MGP-AttTCN: An Interpretable Machine Learning Model for the Prediction of Sepsis
Authors: Margherita Rosnati
Vincent Fortuin
Venue:  (2020)
Keywords: time series analysis
interpretability
Gaussian Processes
attention neural networks

Abstract: With a mortality rate of 5.4 million lives worldwide every year and a healthcare cost of more than 16 billion dollars in the USA alone, sepsis is one of the leading causes of hospital mortality and an increasing concern in the ageing western world. Recently, medical and technological advances have helped re-define the illness criteria of this disease, which is otherwise poorly understood by the medical society. Together with the rise of widely accessible Electronic Health Records, the advances in data mining and complex nonlinear algorithms are a promising avenue for the early detection of sepsis. This work contributes to the research effort in the field of automated sepsis detection with an open-access labelling of the medical MIMIC-III data set. Moreover, we propose MGP-AttTCN: a joint multitask Gaussian Process and attention-based deep learning model to early predict the occurrence of sepsis in an interpretable manner. We show that our model outperforms the current state-of-the-art and present evidence that different labelling heuristics lead to discrepancies in task difficulty.

Under review as a conference paper at ICLR 2020
MGP-ATTTCN: AN INTERPRETABLE MACHINE LEARNING MODEL FOR THE PREDICTION OF SEPSIS
Anonymous authors Paper under double-bling review
Abstract
With mortality rate of 5.4 million lives worldwide every year and healthcare cost of more than 16 billion dollars the USA alone, sepsis is one the leading causes of hospital mortality and an increasing concern in the ageing western world. Recently, medical and technological advances have helped re-define the illness criteria of this disease, which is otherwise poorly understood by the medical society. Together with the rise of widely accessible Electronic Hcalth Records, the advances in data mining and complex nonlinear algorithms are a promising avenue for the early detection of sepsis. This work contributes to the research effort in the field of automated sepsis detection with an open-access labelling of the medical MIMIC-III data set. Moreover, we propose MGG-AtITCN: a joint multitask Gaussian Process and aitention-basee deep learning model early predict the occurrence of sepsis in an interpretable manner. We show that our model outperforms the current -o-th----h--rt and present evidence that different labelling heuristics Icad discrepancies in task difficulty.
INTRODUCTION
Every year, it is estimated that 31.5 million people worldwide contract sepsis. With a mortality rate of 17% in its benign state and 26% for its severe state (Fleischmann et al. 2016). sepsis is one of the leading causes of hospital mortality (Vincent et al. 2014)) costing the healthcare system more than 16 billion dollars in the USA alone (Angus et al. 2001). Studies demonstrated that early treatment has significant positive effect on the survival rate (Kumar et al.) [006]] Nguyen et al., (007). In particular, Castellanos- Ortega al.) (2010) demonstrated that each hour delay in treating a patient results in a 7.6% increase in mortality.
Current methods of screening, such Modified Early Warning System (MEWS) and Systemic Inflammatory Response Syndrome (SIRS) have been criticised for their lack of specificity, leading to low accuracies and high false alarm rates. In 2015, the Third International Consensus Definitions for Sepsis (Singer et al. 2016; Seymour et al.] 2016 Shankar-Hari et al., 2016) committee worked towards incorporating medical and technological advances into an up-to-date definition of sepsis, providing scientists with widely acknowledged illness criteria. Together with the rise of Electronic Health Records (EHR), the scientific community is now armed with both the data and labelling techniques to experiment with novel prediction methods (Islam et al. 2019 Henry et al. 2015 Ghosh et al, 2017| Calvert et al. 2016 Desautels et al.; (016)). which are already proving effective in increasing survival rate (Shimabukuro al. 2017) and promising in decreasing costs.
New models developed so far either relied on some interpretable yet simple prediction methods, such logistic regression (Calvert et al., 2016) and decision tree based classifiers (Mao al. 2018 Delahanty et al. 2019). or on effective yet black-box methods such as Recurrent Neural Networks (Futoma al. [011 2017b). Moreover, the results achieved by different authors are rarely comparable: although most use the MIMIC-III data set, the disparities in labelling rules result in highly variable data sets (eg. Raghu al. (2018) have 17,898 septic patients vs. 2,577 for Desautels et al. (2016)).
This work presents an attempt at reconciling interpretability and predictive performance on the sepsis prediction task and makes the following contributions:
Gold standard for labelling. We provide a gold standard for Sepsis-3 labelling implemented the MIMIC-II data set.

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TON,
YMGP
temporal data
MGP
TONp
static data
MGP ouiput concat. with broadcast static data
ettention over features
attention time
label prediction
Figure I: Proposed model architecture.
Novel interpretable model. We present an explainable and end-to-end trainable model based on Multitask Gaussian Processes and Attentive Neural Networks for the early prediction of sepsis.
Empirical evaluation. We assess our model on real-world medical data and report superior predictive performance and interpretability compared to previous methods.
An overview of our proposed method is shown in Figure
2 RELATED WORK
Medical time series diagnosis Multiple researchers have tackled the task of predicting sepsis and septic shock. Works on septic shock include exploration of survival models (Henry et al. 2015) and Hidden Markov Models (Ghosh et al.) 2017). However, these models rely on the assumption that a patient has already developed sepsis and focus on patterns of patients' further deterioration.
Other authors (Calvert al. 2016 Desautels et al. 2016 Mao et al. 2018 Delahanty et al. 2019) use linear models and decision trees on engineered features to predict sepsis onset, thus failing to capture temporal patterns. More recently, Kam & Kim (017)) and Raghu et al. (2018) employed recurrent neural networks to better capture time dependencies. Crucially. all these models rely on either averaging forward imputation of data points to create equidistant inputs. This transformation creates data artefacts and discards relevant uncertainty: conscious decision made by professionals implying an underlying belief of the patient state. Futoma ctt al. (2017b) and Moor et al. (2019) tackled this issue with Multitask Gaussian Processes (MGPs), however their models lack the interpretability necessary in the medical field.
the medical field, the absence of data is a
Irregularly sampled time series tion (Calvert et al. 2016). Lipton et al. (2016) utilise forward imputation coupled with a missingness indicator fed into black-box model. Although this method retains information about data presence, it is not clear how the information is later interpreted by the model and hence does not meet our transparency criteria. [Gassemm et al. 2015) use MGPs to fit sparse medical data, however they optimise their model for the data fit and use the parametrisation as input for classifier rather than optimising the model for a classification task. Both Fuuooma al., (2017a) and Moor al.] (2019) use MGPs with end-to-end training, although their temporal covariance function is shared across all variables. Finally, Futoma et al. 2b) uses MGPs with multiple time kernels in a similar fashion to model, although they infer the number of kernels from hyperparameter tuning rather than the data itself.
The most common solution missing values is forward imputa-
Attention was first introduced on the topic of machine transla- tion (Bahdanau et al. 2014). Since then, the concept has been used in natural language processing (Yang et al. [016]] Yu et al. 2018) and image analysis (Mnih et al. 2014, |Schlemper et al. 2019). In the same spirit, Qin et al. (2017) used attention mechanisms to improve the performance of a time series prediction model. Although their model easily explains the variable importance, its attention mechanism is based on Long Short Term Memory encodings of the time series. At any given time, such an encoding contains both the information of the current time point and all previous time points seen by the recurrent model. As such, the time domain attention does not allow for easy interpretation. More similar to our implementation is the RETAIN model (Choi et al., 2016), which generates its attention weights through reversed recurrent networks and applies them to simple embedding of the
Attention based neural networks
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time series. The model employs recurrent neural networks which slower to train and suffer from the vanishing gradient problem. Furthermore, the initial and final embeddings decrease the model's interpretablity. Other authors using Temporal Convolutional Network (TCN) based attention include Lin et al. 2019), who only attend to time.
METHOD
3.1 NOTATION
Let us first define some notation for the problem at hand. For each patient encounter p, several features &p.t. are recorded times k.k.i from admission, where {L..... M is the feature identifier. These features are often vital signs and laboratory results. As such, they are rarely observed the same times. Hence, we have sparse matrix representation observations
1p
yp,1,Ng
Mp.
Mp.,,
where N2 is the patient's observation period length. We also define static features Sp (5p. with features identifiers k E {M + 1,..., .M + Q}, corresponding to time- independent quantities, such as age, gender and first admission unit. Finally, we define sepsis labels dp E {0, 1}. Given the sparsity of the data, we can define the compact representation of all observed values:
Yp. 4p- = (ftpikk Up.ik hii.khieoo..... (e..
1/} (2)
The goal of the model is, for given set Yp. we will from now on drop the patient-speciff subscript from all notation, and the feature subscript from time notation, simplifying tp.k.s s to tç.
yy, Sp} predict the label l In order to remove clutter,
3.2 MULTITASK GAUSSIAN PROCESS (MGP)
Gaussian processes are commonly known for their ability to generate coherent function fits to a set of irregular samples, by modelling the data covariance. As they easily account for uncertainty and do not require homogeneously sampled data, Gaussian processes are the perfect candidate model to deal with relatively small amounts of medical data.
Following [onilla et al. (2008), we use a Multitask Gaussian Process (MGP) to capture feature correlation Lnd Marlin (2016)'s 's end-to-end training framework, in similar manner to Futoma al. 2017a). Given an hourly spaced time series [t]] [tJ (where 0 is the time of prediction), the MGP layer produces set of posterior predictions for each feature, which will then be fed into classification model.
We define patient- ieneeedeinde prior over the true values of (vike by (fa(t.)) such that
{brot ~ ((fu(tt)..
(3)
(fu(t)).u Σ (K IEL
(4)
where (KT* (1,, het are time point covariances varying in smoothness, (K?(k, k')he are feature covariances given smoothness level, independent of time, and L smoothness clusters. Over all variables and time points, the multivariate model has covariance
Σ Kt
Ktt 181
(5)
IEL
where D = diag(ag) are the noise terms associated to each feature and @ is the Kronecker product. The posterior over t' (t N₂ is a multivariate Gaussian with mean and covariance:
Kt
KPC (> kt & Ktt + D D
#
LEL
(6)
Σ
Σ 1eL
Kt
Kt't"
Kk & Ktt')
Σ KF & Ktt +D&
1)
Σ Kt & K('t) 1EL
let
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In order to approximate the posterior distribution, we then take Monte Carlo samples YMC from Y MGP ~ (N( E).
main feature clusters: vital signs (vitals) and laboratory results (labs). Vitals are noisier and sampled more often, whereas labs are more monotone and rarely sampled. As opposed to Futoma al. (2017b), we do not treat the number of clusters L as hyperparameters but set I. 2 and define
Note that there
(tt, exp 14 (21)
X
(OU) kemels with lengths A and A2, each representing a cluster smoothness. OU kernels are well suited to capture local variations and do not assume infinite differentiability as Squared Exponential kernels do. In our case, differentiablity implies a level of smoothness which does not apply to medical records and only introduces unnecessary bias. In addition, given the scarce availability of labs, all short lengthscales would be an ill fit to the data. We hence discarded kernels varying over lengthscales such as the Cauchy and the Rational Quadratic kernels. KP (k, k') are free-form covariance matrice that are learned by gradient descent.
as
To feed the MGP samples into the classifier, we fix the model time window to N -25 by either zero padding or truncating the beginning of the time series. We choose to do so at the beginning of the time series in order to align prediction times as the last step of the temporal classification model. Here, we also integrate the static variables by broadcasting them over each time poin
3.3 ATTENTION TIME CONVOLUTIONAL NETWORK (ATTTCN)
The concept of attention was born in machine translation (Bahdanau et al., 2014); given an input sentence embedding S [h1,... hiss} ). the attention mechanism produces weights {aj.... a.ss such that a} E [0, aj = 1, and a context vector c; = Σj a hy used to predict target word i. The weights a² can therefore be interpreted as the importance of the input sentence's jth word to produce the jth word of the translation.
More recently, Choi et al. (2016) have applied attention to clinical time series. Given a time series [x.....xy) C I2, the authors first create time-inneper indepennenn embedding of the data (VI.... Vrr C RT. They then use inversed recurrent neural networks (RNN) to create weights RTTxm where (r E [0. 1] and 3ig E [-1, 1], with softmax and tanh activations respectively. The context vectors then take the form = Σnラr ajB3 ④ Uj and are fed into multilayer perceptron with softmax activation to yield prediction.
R² and
The attention model we devised borrows some ideas from Choi et al. (016)). The interpolated data YиC (M++)) is directly fed into two temporal convolutional networks (TCNs) (Lea et al. 2017) and generates embeddings [Z1...., ZN] E (x++Q)) and z' [z'..... N e
RVX +Q)
TCNs are a class of neural networks composed of causal convolutions stacked into Residual Blocks. causal convolution is ID convolutional layer which only takes inputs from the past to generate its output, avoiding any information leakage from the future. Residual Blocks are made of two causal convolutional layers together with ReLU activation functions, dropout and L2 regularisations. The Residual Blocks also include an identity map from the input of the block added to the output. As we only use up to 12 layers, this last step omitted in our architecture. TCNs have shown to outperform RNNs (Bai et al. (2018)), are faster at training and do not suffer from vanishing gradients. Given the latter, inverting the time series similarly to Lea et al. (0177) also becomes an unnecessary step which we omit.
We generate the attention weights a and / as
æj,0 softmax(z; (z, X W Wa.0 + bo,0)
a₁,1 softmax(z) Wa.1 + ba.1)
(8)
By00 (zz x Wa,0 3.0 + bg.0)
B sigmoid(z), W9,1 g,11% + bg.1)
(9)
W W.,,, Wa,1 E MM++Q
b ba,1 E TR
(10)
W B,o, Wa,1 ((M+Q)((M+Q)
b b E M+Q
(11)
Appendix C.2 for more information on this design choice
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such that (au, a1l N and 3 [Su. 31] (
We then create two context vectors, one for each of negative and positive label predictions
Σ 3355 O YMC.J E [x E {0,
(12)
where YMC,j is broadcast to meet the dimensionality of J
We then predict the labels
M+Q
i softmax Σ
Ci.um
E 1]²
(13)
In our case, we are only interested in making predictions with the latest available data. We therefore only use Jusa to train the model. This of course can be easily modified to suit any specific use-case.
Since the MGP output is directly multiplied by weights c; the classification model can be interpreted as a scoring mechanism where each past point yмC,ij contributes 03,oßij,o to the time series being classified as positive, and Or,, 1 negative scores are then normalised to represent probabilities of the positive or negative labelling. As we design both a and /3 be non-negative, can hence directly look at the average a and B over Monte Carlo samples to see which time points and features contribute most strongly to the network's s positive or negative decision.
the time series being classified negative. The positive and
DATA
Sepsis is defined life-threatening organ dysfunction caused by dysregulated host response to infection (Singer et al. 2016). The latter is usually interpreted as the administration of antibiotics coupled with the culture of blood samples, generating suspicion of infection window, whereas the former is interpreted as two point increase in Sequential Organ Failure Assessment (SOFA) within such a suspected infection window. We make use of the MIMIC-II data set (Johnson et al. 2016) and encode the Sepsis-3 criteria following Johnson & Pollard (218)'s s code available on GitHub, Joowninnnoooonnn
with the help of Moor et al. 22019'ss code that the authors have generously provided.
One key difference between our assumptions and Moor et al. (019)'s 's is the handling of missing SOFA contributor values: if one or more SOFA contributors are missing, Moor et al. do not calculate the total score. On the other hand, a zero contribution. The latter heuristics is in line with the official Sepsis definition in Singer et al. (2016). In order to validate our results, carry out all experiments using both labelling techniques.
assume such contributor to be within healthy norm, implying
We proceed to extract times series of case and control patients for set of commonly recorded vitals, labs and static variables and normalise their values. Following Moor al.) (2019), in order to keep the data set length balanced, we match the time series lengths of control patients to those of case patients using the class balance ratio. In addition, the last zero to six hours of data, effectively creating early prediction patients and augmenting our data set. We remove excessively noisy or computationally intensive data and train the model over
create up seven copies of each time series and truncate
time onset
time step contribution sums to
MGP output
YMGP
static data (broadcasted)
2 channels:
positive negative labels
product: feature contribution
score per label (0, 1)
Figure 2: Interpretation of the different attention weights in model.
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Area under the ROC over time
Using Moor al. labels
Using labels
0.85
InSight MGP-TCN
InSight MGP-TCN
0.75
0.70
0.60
0.50
Time to onset.
Time to onset
Figure 3: Performance of different models. It can be seen that our proposed labels are harder to fit than the ones by Moor et al. (2019). Moreover, proposed model outperforms the baselines both label sets, especially for carlier prediction horizons.
different hyperparameters, randomly resampling an equal number of case and control patients to counteract the data set imbalance.
5 EXPERIMENTAL RESULTS
We compare our model's performance to the performance of the InSight algorithm (Calvert al.) 2016) and to the state-of-the-ee MGP-TCN algorithm (Moor et al., 2019). Figure shows the predictive performance the models for different time horizons.
COMPARISON BETWEEN DIFFERENT DATA LABELS
The first result is the difference performance of models applied the different labelling methods. The SOFA contributor assumption Moor et al. make has two main implications. Firstly, it considerably restricts the number of patients. Assuming that sicker patients receive more medical attention, the patients included are likely to be in worse conditions than the septic patients excluded and hence easier to classify. Secondly, it delays sepsis onset. For example, a patient having severe liver failure with few other recorded vitals, followed by overall collapse further in time will have septic onset at the time of its liver failure in our records, whereas it will only be considered septic at the time of the overall collapse in Moor et al. labels. On the other hand, the labels produce reflect the incomplete nature of medical data: even if only part of all the potentially relevant tests are carried out at any given time. doctor must be able to assess a patient's 's well-being and foresce potential complications. The difference in labels implies a discrepancy in task difficulty: Moor et al. labels present an easier learning problem, however they define more narrow use-case in real- wol-world scenarios.
Indeed, when assessing the performance the different models on the two different data labellings. it becomes evident that proposed labels are harder to fit. This means that predicting sepsis in realistic setting on the intensive care unit is probably much harder than previous work would suggest.
5.2 MODEL. PERFORMANCE
find that our MGP-AUTCN model has better performance when presented with patients further in time from sepsis onset. In the case of Moor et al./s labels the difference is clearly noticeable, whereas with our labels it is of lower statistical significance. With our labels, both MGP-TCN and AGT-AtTCN have stronger performance than InSight. The intuition behind this result is the robustness of the models to missing data: both MGP- PCN and MGP-AttTe account for the data uncertainty and hence have better performance lower resolution and more irregular data.

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for time covariance lenth 1.9
for time covariance lenth 64.4
diabp
meanbp
0.5
resprate
heartrate
spo2_ _ollppyllyyy
tempc
bicarbonate
crealinine
0.3
chloride
glucose
hemaloocrit
hemeg lbbin
platelet
0.1
potassium
pit
inr
sodium
-0.1
bun
wbc
ph_Bloodgas
magnesium
-0.2
Figure 4: Heatmaps the learned MGP covariance matrices between the data features for the two different smoothness clusters.
On Moor et a labels, the MGP-TCN model does not seem significantly outperform the InSight model, suggesting that those labels might be easy enough to not require particularly pronounced robustness to missing data. However, the additional attention of the proposed MGP-AttTO model does seem to gain a clearer advantage here than on our labels, presumably due to a more complete set of features that can be attended to.
5.3 MGP INTERPRETABILITY
Inspecting the learned covariances (Figure 4). we notice that the two OU lengthscales converged to represent clusters within the selected variables: shorter lengthscale (around two hours) represents noisy data, whereas a larger lengthscale (around 64 hours) represents smoother observations. In addition, the feature covariance matrix for the short lengthscale puts more emphasis on vitals, while the one for the long lengthscale puts more emphasis on labs, fitting our initial intuition that vitals vary more rapidly. Graphically, one can observe this by inspecting the diagonals on the covariance heatmaps.
a more granular level, the two covariance matrices also provide insights about the underlying variables. One for instance observe that the body temperature (tempe) has a larger variance than the systolic and diastolic blood pressure (sysbp, diabp), following the general clinical intuition. Moreover, we can observe correlations between different features, such negative correlation between temperature and heart rate, which also seems to coincide with the general medical expectation. These covariances then for instance be used by the model to extrapolate full function from single INR observation with an inverse correlation to the pulse oximetry observations (Fig. 5)
5.4 ATTENTION WEIGHTS
One important benefit of our model compared current approaches is its interpretability due the attention mechanism. Once the samples have been drawn, the weights a and /3 provide us with more information about the importance of different time points and features for the model's behaviour, The attention weights for an exemplary patient trajectory are depicted in Figure
Overall, the absolute values of are small for points further from the prediction time and increasingly larger closer to it. A good example of this behaviour is the fourth row in Figure 5 where feature importance increases in time. We can also see there, that different features can have opposing effects on the prediction. While the elevated heart rate close to the prediction time increases the likelihood of a sepsis prediction (first column, yellow weights), the lowered prothrombin values reduce this likelihood (third column, blue weights). Interestingly, the low prothrombin values not actually measured this example, but predicted by the MGP purely based on the other measured features and the learned covariances.

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Heart Rate
Pulse oximetry (SpO2) var.
Prothrombin time (INR) 17
2.5
-5
-2
-20
-15
10
5
20
-55
-10
5
-20
-15
-10
5
0.0
-2.5
-15
2.5
-5
-2
-2.5
-20
-15
-10
55
-20
-15
-10
-5
-20
-15
-10
-5
2.5
0.0
-2.5
-15
-15
-15
time to prod.
-10
var. 0
var. 5
var. 10
var. 15
var. 20
var. 25
var. 30
Figure 5: Visualization of the journey of an exemplary patient trajectory through our proposed model architecture. The raw features (row 1), measured at irregular time points, are interpolated by an MGP (row 2). Samples from the MGP posterior each feature on fixed, regularly-spaced time grid (row 3). These values are then attended to by the TCN (row 4), where positive attention weights are yellow and negative ones blue. Row 5 shows the attention weights separated by features (X-axis) and time point (y-axis).
then be aggregated into means and variances for
Finally, 3 IMC gives the individual score contribution of each feature at each time point. These weights are shown in the last row of the figure. generally larger in magnitude closer to the prediction time. Moreover, about half of the features have significant non-zero attention weights, while the others seem to not be important for the prediction in this example.
again be seen that the attention weights are
These visualizations could used by doctors to make an informed decision about whether or not to trust the prediction of the model for each given patient, thus facilitating the interpretability and accountability that is crucial in medical applications.
CONCLUSION
We have shown that current data sets for the early prediction of sepsis underestimate the true difficulty of the problem and proposed a new labelling for the MIMIC-III data set that corresponds more closely realistic intensive care setting. Moreover, we have proposed a new machine learning model, the MGP-AITTCN, which outperforms the state-of-the-art approaches on the easier labels from the literature as well as on our proposed harder labels. Additionally, our model provides an interpretable attention mechanism that would allow clinicians to make more informed decisions about trusting its predictions on a case-by-case basis.
Potential avenues for future work include more thorough discussion with clinicians potentially make our proposed labels even more representative the real-world task, and architectural im- provements. for instance by meta-learning the MGP prior (Fortuin & Rätsch 2019), amortizing the latent MGP inference for performance gains (Fortuin et al. 2019). or discretizing the latent space for improved interpretability (Fortuin et al. 2018).
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Alistair EW Johnson, Tom J Pollard, Lu Shen, Lehman Li-wei, Mengling Feng, Mohammad Ghassemi, Benjamin Moody, Peter Szolovits, Leo Anthony Celi, and Roger G Mark. Mimic-iii, freely accessible critical care database. Scientific data, 3: 3:160035, 2016.
Hye Jin Kam and Ha Young Kim. Learning representations for the early detection of sepsis with deep neural networks. Computers in biology and medicine, 89:248-255, 2017.
Anand Kumar, Daniel Roberts, Kenneth E Wood, Bruce Light, Joseph E. Parrillo, Satendra Sharma, Robert Suppes, Daniel Feinstein, Sergio Zanotti, Leo Taiberg, et al. Duration of hypotension before initiation effective antimicrobial therapy the critical determinant of survival human septic shock. Critical care medicine, 3496):159-1156, 2006.
Colin Lea, Michael D Flynn, Rene Vidal, Austin Reiter, and Gregory D Hager. Temporal convolutional networks for action segmentation and detection. In proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 156-165, 2017.
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Qingqing Mao, Melissa Jay, Jana L Hoffman, Jacob Calvert, Christopher Barton, David Shimabukuro, Lisa Shich, Uli Chettipally, Grant Fletcher, Yaniv Kerem, al. Multicentre validation of sepsis prediction algorithm using only vital sign data in the emergency department, general ward and icu. BMJ open, 8(1 783333, 2018
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Michael Moor, Max Horn, Bastian Rieck, Damian Roqueiro, and Karsten Borgwardt. Early recogni- tion of sepsis with gaussian process temporal convolutional networks and dynamic time warping. arXiv preprint 190.::1902.0165550 2019.
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Under review as a conference paper at ICLR 2020
APPENDIX A DATA PROCESSING
A.1 DATA LABELLING
Please refer to link omilted for anonymity for more details how we derived the MIMIC-III sepsis labels.
A.2 DATA EXTRACTION
Patient Inclusion We filter for patients admitted to Intensive Care Units (ICU) who are more than 14 years old and with valid records. Case patients are patients having sepsis onset within their ICU stay, whereas control patients have not developed sepsis nor have an ICD discharge code referring to sepsis. Starting with 58 976 patients, we find 14'071 control patients and 7'936 case patients using our labels, versus 1'797 cases using Moor et al. labels.
Feature extraction Reviewing sepsis related literature and commonly extracted laboratory and vital recordings, extracted all features which were reported at least once for more than 75% of the included population. The final 24 dynamic features are reported in Table 3 We also extracted static features age, gender and first ICU admission department.
Case-control matching As the goal is to predict sepsis prior onset, the cases data was extracted between ICU admission and sepsis onset. Note that sepsis onset happens early within ICU admission, with the median patient getting sick at 3.4 hours of admission. developing sepsis are more likely to recover completely, and do so in lengthier time frame. In addition, once they are close to discharge, their vitals and labs are within the norms. Hence, both the length and the values of the time series strong discriminatory factors which the classification. We hence carry out matching strategy similar to Moor et al. (2019): following the class imbalance ratio, we associate each control time series same length as the case from ICU admission. We then discard patients with less than 40 data points within the selected window, and for computational tractability truncate the first N,- 250 initial values of patients' time series in order to keep a maximum of 250 data points per patient.
the other hand, patients not
time series and truncate the control have the
Horizon augmentation As our goal is to predict sepsis early, we augment the data by creating new shorter time series. For each time series, we create six copies, where each copy represents a different horizon to onset. We then proceed to truncate the last one to six hours prior to onset from the time series copies. In order to keep data consistency, we once again discard time series with less than 40 observations. In Tables and we illustrate the data distribution per horizon.
Table 1: Augmented Dataset Description with Moor al. labels
Horizon to onset
N. of patients
N. of obs. per patient
Oh
15'
69.9 + 59.6
h
11'258
56.6 + 59.1
h
8'478
61.4 - 62.8
3 h
6'554
66.5 = 65.9
4 h
5'233
70.6 + 69.0
5 h
4'162
76.3 + 71.9
6h
3'390
81.9 = 74.3
Data split Finally split the data into training, validation and testing sets, respectively capturing 80%, 10% and 10% of the data. We then normalise the data by subtracting the training set mean and dividing by the training set standard deviation of each feature.
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Table Augmented Dataset Description with authors labels
Horizon to onset
N. of patients
N. of obs. per patient
0h
20'075
64.0 65.5
h
15'832
62.5 + 65.6
h
127080
66.1 67.2
3 h
9'441
69.7 = 68.1
4h
7'484
73.4 = 68.5
5h
6'007
77.1 = 68.2
6h
4'876
81.2 = 67.4
Table 3: List of dynamic features
Vitals
Labs
Sys. blood pressure
Bicarbonate
PTT
Dia. blood pressure
Creatinine
INR
Mean blood pressure
Chloride
PT
Resp. rate
Glucose
Sodium
Heart rate
Hematocrit
BUN
SpO2 pulse ox.
Hemoglobin
WBC
Temperature (C)
Lactate
Magnesium pH blood gas
Platelet
Potassium
APPENDIX B BASELINES
B. DATA PREPARATION
In order to benchmark MGP model, we build some baselines homogenising the data sampling. For each hour and variable, we take the average of the available observations. If given hour has no observations, hourly sampled time series for each patient. We then proceed to normalise the size of each patient matrix by setting a time window of observation N. For patients having more than N observations Np. we discard the first N N, observation; whereas for patients having less than N observations we pad the beginning of the matrix with zeros.
carry forward the average the previous hour. In this manner, we generate an
1p,1,ta
Up.1NN
Up.1.1 :
Up,I,NN
carry forward
(14)
Mp.
Mp.,,
Vp,M,1
Mp.M.N,
Up.INN-N No
Up.LN
if N 2 N
normalise
Up.MMN No
UpMMN
Up.1NN-N, N
Up.1.N
oth.
0 Up.M,NNN
M.
(15)
We choose to align the end of the time series as opposed to the beginning as the relative importance of time points is when a patient becomes sick rather when he is admitted the ICU.
As next step, we augment the data to focus on different time series in a similar manner than for irregularly sampled data. We create seven copies of each time series, for each copy we discard the last zero to six hours, then normalise the matrix as above. We hence generate dataset YBL (Y), N.M (1 ) where q represent all augmented the time series.
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B.2 INSIGHT
The InSight scoring model is one of the few machine learning algorithms to surpass the proof-of- concept stage with multiple research, economic and clinical trials (Calvert al., 2016 Desautels et al. 2016 Calvert et al. 2017, Mao et al. 2018). We therefore include as a base line to our model.
The key concept of the model to use few largely available vitals, build some handcrafted features and train a simple classification model.
Here an account of our interpretation of the author's method. The features extracted based six consecutive hour window. For each six hour window, we extract each variable's 's mean M, and difference D; (last observation minus first observation) over the window. We also extract variables pairs correlation Dij and triplet correlation Disks where i, j. k are observed variables. We interpret the latter as a relaxation of Pearson correlation: if the correlation between two variables is
[ px) -y
PXY
(16)
oxoY
then we define the triplet correlation as
PXYZ E[(X - -x) pY) uz)]
(17)
σxoyoz
We then classify the difference and correlations as either positive, negligible or negative using their distribution quantiles over every patient and six hour window observed. Note that given the high level of data missingness, many variables calculated by forward imputation and hence have variance over six hours. To adjust for the high number of zero correlations, we calcualte the quantiles of non-zero correlations and define:
f
if D; n" (2/3) D <1
D
(18)
0
otherwise
where q is the adjusted quantile function. We proceed similar manner for the correlations and triplet correlations.
In order to keep the results comparable the AtTCN fixed window N, extract N (6 six consecutive hour window and vectorise the resulting features, generating in total
(N-5) 5) (2 M
(
MM
M
Aeeaures
(19)
3
features per patient.
Although the original paper does not specify which classification method the authors employ, we derive by their description of dimensionless score that the method is a logistic regression.
APPENDIX C MODEL DETAILS
C.1 TCN PROPERTIES
TCNs are class of neural networks composed of causal convolutions stacked into Residual Blocks. causal convolution ID convolutional layer which only takes inputs from the past to generate its output, avoiding any data leakage. Residual Blocks are made of two causal convolutional layers together with ReLU activation functions, dropout and L.2 regularisations.
C.2 STATIC VARIABLES
In our model implementation. we decide to integrate the static variables to the MGP output. Another choice we considered to integrate the data to the output of the attention model. Once the weights a and (3 have been created, introduce a bias term
M+Q Σ m
i, = Softmax
Ci,m + beratic
E [0, 1]2
(20)
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Table 4: Hyperparameter search
Hyperparameter
Random Search
min
max
MGP Monte Carlo samples
4
20
TCN kernel size
2
6
TCN number of Residual Blocks
2
12
TCN number of hidden layers
10
55
TCN dropout rate
0
0.99
TCN L2 regularisation
0
250
Table 5: Area under the ROC curve for Moor al. labels
Time to onset
InSight
MGP-TCN
MGP-AUTCN
6h
66.4 + 0.7
65.0 2.2
67.0 + 4.3
5h
65.9 + 1.5
66.4 2.8
73.2 + 2.7
4h
64.7 0.6
2.9
73.4
3h
17.01.000
2..6
72.2 + 3.6
2h
67.7 + 1.2
6..4
73,9 + 2.5
1h
69.5 0.8
2.0
76.8 + 1.7
Oh
76.4 0.9
81.4 0.9
80.5 + 0.5
where Dstatic is generated by the output of two layers multilayer perceptron applied the static data. Although this solution is computationally lighter and provides more elegant interpretation, it does not allow the attention mechanism utilise the information about the patient's 's static state when making decision about its vitals and labs values. For the scope of this paper, we hence decided for earlier static data integration.
C.3 PARAMETER HYPERSEARCII AND TRAINING
As the datasets are highly unbalanced, carry the case set to have the same size as the control set. In addition, at each iteration we sample equally the number of cases and controls, then feed shuffled version into the model. In this manner the model will see equal number of controls and cases and will not become biased towards zero labels. This procedure does not happen for either of the validations and test sets, the results would not compare to real life settings.
oversampling: randomly resample
For both our core model MGP-AtITCN and all baselines, in order to select the best possible hyperpa- rameters, we performed hyperparameter random search, as described in Table 4
C.4 NUMERICAL RESULTS
The results are shown Tables and
Table 6: Area under the ROC curve for our labels
Time to onset
InSight
MGP-TCN
MGP-ARTCN
6h
55.5 + 2.7
60,9 +
0.9
63.6 + 0.9
5h
55.5 + 1.4
62.4
63.9 + 1.6
4h
55.5 + 1.6
0.9
64.1 1.2
3h
55.9 + 1.3
6..6
63.6 0.9
2h
57.3 + 1.5
0.9
63.6
lh
58.8 + 1.8
6.95
6..7
Oh
61.4 1.1
67.0 + 0.6
66.5
15


Reviews:
[{"review_id": "r1ge0ZnWcS", "reviewer": "AnonReviewer3", "summary": "", "questions": "", "limitations": "", "rating": 1, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "The authors present a Sepsis-3 compliant labeling of the MIMIC-III dataset and a sepsis-prediction model largely based on MGP-TCN that uses attention mechanisms to enable explainability.\n\nIt is not entirely clear what the authors mean by MC samples from Y_MGP, are these simply samples from the posterior in (6)?\n\nIf z_j and z'_j are M-dimensional, how does one apply (8) and (9) for W_{\\alpha,0}, W_{\\alpha,1} being (M+Q)-dimensional or W_{\\beta,0}, W_{\\beta,1} being matrices?\n\nThe labelling of the data, largely following Johnson & Pollard (2018) and Moor et al (2019), is only different to Moor et al (2019) in the assumption that in the SOFA calculation missing values have zero contribution. Unless the authors provide evidence that this is reasonable, it is not necessarily clear whether labels resulting from the proposed scheme will be biased and affected by differences in clinical practice at different sites or data collection practices. That being said, it is not clear whether the proposed labeling is a contribution from the work.\n\nThe fact that the proposed labels are harder to fit does not imply that the proposed labels are better or more reasonable. This provided that is difficult to know (without ground truth) whether the difficulty originates from a broader use case (not as easy as Moor et al (2019)) or labels being noisy, imperfect proxies for sepsis diagnosis. I understand the author's motivation for doing it, however, their approach is not sufficiently justified. I also agree that predicting sepsis in a realistic setting is harder than suggested in prior work, however, the proposed labeling does not necessarily yields evidence of that being the case.\n\nThe interpretation of the covariance matrices of the MGP is interesting, though not surprising considering that covariates in green are measured regularly while blue covariates are ordered sparingly.\n\nFigure 5 is interesting, though raises questions about of interpretability of the model. How should unobserved covariates be interpreted (INR in Figure 5)?\n\nIn summary, the contributions of the present work are not sufficiently justified (labeling), the novelty of the proposed model is minor, relative to MGP-TCN, and the added value of the attention mechanism as a means to interpret predictions in terms of the journey of a patient is not clear.\n\nMinor:\n- Figure 1 needs a better caption. Being in page 2 makes it very difficult to understand.\n- TCN is used before being defined.\n- In (1) it should be t_{p,i,k} not t_{p,k,i}", "extra_scores": {"experience_assessment": "I have published one or two papers in this area.", "review_assessment:_thoroughness_in_paper_reading": "I read the paper thoroughly.", "review_assessment:_checking_correctness_of_experiments": "I carefully checked the experiments.", "review_assessment:_checking_correctness_of_derivations_and_theory": "I carefully checked the derivations and theory."}, "extra_text": {}}, {"review_id": "H1gqUrzD5H", "reviewer": "AnonReviewer2", "summary": "", "questions": "", "limitations": "", "rating": 8, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "The authors consider a combination of an Gaussian model and neural network learned together to be able to find specific Gaussian features that would predict sepsis in a more intuitive, interpretable way for a medical experts. Also, they have provided a new labelling for the MIMIC-III dataset, which is of great value.\n\nUsually constraining the feature space reduces the accuracy, as one tends to miss important features. However, here, one is using a Gaussian model to generate a feature space that is easier to train with a neural network (by filling the sparse data by Gaussian process interpolation) but also augment the dataset.\n\nThe author report that his improves prediction. Unfortunately, I did not find tables of solutions where one could the actual impact. The authors should include a numerical table of their result comparison results.  Now there is only a narrative in section 5.3 and an image showing that at different covariance times, different feature groups starts to interpret the results. Obviously, a question arises if the model would perform even better with a combination of covariance times, or is there some covariance time range that is missing that would improve the result even more.\n\nThe Gaussian model creates smooth interpolation of data spaces and also forces the training to look at corresponding smoothened features - that are very good for human eyes. However, there are situations (like the detecting heart beat from a video from a head moving with a recoil from the blood rushing to the brain) in where the signal is too weak for human to see, but is definitely there for a computer.  I would state that this as interpretable,  as an explicitly visible signal would be. Even  shorter time constant signal might be valuable as well, but it would not be visible here...  It seems that in sepsis, it was a good idea, as it improves the result compared to the situation of not using the Gaussian model. \n\nOne has to be careful to state that this would address the interpretability of the results. Gaussian process by itself is not giving understanding nor interpretability as it is too general. But it can make the provided solution \"teachable\" to a human expert by showing what visible features one can track.\n\nCompare this to a situation where one is using physical model to regularize detection. It has the analogous two model structure like the one in the manuscript. In https://xbpeng.github.io/projects/SFV/index.html the authors of the paper report that that one can achieve a better pose estimation by constraining the pose to only those that are achievable by a physical model based policy trained by reinforcement learning. This one is able to \"interpret\" the pose.\n\nAs a summary, the authors have done solid and valuable work in improving the accuracy detection. They should have a more formal way to present the results and baseline comparisions as tables. On the explainability and interpretability, there remains a lot of interpretations and one has lots of explaining to do, even after this manuscript.\n\n\n\n\n", "extra_scores": {"experience_assessment": "I have read many papers in this area.", "review_assessment:_thoroughness_in_paper_reading": "I read the paper thoroughly.", "review_assessment:_checking_correctness_of_experiments": "I assessed the sensibility of the experiments.", "review_assessment:_checking_correctness_of_derivations_and_theory": "I assessed the sensibility of the derivations and theory."}, "extra_text": {}}, {"review_id": "BylDbvpdtB", "reviewer": "AnonReviewer1", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "I've read the rebuttal and I'd like to keep my score as is. My main concern is the questionable role of attention in making the model more interpretable (which is the main contribution of the paper).\n\n###########################\n\nThe paper proposes a new model for automated sepsis detection using multitask GP and attention-based GP. The sepsis detection problem is of paramount importance in the clinical domain and the authors rightly emphasized that point. Also the paper tries to combine interpretability with prediction accuracy by using attention mechanism. \n\nThe paper is generally well written and well motivated; however, in terms of technical novelty and empirical evidence the paper can be further improved. \n\nThe MGP-AttnTCN model is mostly a minor modification of the model proposed by Moor et al. 2019 and has the additional attention element to be more interpretable. Unfortunately, it’s not easy for an ICLR reader without any medical background to evaluate the validity of the interpretability results provided in the paper. Furthermore, the recent works in NLP have agued against the value of attention for interpretability (see for instance “Attention is not Explanation” by Jain & Wallace 2019). That said, I believe the paper is probably a better fit for a machine learning in healthcare venue (such as MLHC). \n\nIn terms of empirical evidence of the prediction accuracy the paper only compares with Moor et al 2019 (which does not show a significant improvement in the realistic setting) and a much older InSight paper (2016). This would have been typically enough for a paper with major technical novelty; however, for this paper, I believe adding more recent baselines and discussing the advantages of the method over these baselines would be necessary. \n\nMinor:\nCaption in Figure 1 can be more informative and useful for the reader if you add more details on different parts of the model. \n“Graphically, once can observe” should be “one can observe” . ", "extra_scores": {"experience_assessment": "I have read many papers in this area.", "review_assessment:_checking_correctness_of_experiments": "I assessed the sensibility of the experiments.", "review_assessment:_thoroughness_in_paper_reading": "I read the paper at least twice and used my best judgement in assessing the paper.", "review_assessment:_checking_correctness_of_derivations_and_theory": "I assessed the sensibility of the derivations and theory."}, "extra_text": {}}]

Author rebuttal:

Meta-review: The problem of introducing interpretability into sepsis prediction frameworks is one that I find a very important contribution, and I personally like the ideas presented in this paper. However, there are two reviewers, who have experience at the boundary of ML and HC, who are flagging this paper as currently not focusing on the technical novelty, and explaining the HC application enough to be appreciated by the ICLR audience. As such my recommendation is to edit the exposition so that it more appropriate for a general ML audience, or to submit it to an ML for HC meeting. Great work, and I hope it finds the right audience/focus soon. 
Decision: Reject