In health, machine learning is increasingly common, yet neural network embedding (representation) learning is arguably under-utilized for physiological signals.   This inadequacy stands out in stark contrast to more traditional computer science domains, such as computer vision (CV), and natural language processing (NLP).   For physiological signals, learning feature embeddings is a natural solution to data insufficiency caused by patient privacy concerns -- rather than share data, researchers may share informative embedding models (i.e., representation models), which map patient data to an output embedding.    Here, we present the PHASE (PHysiologicAl Signal Embeddings) framework, which consists of three components: i) learning neural network embeddings of physiological signals, ii) predicting outcomes based on the learned embedding, and iii) interpreting the prediction results by estimating feature attributions in the "stacked" models (i.e., feature embedding model followed by prediction model).   PHASE is novel in three ways: 1) To our knowledge, PHASE is the first instance of transferal of neural networks to create physiological signal embeddings. 2) We present a tractable method to obtain feature attributions through stacked models.   We prove that our stacked model attributions can approximate Shapley values -- attributions known to have desirable properties -- for arbitrary sets of models. 3) PHASE was extensively tested in a cross-hospital setting including publicly available data.   In our experiments, we show that PHASE significantly outperforms alternative embeddings -- such as raw, exponential moving average/variance, and autoencoder -- currently in use. Furthermore, we provide evidence that transferring neural network embedding/representation learners between distinct hospitals still yields performant embeddings and offer recommendations when transference is ineffective. Representation learning (i.e., learning embeddings) BID14 has been applied to medical images and clinical text (Tajbakhsh et al., 2016; BID16 BID13 ) but has been under-explored for time series physiological signals in electronic health records. This paper introduces the PHASE (PHysiologicAl Signal Embeddings) framework to learn embeddings of physiological signals FIG1 ), which can be used for various prediction tasks FIG1 , and has been extensively tested in terms of its transferability using data from multiple hospitals ( FIG1 ). In addition, this paper introduces an interpretability method to compute per-sample feature attributions of the original features (i.e., not embeddings) for a prediction result in a tricky "stacked" model situation (i.e., embedding model followed by prediction model) ( FIG1 ).Based on computer vision (CV) and natural language processing (NLP), exemplars of representation learning, physiological signals are well suited to embeddings. In particular , CV and NLP share two notable traits with physiological signals. The first is consistency. For CV, the domain has consistent features: edges, colors, and other visual attributes. For NLP, the domain is a particular language with semantic relationships consistent across bodies of text. For sequential signals, physiological patterns are arguably consistent across individuals. The second attribute is complexity. Across these three domains , each particular domain is sufficiently complex such that learning embeddings is non-trivial. Together, consistency and complexity suggest that for a particular domain, every research group independently spends a significant time to learn embeddings that may ultimately be Figure 1: The PHASE framework, which consists of embedding learning, prediction, interpretation, and transference. The checkered patterns denote that a model is being trained in the corresponding stage, whereas solid colors denote fixed weights/models. The red side of the LSTM denotes the hidden layer we will use to generate embeddings. In (c), the size of the black circles on the left represent the feature attributions being assigned to the original input features. The signals and the outputs of the LSTMs are vectors. Multiple connections into a single XGB model are simply concatenated. More details on the experimental setup can be found in Sections 4.1 and 6.1.quite similar. In order to avoid this negative externality, NLP and CV have made great progress on standardizing their embeddings; in health, physiological signals are a natural next step.Furthermore, physiological signals have unique properties that make them arguably better suited to representation learning than traditional CV and NLP applications. First, physiological signals are typically generated in the health domain, which is constrained by patient privacy concerns. These concerns make sharing data between hospitals next to impossible; however, sharing models between hospitals is intuitively safer and generally accepted. Second, a key component to successful transfer learning is a community of researchers that work on related problems. According to Faust et al. (2018) , there were at least fifty-three research publications using deep learning methods for physiological signals in the past ten years. Additionally, we discuss particular examples of neural networks for physiological signals in Section 2.2. These varied applications of neural networks imply that there is a large community of machine learning research scientists working on physiological signals, a community that could one day work collaboratively to help patients by sharing models.Although embedding learning has many aforementioned advantages, it makes interpretation more difficult. Naive applications of existing interpretation methods ( Shrikumar et al., 2016; Sundararajan et al., 2017; do not work for models trained using learned embeddings, because they will assign attributions to the embeddings. Feature attributions assigned to embeddings will be meaningless , because the embeddings do not map to any particular input feature. Instead, each embedding is a complicated, potentially non-linear combination of the original raw physiological signals. In a health domain, inability to meaningfully interpret your model is unsatisfactory. Healthcare providers and patients alike generally want to know the reasoning behind predictions/diagnoses. Interpretability can enhance both scientific discovery as well as provide credibility to predictive models. In order to provide a principled methodology for mapping embedding attributions back into physiological signal attributions, we provide a proof that justifies PHASE's Shapley value framework in Section 3.3. This framework generalizes across arbitrary stacked models and currently encompasses neural network models (e.g., linear models, neural networks) and tree-based models (e.g., gradient boosting machines and random forests).In the following sections, we discuss previous related work (Section 2) and describe the PHASE framework (Section 3). In Section 4, we first evaluate how well our neural network embeddings make accurate predictions (Section 4.2.1). Second, we evaluate whether transferring these embedding learners still enables accurate predictions across three different hospitals separated by location and across hospital departments (Section 4.2.2). Lastly, we present a visualization of our methodology for providing Shapley value feature attributions through stacked models in Section 4.2.3. This paper presents PHASE, a new approach to machine learning with physiological signals based on transferring embedding learners. PHASE has potentially far-reaching impacts, because neural networks inherently create an embedding before the final output layer. As discussed in Section 2.2, there is a large body of research independently working on neural networks for physiological signals. PHASE offers a potential method of collaboration by analyzing partially supervised univariate networks as semi-private ways to share meaningful signals without sharing data sets.In the results section we offer several insights into transference of univariate LSTM embedding functions. First, closeness of upstream (LSTM) and downstream prediction tasks is indeed important for both predictive performance and transference. For performance, we found that predicting the minimum of the future five minutes was sufficient for the LSTMs to generate good embeddings. For transference, predicting the minimum of the next five minutes was sufficient to transfer across similar domains (operating room data from an academic medical center and a trauma center) when predicting hypoxemia. However when attempting to utilize a representation from Hospital P, we found that the difference between operating rooms and intensive care units was likely too large to provide good predictions. Two solutions to this include fine tuning the Min LSTM models as well as acknowledging the large amount of domain shift and training specific LSTM embedding models with a particular downstream prediction in mind. Last but not least, this paper introduced a way to obtain feature attributions for stacked models of neural networks and trees. By showing that Shapley values may be computed as the mean over single reference Shapley values, this model stacking framework generalizes to all models for which single reference Shapley values can be obtained, which was quantitatively verified in Section 4.2.3.We intend to release code pertinent to training the LSTM models, obtaining embeddings, predicting with XGB models, and model stacking feature attributions -submitted as a pull request to the SHAP github (https://github.com/slundberg/shap). Additionally, we intend to release our embedding models, which we primarily recommend for use in forecasting "hypo" predictions.In the direction of future work, it is important to carefully consider representation learning in health -particularly in light of model inversion attacks as discussed in Fredrikson et al. (2015) . To this end, future work in making precise statements about the privacy of models deserves attention, for which one potential avenue may be differential privacy (Dwork, 2008) . Other important areas to explore include extending these results to higher sampling frequencies. Our data was sampled once per minute, but higher resolution data may beget different neural network architectures. Lastly, further work may include quantifying the relationship between domain shifts in hospitals and PHASE and determining other relevant prediction tasks for which embeddings can be applied (e.g., "hyper" predictions, doctor action prediction, etc. Labels For hypoxemia, a particular time point t is labelled to be one if the minimum of the next five minutes is hypoxemic (min(SaO t+1:t+6 2 ) ≤ 92). All points where the current time step is currently hypoxemic are ignored (SaO t 2 ≤ 92). Additionally we ignore time points where the past ten minutes were all missing or the future five minutes were all missing. Hypocapnia and hypotension are only labelled for hospitals 0 and 1. Additionally, we have stricter label conditions. We labeled the current time point t to be one if (min(S t−10:t ) > T ) and the minimum of the next five minutes is "hypo" (min(S t+1:t+5 ) ≤ T ). We labeled the current time point t to be zero if (min(S t−10:t ) > T ) and the minimum of the next ten minutes is not "hypo" (min(S t+1:t+10 ) > T ). All other time points were not considered. For hypocapnia, the threshold T = 34 and the signal S is ETCO 2 . For hypotension the threshold is T = 59 and the signal S is NIBPM. Additionally we ignore time points where the past ten minutes were all missing or the future five minutes were all missing. As a result, we have different sample sizes for different prediction tasks (reported in TAB7 ). For Min predictions, the label is the value of min(S t+1:t+5 ), points without signal for in the future five minutes are ignored. For Auto predictions, the label is all the time points: S t−59:t . The sample sizes for Min and Auto are the same and are reported in Table 3. Table 3 : Sample sizes for the Min and Auto predictions for training the LSTM autoencoders. For the autoencoders we utilize the same data, without looking at the labels. We only utilize the 15 features above the line in both hospitals ( Figure 5 ) for training our models. (2000) , implemented in the Keras library with a Tensorflow back-end. We train our networks with either regression (Auto and Min embeddings) or classification (Hypox) objectives. For regression, we optimize using Adam with an MSE loss function. For classification we optimize using RMSProp with a binary cross-entropy loss function (additionally, we upsample to maintain balanced batches during training). Our model architectures consist of two hidden layers, each with 200 LSTM cells with dense connections between all layers. We found that important steps in training LSTM networks for our data are to impute missing values by the training mean, standardize data, and to randomize sample ordering prior to training (allowing us to sample data points in order without replacement). To prevent overfitting, we utilized dropouts between layers as well as recurrent dropouts for the LSTM nodes. Using a learning rate of 0.001 gave us the best final results. The LSTM models were run to convergence (until their validation accuracy did not improve for five rounds of batch stochastic gradient descent). In order to train these models, we utilize three GPUs (GeForce GTX 1080 Ti graphics cards). DISPLAYFORM0
Physiological signal embeddings for prediction performance and hospital transference with a general Shapley value interpretability method for stacked models.
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