simulations demonstrate high robustness in practical scenarios.

Designs facilitate flexible experimental management.

Abstract

The paper describes an algorithm that, given an initial design $\mathcal{F}_n$ of size $n$ and a linear model with $p$ parameters, provides a sequence $\mathcal{F}_n \supset \ldots \supset \mathcal{F}_{n-k} \supset \ldots \supset \mathcal{F}_p$ of nested \emph{robust} designs. The sequence is obtained by the removal, one by one, of the runs of $\mathcal{F}_n$ till a $p$-run \emph{saturated} design $\mathcal{F}_p$ is obtained. The potential impact of the algorithm on real applications is high. The initial fraction $\mathcal{F}_n$ can be of any type and the output sequence can be used to organize the experimental activity. The experiments can start with the runs corresponding to $\mathcal{F}_p$ and continue adding one run after the other (from $\mathcal{F}_{n-k}$ to $\mathcal{F}_{n-k+1}$) till the initial design $\mathcal{F}_n$ is obtained. In this way, if for some unexpected reasons the experimental activity must be stopped before the end when only $n-k$ runs are completed, the corresponding $\mathcal{F}_{n-k}$ has a high value of robustness for $k \in \{1, \ldots, n-p\}$. The algorithm uses the circuit basis, a special representation of the kernel of a matrix with integer entries. The effectiveness of the algorithm is demonstrated through the use of simulations.