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Title: Uncertainty-aware Variational-Recurrent Imputation Network for Clinical Time Series

Paper content:
Electronic Health Records (EHR) comprise of longitudinal clinical observations portrayed with sparsity, irregularity, and high-dimensionality which become the major obstacles in drawing reliable downstream outcome.
Despite greatly numbers of imputation methods are being proposed to tackle these issues, most of the existing methods ignore correlated features or temporal dynamics and entirely put aside the uncertainty.
In particular, since the missing values estimates have the risk of being imprecise, it motivates us to pay attention to reliable and less certain information differently.
In this work, we propose a novel variational-recurrent imputation network (V-RIN), which unified imputation and prediction network, by taking into account the correlated features, temporal dynamics, and further utilizing the uncertainty to alleviate the risk of biased missing values estimates.
Specifically, we leverage the deep generative model to estimate the missing values based on the distribution among variables and a recurrent imputation network to exploit the temporal relations in conjunction with utilization of the uncertainty.
We validated the effectiveness of our proposed model with publicly available real-world EHR dataset, PhysioNet Challenge 2012, and compared the results with other state-of-the-art competing methods in the literature.
Electronic Health Records (EHR) store longitudinal data comprising of patient's clinical observations in the intensive care unit (ICU).
Despite the surge of interest in clinical research on EHR, it still holds diverse challenging issues to be tackled with, such as high-dimensionality, temporality, sparsity, irregularity, and bias (Cheng et al., 2016; Lipton et al., 2016; Yadav et al., 2018; Shukla & Marlin, 2019) .
Specifically, sequences of the medical events are recorded irregularly in terms of variables and time, due to various reasons such as lack of collection or documentation, or even recording fault (Wells et al., 2013; Cheng et al., 2016) .
In fact, since it carries essential information regarding the patient's health status, improper handling of missing values might draw an unintentional bias (Wells et al., 2013; Beaulieu-Jones et al., 2017) yielding unreliable downstream analysis and verdict.
Complete-case analysis is one approach to draw the clinical outcome by disregarding the missing values and relying only on the observed values.
However, excluding the missing data shows poor performance at high missing rates and also requires modeling separately for different dataset.
In fact, the missing values and their patterns are correlated with the target labels (Che et al., 2018) .
Thus, we resort to the imputation approach to improve clinical outcomes prediction as the downstream task.
There exist numerous proposed strategies in imputing missing values in the literature.
Brick & Kalton (1996) classified the imputation methods of being deterministic or stochastic in terms of the utilization of the randomness.
While deterministic methods such as mean (Little & Rubin, 1987) and median filling (Acuña & Rodriguez, 2004) produced only one possible value, it is desirable to generate samples by considering the data distribution, thus leading to stochastic-based imputation methods.
Moreover, since we are dealing with multivariate time series, an adequate imputation model should reflect several properties altogether, namely,
1) temporal relations,
2) correlations across variables, and additionally
3) offering a probabilistic interpretation for uncertainty estimation (Fortuin et al., 2019) .
Recently, the rise of the deep learning models offers potential solutions in accommodating aforementioned conditions.
Variational autoencoders (VAEs) (Kingma & Welling, 2014) and generative adversarial networks (GANs) (Goodfellow et al., 2014) exploited the latent distribution of highdimensional incomplete data and generated comparable data points as the approximation estimates for the missing or corrupted values (Nazabal et al., 2018; Luo et al., 2018; Jun et al., 2019) .
However, even though these models employed the stochastic approach in inferring and generating samples, they scarcely utilized the uncertainty.
In addition, such deep generative models are insufficient in estimating the missing values of multivariate time series, due to their nature of ignoring temporal relations between a span of time points.
Hence, it requires additional approaches to model the temporal dynamics, such as Gaussian process (Fortuin et al., 2019) or recurrent neural network (RNNs) (Luo et al., 2018; Jun et al., 2019) .
On the other hand, by the virtue of RNNs which have proved a remarkable performance in modeling the sequential data, we can estimate the complete data by taking into account the temporal characteristics.
GRU-D (Che et al., 2018) proposed a modified gated-recurrent unit (GRU) cell to model missing patterns in the form of masking vector and temporal delay.
Likewise, BRITS (Cao et al., 2018) modeled the temporal relations by bi-directional dynamics, and also considered features correlation by regression layers in estimating the missing values.
However, they didn't take into account the uncertainty in estimating the missing values.
That is, since the imputation estimates are not thoroughly accurate, we may introduce their fidelity score denoted by the uncertainty, which enhances the task performance by emphasizing the reliable or less uncertain information and vice versa (He, 2010; Gemmeke et al., 2010; Jun et al., 2019) .
In this work, we define our primary task as prediction of in-hospital mortality on EHR data.
However, since the data are characterized by sparse and irregularly-sampled, we devise an effective imputation model as the secondary problem but major concern in this work.
We propose a novel variational-recurrent imputation network (V-RIN), which unified imputation and prediction network for multivariate time series EHR data, governing both correlations among variables and temporal relations.
Specifically, given the sparse data, an inference network of VAE is employed to capture data distribution in the latent space.
From this, we employ a generative network to obtain the reconstructed data as the imputation estimates for the missing values as well as the uncertainty indicating the imputation fidelity score.
Then, we integrate the temporal and feature correlations into a combined vector and feed it into a novel uncertainty-aware GRU in the recurrent imputation network.
Finally, we obtain the mortality prediction as a clinical verdict from the complete imputed data.
In general, our main contributions in this paper are as follows:
• We estimate the missing values by utilizing deep generative model combined with recurrent imputation network to capture both features correlations and the temporal dynamics jointly, yielding the uncertainty.
• We effectively incorporate the uncertainty with the imputation estimates in our novel uncertainty-aware GRU cell for better prediction result.
• We evaluated the effectiveness of the proposed models by training the imputation and prediction networks jointly using the end-to-end manner, achieving the superior performance among other state-of-the-art competing methods on real-world multivariate time series EHR data.
In this paper, we proposed a novel unified framework comprising of imputation and prediction network for sparse high-dimensional multivariate time series.
It combined deep generative model with recurrent model to capture features correlations and temporal relations in estimating the missing values and yielding uncertainty.
We utilized the uncertainties as the fidelity of our estimation and incorporated them for clinical outcome prediction.
We evaluated the effectiveness of proposed model with PhysioNet 2012 Challenge dataset as the real-world EHR multivariate time series data, proving the superiority of our model in the in-mortality prediction task, compared to other state-of-the-art comparative models in the literature.

assistant: text: Our variational-recurrent imputation network (V-RIN) takes into account the correlated features, temporal dynamics, and further utilizes the uncertainty to alleviate the risk of biased missing values estimates.