## 1 Introduction
In this regard, the amplitude of the EEG signal, and so of the EEG power spectrum, used often as a control feature of the passive BCI system for the mental states measurement, is dependent on many external variables, apart from the variations in user's mental states, for example, the impedance values of the EEG electrodes, and the specific positioning of the EEG sensors on the scalp [29]. Usually, good practice in a controlled setting is to keep impedance values below a certain threshold (e.g., 5 k\(\Omega\), [30]) and to position the EEG cap in a standardized way by following the standard 10-20 [31] (Figure 1). After placing the EEG cap on the user's head, the technician measures the distance between the Nasion and Inion, as well as the distance between the participant's left and right preauricular points. The vertex Cz is defined to be positioned on the cap at the midpoint of both distances. Consequently, the electrode Cz is aligned with the midpoint of the two distances. Once the alignment is deemed satisfactory, the EEG cap can be confirmed to be in the correct position [32]. All these procedural steps would not obviously be performed in a real setting,where the wearable EEG headset should instead be worn as soon as possible without wasting time for the upcoming operational activities. So, keeping the boundary conditions of the measuring system stable between one session and another could not be easily feasible. Anyhow, while impedance stability among repeated sessions seems to be a minor issue, since wearable sensors are often completely dry or wet with a saline solution, ensuring that the EEG headset is always worn in the same position between sessions seems to be a dubious assumption. Therefore, the change in sensors position along repeated sessions could compromise the effectiveness of the passive BCI system, inducing changes in the related control features (e.g., EEG spectrum amplitude), with the consequent decreasing in overall accuracy of mental states detection (e.g., mental workload). This variation in control features, known as \"covariate shift\", can undermine the stability and efficacy of the entire passive BCI system. Although our study primarily focuses on detecting covariate shifts resulting from changes in the position of the EEG headset, it is essential to note that there are various sources of possible shifts in real-world environments outside of laboratories [33]. Among these, the potential for variations in EEG recordings due to involuntary or voluntary subject movements during task execution is relevant. While this scenario is not the primary focus of our paper, we believe that our approach can still be applied to identify covariate shifts following such movements, provided they result in a lasting change in the headset's position. It is crucial to emphasize that currently, subject muscle movements that do not involve a physical displacement of the headset from its initial position are treated as artifacts and addressed via resizing or elimination. However, this shift in the EEG headset position can result in a variation in the EEG amplitude or a distortion of the signal recorded by the electrodes in the new position. Therefore, even if the participant is experiencing the same level of mental state (e.g., workload) across different recording sessions, control features (e.g., amplitude of EEG power spectrum) can significantly change. This variability, caused by the covariate shift phenomenon, introduces a challenging element in the generation of processing models that can detect and ideally fix the negative effect that covariate shift may induce in passive BCI systems accuracy. In the field of Artificial Intelligence, the covariate shift problem has been extensively investigated, as it poses a significant challenge across various domains [34; 35]. This work focuses on the domain of Brain-computer Interfaces, where covariate shift may play a notably significant role.