# Machine Learning Regressors to Estimate Continuous Oxygen Uptakees (\(\dot{VO}_{2}\))
## 1 Introduction  
Oxygen consumption (\(\dot{VO}_{2}\)) estimation is a vital feature in exercise physiology and human performance assessment that offers significant insights into an individual's physiological response to exercise [1]. While traditional studies have focused on maximal oxygen consumption (\(\dot{VO}_{2 max}\)) to measure aerobic capacity at peak exertion, the potential for wearable device applications in continuous \(\dot{VO}_{2}\) estimation is substantial [2; 3; 4]. Continuous \(\dot{VO}_{2}\) monitoring, explicit in various studies [5; 6; 7; 8], provides real-time data on oxygen consumption, vital for matching total body oxygen consumption and delivery. This capability ensures optimal oxygen utilization, potentially improving overall performance and health outcomes. Additionally, it allows for the assessment of physical activity levels, personalized fitness tracking using heart rate-based algorithms, comparison of the effects of different exercises on oxygen uptake, and facilitation of personalized data-driven interventions for optimized health outcomes.  
These devices facilitate continuous monitoring of \(\dot{VO}_{2}\) levels, enabling ongoing adjustments in training intensity, duration, and recovery strategies. They optimize performance outcomes across various athletic endeavors. Significantly, wearable devices extend the utility of \(\dot{VO}_{2}\) estimation beyond exercise physiology to include personalized training optimization, fatigue management, and health risk assessment during physical activities [9; 10].  
Machine learning strategies are increasingly recognized for their efficiency in \(\dot{V}O_{2}\) estimation [2; 11; 12]. They allow the investigation of complex relationships between physiological parameters and \(\dot{V}O_{2}\) levels. This offers insights into individual exercise capacities and performance optimization strategies. By leveraging machine learning algorithms, this study aims to enhance the methodology for continuous \(\dot{V}O_{2}\) and \(\dot{V}O_{2 max}\) estimation for wearable devices, broadening our understanding of its applications in exercise physiology and human performance assessment.  
The field has primarily focused on incorporating \(\dot{V}O_{2 max}\) into machine learning models using various approaches, such as Graph Neural Networks (GNN) [13] and regression models [14]. These studies typically utilize demographic factors like age, weight, and height to predict \(\dot{V}O_{2 max}\)[12; 15]. However, our research takes a novel approach by considering additional physiological parameters, including heart rate, age, sex, weight, height, and categorically mapped \(\dot{V}O_{2}\) level. This comprehensive approach draws inspiration from the works by [PERSON] et al. [16], [PERSON] et al. [17], [PERSON] et al. [18], and [PERSON] et al. [19], which emphasize the multifactorial nature of \(\dot{V}O_{2 max}\) estimation. The study integrates these physiological variables into regression models to develop a continuous \(\dot{V}O_{2}\) and \(\dot{V}O_{2 max}\) estimation model. The studies utilizing PhysioNet [20] for \(\dot{V}O_{2 max}\) estimation encounter limitations impacting the accuracy and reliability of their findings. This includes challenges in measuring accurate \(\dot{V}O_{2 max}\) values differences between predicted and actual values. Specific equations and methods, such as the American College of Sports Medicine (ACSM) running equation [21], raise concerns about generalizability and methodological issues [22; 23]. Lastly, there are challenges specific to certain populations, such as patients with chronic conditions like chronic obstructive pulmonary disease (COPD) [24]. This approach represents a significant departure from traditional methods and holds promise for additional precise and personalized \(\dot{V}O_{2}\) predictions, with potential applications in sports science, healthcare, and fitness monitoring.