During routine sleep diagnostic procedure, sleep is broadly divided into three states: rapid eye movement (REM), non-REM (NREM) states, and wake, frequently named macro-sleep stages (MSS). In this study, we present a pioneering attempt for MSS detection using full night audio analysis. Our working hypothesis is that there might be differences in sound properties within each MSS due to breathing efforts (or snores) and body movements in bed. In this study, audio signals of 35 patients referred to a sleep laboratory were recorded and analyzed. An additional 178 subjects were used to train a probabilistic time-series model for MSS staging across the night. The audio-based system was validated on 20 out of the 35 subjects. System accuracy for estimating (detecting) epoch-by-epoch wake/REM/NREM states for a given subject is 74% (69% for wake, 54% for REM, and 79% NREM). Mean error (absolute difference) was 36±34 min for detecting total sleep time, 17±21 min for sleep latency, 5±5% for sleep efficiency, and 7±5% for REM percentage. These encouraging results indicate that audio-based analysis can provide a simple and comfortable alternative method for ambulatory evaluation of sleep and its disorders.

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This paper presents a method for building a preconditioner for a kernel ridge regression problem, where the preconditioner is not only effective in its ability to reduce the condition number substantially, but also efficient in its application in terms of computational cost and memory consumption. The suggested approach is based on randomized matrix decomposition methods, combined with the fast multipole method to achieve an algorithm that can process large datasets in complexity linear to the number of data points. In addition, a detailed theoretical analysis is provided, including an upper bound to the condition number. Finally, for Gaussian kernels, the analysis shows that the required rank for a desired condition number can be determined directly from the dataset itself without performing any analysis on the kernel matrix.

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