[Paper Review] Active learning for level set estimation under cost-dependent input uncertainty.

I. Yu, Masayuki Karasuyama+2 more|arXiv (Cornell University)|Sep 13, 2019

Machine Learning and Algorithms25 references4 citations

TL;DR

This paper proposes a novel active learning algorithm for level set estimation under cost-dependent input uncertainty, where multiple inspection tools with varying costs and precision are available. By strategically selecting both the input location and inspection tool to minimize cost while maintaining accuracy, the method achieves theoretical convergence and demonstrates superior performance on synthetic and real-world datasets.

ABSTRACT

As part of a quality control process in manufacturing it is often necessary to test whether all parts of a product satisfy a required property, with as few inspections as possible. When multiple inspection apparatuses with different costs and precision exist, it is desirable that testing can be carried out cost-effectively by properly controlling the trade-off between the costs and the precision. In this paper, we formulate this as a level set estimation (LSE) problem under cost-dependent input uncertainty - LSE being a type of active learning for estimating the level set, i.e., the subset of the input space in which an unknown function value is greater or smaller than a pre-determined threshold. Then, we propose a new algorithm for LSE under cost-dependent input uncertainty with theoretical convergence guarantee. We demonstrate the effectiveness of the proposed algorithm by applying it to synthetic and real datasets.

Motivation & Objective

• To address the challenge of cost-effective quality control in manufacturing by minimizing inspections while maintaining precision.
• To model inspection processes where input uncertainty depends on the cost of the inspection tool used.
• To formulate the problem as active learning for level set estimation under cost-dependent uncertainty.
• To develop an algorithm that adaptively selects both input locations and inspection tools to optimize cost-precision trade-offs.
• To provide theoretical convergence guarantees for the proposed method in the context of level set estimation.

Proposed method

• The method formulates level set estimation as an active learning problem where the function of interest is unknown and must be learned through selective sampling.
• It introduces a cost-dependent uncertainty model where the precision of function evaluation depends on the chosen inspection tool, each with a distinct cost.
• The algorithm uses an acquisition function that balances exploration (uncertainty reduction) and exploitation (targeting the level set boundary) while considering tool costs.
• It dynamically selects both the input location and inspection tool at each step to minimize cumulative cost while improving estimation accuracy.
• Theoretical convergence is established by proving that the estimated level set converges to the true level set as the number of evaluations increases.
• The method is implemented using a Gaussian process surrogate to model the unknown function and quantify uncertainty.

Experimental results

Research questions

• RQ1 How can we efficiently estimate the level set of an unknown function when multiple inspection tools with different costs and precision are available?
• RQ2 What acquisition strategy optimally balances cost, uncertainty, and proximity to the level set boundary in active learning under cost-dependent uncertainty?
• RQ3 Can theoretical convergence be guaranteed for level set estimation when input uncertainty depends on the choice of inspection tool?
• RQ4 How does the proposed method compare to baseline approaches in terms of cost efficiency and estimation accuracy?
• RQ5 What is the impact of varying cost-precision trade-offs on the performance of level set estimation in real-world manufacturing scenarios?

Key findings

• The proposed algorithm achieves faster convergence to the true level set compared to baseline methods that do not account for cost-dependent uncertainty.
• By incorporating tool cost into the acquisition function, the method reduces total inspection cost while maintaining or improving estimation accuracy.
• Theoretical analysis confirms that the algorithm converges to the true level set as the number of evaluations increases, ensuring reliability.
• Empirical results on synthetic and real datasets show that the method effectively balances cost and precision, outperforming cost-agnostic approaches.
• The method demonstrates robustness across different cost-precision trade-offs, making it suitable for diverse manufacturing inspection scenarios.
• The integration of multiple inspection tools through a cost-aware acquisition function leads to significant cost savings without sacrificing estimation quality.