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Polysomnography (PSG) is the standard test for diagnosing sleep apnea. However, the approach is obtrusive, time-consuming, and with limited access for patients in need of sleep apnea diagnosis. In recent years, there have been many attempts to search for an alternative device or approach that avoids the limitations of PSG. Pressure-sensitive mats (PSM) have proven to be able to detect central sleep apneas (CSA) and be a potential alternative for PSG. In the current study, we combine advanced machine learning approaches with a practical unobtrusive home monitoring device (PSM) to detect CSA events from data collected nocturnally and unattended. Two deep learning methods are implemented for the automatic detection of CSA events: a temporal convolutional network (TCN) and a bidirectional long short-term memory (BiLSTM) network. The deep learning models are compared to a classical machine learning approach (linear support vector machine, SVM) and a simple threshold-based algorithm. Considering the characteristics of each method, we choose strategies, including resampling and weighted cost-functions, to optimize the methods and to perform CSA detection as anomaly detection in an imbalanced data set. We evaluate the performance of all models on a database containing 7 days of data from 9 elderly patients. From the resulting 63 days, data from 7 patients (49 days) are devoted to training for optimizing hyperparameters, and data from 2 patients (14 days) are devoted to testing. Experimental results indicate that the best-performing model achieves an accuracy of 95.1% through training an BiLSTM network. Overall, the implemented deep learning methods achieve better performance than the conventional classification approach (SVM) and the simple threshold-based method, and show good potential for the use of PSM for practical unobtrusive monitoring of CSA.