AN EXPERIMENT DESIGN PARADIGM USING JOINT FEA-TURE SELECTION AND TASK OPTIMIZATION Anonymous

Abstract

This paper presents a subsampling-task paradigm for data-driven task-specific experiment design (ED) and a novel method in populationwide supervised feature selection (FS). Optimal ED, the choice of sampling points under constraints of limited acquisition-time, arises in a wide variety of scientific and engineering contexts. However the continuous optimization used in classical approaches depend on a-priori parameter choices and challenging non-convex optimization landscapes. This paper proposes to replace this strategy with a subsampling-task paradigm, analogous to populationwide supervised FS. In particular, we introduce JOFSTO, which performs JOint Feature Selection and Task Optimization. JOFSTO jointly optimizes two coupled networks: one for feature scoring, which provides the ED, the other for execution of a downstream task or process. Unlike most FS problems, e.g. selecting protein expressions for classification, ED problems typically select from highly correlated globally informative candidates rather than seeking a small number of highly informative features among many uninformative features. JOF-STO's construction efficiently identifies potentially correlated, but effective subsets and returns a trained task network. Changed: We demonstrate the approach using parameter estimation and mapping problems in clinically-relevant applications in quantitative MRI and in hyperspectral imaging. Results from simulations and empirical data show the subsampling-task paradigm strongly outperforms classical ED, and within our paradigm, JOFSTO outperforms state-of-the-art supervised FS techniques. JOFSTO extends immediately to wider image-based ED problems and other scenarios where the design must be specified globally across large numbers of acquisitions. Our code is available for reviewers Code (2022).

1. INTRODUCTION

Experiment design (ED) seeks an optimally informative sampling scheme within a budget of measurement time Antony (2003) . The problem arises across a wide range of scientific disciplines and applications wherever mathematical models are fitted to resal-world noisy measurements to estimate quantities that cannot be measured directly e.g. agriculture Gupta et al. (2015) , civil engineering Lye (2002), economics Jacquemet & L'Haridon (2019), microbiology Vanot & Sergent (2005) . Classical approaches Frieden (2004) ; Montgomery (2001) optimize the design to minimize the uncertainty of parameter values of a prespecified model, often derived from the Fisher information matrix. For any non-linear model, these approaches require a-priori specification of model parameter values to optimize the design for, which leads to circularity, as parameter values are by definition unknown at application stage. Moreover the optimization itself is usually cumbersome over a high-dimensional and highly non-convex space. For example, quantitative imaging techniques estimate and map model parameters pixel by pixel from multi-channel images. Multiple acquisition parameters often control the contrast in each channel. The ED challenge is to identify the combination of acquisition parameters that best inform the estimation of the model parameters, which vary substantially over the image. The popular MRI brain-imaging technique NODDI exemplifies the challenges: five acquisition parameters can vary for each of around 100 channels, thus the ED optimization is 500 dimensional. The standard acquisition protocol was designed by optimizing the Fisher-matrix for one specific combination of parameter values, although the aim of the technique is to highlight contrast in those parameters over the extent of the brain -the acquisition protocol is therefore by definition suboptimal.

