# Application of Machine Learning to Express Measurement Uncertainty
## 1 Introduction  
The latest development of information and communication technologies in daily life enables more and more implementation of different devices and tools, their connectivity, and automatization of the work. Some of the essential characteristics of these systems are the generation of a large amount of data, various parameters' monitoring and prediction, and the possibility to mitigate resource usage. To achieve the best results, artificial intelligence is used during the development of such platforms [1], but the evaluation of the measurement uncertainty of the applied models is also required. The permanent increase in data processing power in modern devices and the availability of a vast amount of data via the internet and the internet of things (IoT) enabled the accelerated development of artificial intelligence (AI) methods. Given trends have actualized issues of AI hardware and algorithms' energy efficiency and the possibility of optimal application of AI in real-time (autonomous cars, mobile phones, unmannedaerial vehicles, etc.). In addition to energy efficiency, current topics in the literature deal with the possibility of sudden outages, wrong decisions, sabotage and fraud, and optimal maintenance techniques for intelligent agents. In simpler terms, researchers are trying to answer the increasingly frequently asked question: \"To what extent can intelligent agents be trusted?\" There is no simple answer to this question because it involves the evaluation of intelligent agents (AI methods) in terms of transparency, controllability, availability, usability, resilience, reliability, accuracy, security, privacy, quality, etc. [2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12]. AI and machine learning (ML) techniques are used to analyze complex data and take proper actions. In modern society, various sectors that play vital roles, such as smart grids, intelligent transportation, cyber-security, and communication technologies, are supported by big data analysis and the effective use of AI and ML techniques [13; 14; 15; 16]. The data collected from IoT (sensors, monitoring systems, financial records, health records, social media, etc.) can be inconsistent, incomplete, and noisy, leading to a decreased confidence in data analysis [17]. Controlling and quantifying ML models' uncertainty improves data analysis's reliability. It also enhances the belief in the model's decisions. An ML model consists of knowledge about model structure and training dataset. In the context of ML, the nature of uncertainty can be classified as epistemic (parameter uncertainty) and aleatoric (data uncertainty) [17; 18; 19; 20]. In the literature, uncertainty quantification concepts relevant to ML are grouped as frequentist inference and Bayesian inference. Frequentist inference deals with errors in parameters' estimates. Bayesian inference is used in traditional ML (Gaussian process regression (GPR), and GPR and physics-informed neural networks) and deep learning (Bayesian neural network and Bayesian physics informed neural network) [17; 21]. These concepts primarily deal with model uncertainty [22; 23; 24] (inverse propagation problem) over measurement uncertainty [25]. Recently, researchers have had increased interest in quantifying the uncertainty related to ML models [26; 27; 28]. In the systematic literature reviews of ML and deep learning applications in smart cities [11], and the COVID-19 epidemic [12], the accuracy parameter received the most attention from the reviewed articles (28.1% and 48.8%, respectively). The number of research publications related to the topic has grown from around 7000 in 2011 to about 24,000 in 2020 [17]. The contributions of the research presented in the paper are:  
* To address the abovementioned issues, a novel \"judgmental\" [21] approach to evaluating the measurement uncertainty of the ML model is proposed. The method is based on the analogy of an ML model and an actual measurement device.