Sleep apnea (SA) is the most common respiratory sleep disorder, leading to some serious neurological and cardiovascular diseases if left untreated. The diagnosis of SA is traditionally made using Polysomnography (PSG). However, this method requires many electrodes and wires, as well as an expert to monitor the test. Several researchers have proposed instead using a single channel signal for SA diagnosis. Among these options, the ECG signal is one of the most physiologically relevant signals of SA occurrence, and one that can be easily recorded using a wearable device. However, existing ECG signal-based methods mainly use features (i.e. frequency domain, time domain, and other nonlinear features) acquired from ECG and its derived signals in order to construct the model. This requires researchers to have rich experience in ECG, which is not common. A convolutional neural network (CNN) is a kind of deep neural network that can automatically learn effective feature representation from training data and has been successfully applied in many fields. Meanwhile, most studies have not considered the impact of adjacent segments on SA detection. Therefore, in this study, we propose a modified LeNet-5 convolutional neural network with adjacent segments for SA detection. Our experimental results show that our proposed method is useful for SA detection, and achieves better or comparable results when compared with traditional machine learning methods.

Sleep apnea (SA) is a ubiquitous sleep-related respiratory disease. It can occur hundreds of times at night, and its long-term occurrences can lead to some serious cardiovascular and neurological diseases. Polysomnography (PSG) is a commonly used diagnostic device for SA. But it requires suspected patients to sleep in the lab for one to two nights and records about 16 signals through expert monitoring. The complex processes hinder the widespread implementation of PSG in public health applications. Recently, some researchers have proposed using a single-lead ECG signal for SA detection. These methods are based on the hypothesis that the SA relies only on the current ECG signal segment. However, SA has time dependence; that is, the SA of the ECG segment at the previous moment has an impact on the current SA diagnosis. In this study, we develop a time window artificial neural network that can take advantage of the time dependence between ECG signal segments and does not require any prior assumptions about the distribution of training data. By verifying on a real ECG signal dataset, the performance of our method has been significantly improved compared to traditional non-time window machine learning methods as well as previous works.

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Summary We propose a linearized maximum rank correlation estimator for the single index model. Unlike the existing maximum rank correlation and other rank-based methods, the proposed estimator has a closed-form expression, making it appealing in theory and computation. The proposed estimator is robust to outliers in the response and its construction does not need the knowledge of the unknown link function or the error distribution. Under mild conditions, it is shown to be consistent and asymptotically normal when the predictors satisfy the linearity of expectation assumption. A more general class of estimators is also studied. Inference procedures based on the plug-in rule or random weighting resampling are employed for variance estimation. The proposed method can be easily modified to accommodate censored data. It can also be extended to deal with high-dimensional data combined with a penalty function. Extensive simulation studies provide strong evidence that the proposed method works well in various practical situations. Its application is illustrated with the Beijing PM 2.5 dataset.

In this paper, we study the properties of robust nonparametric estimation using deep neural networks for regression models with heavy tailed error distributions. We establish the non-asymptotic error bounds for a class of robust nonparametric regression estimators using deep neural networks with ReLU activation under suitable smoothness conditions on the regression function and mild conditions on the error term. In particular, we only assume that the error distribution has a finite p-th moment with p greater than one. We also show that the deep robust regression estimators are able to circumvent the curse of dimensionality when the distribution of the predictor is supported on an approximate lower-dimensional set. An important feature of our error bound is that, for ReLU neural networks with network width and network size (number of parameters) no more than the order of the square of the dimensionality d of the predictor, our excess risk bounds depend sub-linearly on the d. Our assumption relaxes the exact manifold support assumption, which could be restrictive and unrealistic in practice. We also relax several crucial assumptions on the data distribution, the target regression function and the neural networks required in the recent literature. Our simulation studies demonstrate that the robust methods can significantly outperform the least squares method when the errors have heavy-tailed distributions and illustrate that the choice of loss function is important in the context of deep nonparametric regression.