Temporal Probabilistic Asymmetric Multi-task Learning
Authors: Nguyen Anh Tuan
Hyewon Jeong
Eunho Yang
Sungju Hwang
Venue:  (2020)
Keywords: Multi-task learning
Time-series analysis
Variational Inference

Abstract: When performing multi-task predictions with time-series data, knowledge learned for one task at a specific time step may be useful in learning for another task at a later time step (e.g. prediction of sepsis may be useful for prediction of mortality for risk prediction at intensive care units). To capture such dynamically changing asymmetric relationships between tasks and long-range temporal dependencies in time-series data, we propose a novel temporal asymmetric multi-task learning model, which learns to combine features from other tasks at diverse timesteps for the prediction of each task. One crucial challenge here is deciding on the direction and the amount of knowledge transfer, since loss-based knowledge transfer Lee et al. (2016; 2017) does not apply in our case where we do not have loss at each timestep. We propose to tackle this challenge by proposing a novel uncertainty- based probabilistic knowledge transfer mechanism, such that we perform knowledge transfer from more certain tasks with lower variance to uncertain ones with higher variance. We validate our Temporal Probabilistic Asymmetric Multi-task Learning (TP-AMTL) model on two clinical risk prediction tasks against recent deep learning models for time-series analysis, which our model significantly outperforms by successfully preventing negative transfer. Further qualitative analysis of our model by clinicians suggests that the learned knowledge transfer graphs are helpful in analyzing the model’s predictions.

Under review as a conference paper at ICLR 2020
TEMPORAL PROBABILISTIC ASYMMETRIC MULTI-TASK LEARNING
Anonymous authors Paper under double-blind review
ABSTRACT
When performing multi-task predictions with time-series data, knowledge learned for one task at a specific time step may be useful in learning for another task at a later time step (e.g. prediction of sepsis may be useful for prediction of mortality for risk prediction at intensive care units). To capture such dynamically changing asymmetric relationships between tasks and long-range temporal dependencies in time-series data, we propose novel temporal asymmetric multi-task learning model, which learns to combine features from other tasks at diverse timesteps for the direction
the prediction of each task. One crucial challenge here is deciding and the amount of knowledge transfer, since loss-based knowledge transfer (Lee et al., 2016; 2017) does not apply in case where we do not have loss at each timestep. We propose to tackle this challenge by proposing a novel uncertainty- based probabilistic knowledge transfer mechanism, such that we perform knowl- edge transfer from more certain tasks with lower variance to uncertain ones with higher variance. We validate our Temporal Probabilistic Asymmetric Multi-task Learning (TP-AMTL) model on two clinical risk prediction tasks against recent deep learning models for time-series analysis, which our model significantly out- performs by successfully preventing negative transfer. Further qualitative analysis of our model by clinicians suggests that the learned knowledge transfer graphs are helpful in analyzing the model's s predictions.
INTRODUCTION
Multi-task learning (MTL) (Caruana, 1997) is a method to train a model, or multiple models jointly for multiple tasks to obtain improved generalization, by sharing knowledge among them. One of the most critical problems in multi-task learning is the problem known as negative transfer, where unreliable knowledge from other tasks adversely affects the target task. To prevent negative transfer, researchers have sought ways to allow knowledge transfer only among closely related tasks, by either identifying the task groups or learning optimal sharing structure among task (Duong et al., 2015; Misra et al., 2016). However, not only the task relatedness but the relative reliability of the task-specific knowledge also matters, and recent asymmetric multi-task learning models Lee et al. (2016; 2017) tackle this challenge by allowing tasks with low loss transfer more.
While the asymmetric knowledge transfer between tasks is useful, does not fully exploit the asym- metry in the case of time-series analysis, which has additional dimension of the time axis. With time-series data, knowledge transfer direction may need to be different depending on the timestep. For instance, suppose that we predict infection and mortality for patients in intensive care units based on their medical records. At earlier timesteps, prediction of infection may be more reliable than mortality, thus we may want knowledge transfer to happen from task infection to mortality; at later timesteps, we may want the opposite situation to happen. Moreover, knowledge transfer may happen across timesteps. For example, a high risk of infection in early timestep will alarm high risk of mortality at later timesteps. To exploit such temporal relationships between tasks, we need a model that does not perform static knowledge transfer between two tasks (Figure la), but dynamically changes the knowledge transfer amount and direction at each timestep, and also transfers knowledge across timesteps (Figure lb). Toward this objective, we propose a multi-task learning framework for time-series data, where each task not only learns its own latent features at each timestep but also aggregates the latent features from the other tasks at the same or different timesteps via attention allocation.

---

Under review as a conference paper at ICLR 2020
Moltppe fentures across timesteps
Maliipple features timestens
n
12
1
1
1
Lose
Infection Task
Low
M Mortality (lokk
M
2
MT
M
M
MT
High Uc
Step
Step
Step I'
Step
Step 2
Step
(a) AMTL (Lec et al., 2016)
(b) Temporal Probabilistic AMTL
Figure 1: Concept: (a) Existing asymmetric multi-task learning model utilize task loss to perform static knowledge transfer from one task to another; thus cannot capture dynamically changing relationships between time-steps steps and tasks in the time-series domain. (b) Our model tackles the lack of loss by performing knowledge transfer based tasks and across timesteps.
feature-level uncertainty. This allows dynamic asymmetric knowledge transfer among
Yet this brings in another challenge. On what basis should we promote asymmetric knowledge transfer? For asymmetric knowledge transfer between tasks, we could use task loss as proxy of knowledge reliability. However, loss not direct measure of reliability, since model trained with few instances may have small loss, while the knowledge from the model could be highly biased and unreliable. Further, for prediction with time-series data, loss may not be available at every timestep. Thus, instead of task loss, we focus on the uncertainty, which can be obtained with probabilistic Bayesian models. Basically, uncertainty (variance), we can consider its knowledge as unreliable. In such case, the model may allocate small attention values for the feature; that is, the attention will be attenuated based on the uncertainty.
latent feature learned certain timestep has large
To validate the superiority of our model, we experiment with on three clinical risk prediction datasets against multiple baselines. The results show that our model obtains significant improve- ments over strong multi-task learning baselines. Further, both the asymmetric knowledge transfer between tasks at two different timesteps as well the uncertainty- based attenuation of attention weights are found to be useful in improving the generalization performance.
Our contribution in this work is threefold:
We propose novel asymmetric multi-task learning framework for time-series analysis, which utilizes feature-level uncertainty to perform knowledge transfer among tasks and across sime-steps, thereby exploiting both the task-relatedness and temporal dependencies.
We use probabilistic Bayesian formulation for asymmetric knowledge transfer, where the amount of knowledge transfer depends on the uncertainty at the feature level.
We validate our model on clinical risk prediction tasks, on which it achieves significant improvements over baselines and provides meaningful interpretations, including temporal relationships between tasks.
2 RELATED WORK
Multi-task Learning While the literature on multi-task learning (Caruana, 1997; Argyriou et al., 2008) is vast, we selectively mention the prior works that closely related ours. Historically, multi-task learning models have focused on what to share (Yang & Hospedales, 20; Ruder12 et al.), the jointly learned models could share instances, parameters, 2011; Kumar & Daume III, 2012; Maurer et al., 2013). With deep learning, multi-task learning can be implemented rather straightforwardly by making multiple tasks share the same deep network. However, since solving different tasks will require heterogeneous knowledge, complete sharing of the underlying network may suboptimal and brings in a problem known as negative transfer, where certain tasks are negatively affected by knowledge sharing. To prevent this, researchers are exploring more effective knowledge sharing structures. Duong al. (2015) proposed a soft param- eter sharing method that uses a regularizer to enforce the network parameters for each task to be similar, while Mísra et al. (2016) proposed to learn the optimal combination of shared and task- specific representations in computer vision. Kendall et al. (2018) proposed a multi-task framework when the losses are weighed based on tasks' uncertainty, thereby reducing negative transfer from un- certain tasks. While finding good sharing structure alleviate negative transfer, negative transfer will still persist we perform symmetric knowledge transfer among tasks. To resolve this symme- try issue, Lee al. (2016) proposed asymmetric MTL model with inter-task knowledge transfer
features (Kang et al.,
2

---

Under review as a conference paper at ICLR 2020
that allows task-specific parameters for tasks with smaller loss to transfer more. Lee et al. (2017) proposed a model for asymmetric task-to-feature transfer that allows reconstructing features with task-specific features while considering their loss, which is more suitable for deep neural networks and scalable. Our model is also targetting asymmetric multi-task learning, but is different from these previous works in that it utilizes uncertainty rather than loss as the measure of task reliability, and performs asymmetric knowledge transfer at each timestep, and across timesteps.
Clinical time-series analysis While our method is generic and applicable to any time-series predic- tion tasks, we mostly focus on clinical time-series analysis in this paper. Recently, there has been some progress on this topic, mostly focusing on interpretability and reliability of the model. Choi et al. (2016) proposed an intention-basee model that generates attention for both the timesteps (hos- pital visits) and features (medical examination results), to provide interpretations of the predictions. However, attentions are often unreliable since they are learned in a Heo et al. (2018) proposed obtain reliable interpretation and prediction by proposing a probabilis- tic attention mechanism that considers uncertainty to how to trust the input. Our work shares the motivation with these prior works as we target interpretability and reliability. Recently, Song et al. (2018) proposed model that uses the Transformer architecture perform time-series prediction with multi-task learning experiments. However, their model takes a straightforward approach where all tasks share a single base network, which is susceptible to negative transfer.
manner, and
3 APPROACH
We now formally describe the problem setting and our probabilistic asymmetric multi-task learning framework for time-series prediction.
3.1 TIEESEEIES PREDICTION WITH FEATURE-LEVES UNCERTAINTY
Our goal is to jointly train time-series prediction models for multiple tasks at once. Suppose that are given training data for D tasks, ID = {(X1, YI)...., (Xp, data instance x(x E X for some d) consists of T timesteps. That is, x = (x(2), (x2)) ,(?)).... x()), where x(1) E R 1mm denote the data instance for the timestep t. Additional, y/ is the label for task d; for binary classification task, Va {0, and for regression case, Yd R. Given time-series data and tasks, we want to learn the task-specific latent features for each task and timestep, and then perform asymmetric knowledge transfer between them. Our multi-task learning framework is comprised of the following components:
YD) (XD, Further suppose that each
Shared Low-Level Layers (Figure 2a) We allow our model to share low-level layers for all the tasks in order to learn a common data representation before learning task-specific features. At the lowest layer, we have shared linear data embedding layer to embed the data instance for each timestep into a continuous shared feature space. Given time-series data instance x, we first linearly transform the data point for each timestep f, x(() E IR",, which contains m variables.
(v)))
xW emb E IR T
(1)
where W emb E mxk and l is the number of hidden units. After embedding the data instances, we input them into a shared RNN layer for pre- pre-processing:
(1) (2))
(2)
(T)) RNN(V (2)) (1))
(2)
Task- and Timestep Embedding Layers After embedding and pre-pro preprroesssing the input into a continuous space, we further encode them into task- and timestep-specifis features. Since hard- sharing layers may result in negative transfer between tasks, we use separate embedding layers for each task to encode task-specific knowledge. For each task d, the separate network consists of I. layers (Figure 2b) of feed-forward networks, to learn disentangled knowledge for each timestep. The L feed-forward layers for task embedding (Figure 2b) can be formalized as:
ha = ((r.o + bb)) + b))...) + bb)) R Txk
(3)
where W RR b/ E R and is non-linear activation function (e.g. leaky relu).
Modeling feature-level uncertainty While the above embedding can capture knowledge for each task and timestep, want to further model their uncertainties well, to measure the reliability of the knowledge captured. Towards this objective, we model the latent variables as probabilistic ran- dom variables, with two types of uncertainty (Kendall & Gal, 2017): 1) epistemic uncertainty, which
3

---

Under review as a conference paper at ICLR 2020
Intra Tack
Prediction [Rosk !|
9
Inben taak
Adagthv
RNN
Atzention Layer
Ingut Dota
Input Embeddings
Tack Specific
(8)
(b) Adeptive Layers
Knowledge Transfer
Figure 2: Architecture overview. The amount and form of (d) knowledge transfer is computed networks and G. which will described detail on subsections 3.2 and 3.3.
comes from the model's unreliability from the lack of training data, and 2) aleatoric uncertainty, that comes from the inherent ambiguity in the data. We capture the former by using dropout variational inference (Gal Ghahramani, 2016), and the latter by explicitly learning the model variance as function of the input (Figure 2c).
Suppose that our generative model is: Zd ~ po(za Xx, w), Ya ~ Polua|x x, Zd, w) where w is the set of all parameters, po(2a]X Xx, w) and po(ua]x x, Za, w) are networks parameterized by 0. We denote all joint, marginal and conditional distributions arising from this generative model by p. 2d X M (zdi pa, diag(ar))
pd o (bs W + b a
(5)
W + bS)
(6)
The posterior distributions p(za|x, yd, w) and p( (D) are intractable so we use variational inference to approximate the joint distribution. The variational distribution is defined by:
q(z,, w Va. DD= = 4M (w| (D))(D) Va: w)
(7)
We set (M)IIID) by dropout approximation (Gal & Ghahramani, 2016) with parameter M and simply set q(za),, x. Yd, w) to the prior network (z(zal w) (which works well in practice (Sohn et al., 2015; Heo et al., 2018)) for the model consistency at both training and test time.
3.2 UNCERTAINTY-WWARR KNOWLEDGE TRANSFER
We perform asymmetric knowledge transfer the feature space. Suppose that we have latent feature vectors f and for two tasks at different timesteps. Then the model needs to decide on both 1) the amount of knowledge to transfer, and 2) 'the transferred knowledge:
1) The amount of knowledge to transfer Existing AMTL models (Lee et al., 2016; 2017) often use task loss to decide on the amount of knowledge transfer, such that task-specific parameters with low task loss transfer more, while tasks with high loss only receive knowledge transfer. Yet. the task loss may be unreliable as a measure of the knowledge from the task and may not be available at each timestep. To overcome these limitations, based on the feature-level uncertainty. With our probabilistic time-series prediction model described in the previous subsection, the source features f and the target features g follow some distributions. Specifically, f ~ pff; jy, o and g ~ p(g; Mgg og). Our model learns the distribution of the transfer weight from f g by a small network Fe parameterized by 6, which takes both (instances of) f and as its input:
propose learn the amount of knowledge transfer
a = (a)
= N Ma a ~ =
(9)
(Ma, Ff
(10)
In general, Fg is a function from R 2k to R2. In practice, to avoid the concatenation of f and g (which be slow), adopt simple implementation: Na afo(f by) o b,)) and o, = soft_ fir__puus(,, (n w + b). where a is some activation function (which should not confused with o.) and is the inner product.
4

---

Under review as a conference paper at ICLR 2020
a'
g
Muttiplo Features
fk
Muttiple Features
Cj
d
Feature map (Task J)
Feature map (Task d))
(a) Uncertainty-awan knowledge transfer
(b) Temporal asymmetric knowledge transfer
Figure 3: Temporal probabilistic asymmetric knowledge transfer. 3a illustrates the uncertainty-awarc knowledge transfer between two latent features. In this case, is more reliable than g. so the model will leamn transfer more from g and transfer less from & f. 3b shows how apply for knowledge transfer between two tasks the same timestep and at different timesteps.
By using Stochastic Gradient Variational Bayes (SGVB), the network F can learn a meaningful distribution the transfer weight, such that sets the value of a high when the and g are related, with low uncertainty on and high uncertainty on g.
2) The form transferred knowledge Because f and g may have completely different represen- tations, directly combining the two by adding of to g is suboptimal. Instead, we network G& parameterized by & to non-linearly transform f into a compatible representation for g (Figure 3a). The combined features C then can be expressed follows:
C g + (G)
(11)
G&(f) = (IW b)
(12)
where W R E R& and is a non-linear activation (e.g. leaky relu). Furthermore, when transferring knowledge from source task to a target task, the target task should only borrow knowl- edge from the souree task without affecting its feature map via backpropagation. To this end, we block the gradient of f in the formulation of C in 11. We also empirically found that this gradient blocking makes the obtained knowledge transfer graph significantly more interpretable.
3.3
ASYMMETRIC KNOWLEDGE TRANSFER ACROSS TASKS AND TIME STEPS
Now we apply the proposed probabilistic asymmetric knowledge transfer method to perform knowl- edge transfer across timesteps, both within each task and across tasks, to exploit intra- and inter-task temporal dependencies.
order to transfer knowledge from task j to task d with temporal depen-
dencies, we allow the latent features of task d at time step t (f(()) with z = (e()) p(2)
p!(2) to
...., fd obtain knowledge from task j all previous time steps (see Figure 3b), and then combine them into a single feature map
((1)
((2) ".. (T))
d
D
(1 (()) + d
(1.)) jdd * GJ,d (1,5) 1I E (1,
o Ø=1==1
Here, we chose to constrain the knowledge transfer to happen only from past to future timesteps because of the time complexity inference time. With our proposed model, for each update the clinical environment in online manner, we only need to transfer the knowledge from previous time steps to the current one, making the complexity be OTT). This on a par with other models like RETAIN (Choi et al., 2016) or UA (Heo et al., 2018), making it highly scalable. However, if we allow the knowledge to transfer from future timestep to past timestep, we also need update the knowledge at previous timesteps for single update. The time complexity of the model in this case OTT2), which is undesirable. In the ablation study in Section 4.5, we show that this constraint also brings in small performance gain. The total complexity of the whole training or inference is still (T²). However, it is expected due to the inter-timestep transfer, and is on a par with state-of- the-art models such as Transformer( Vaswani et al., 2017) RETAIN(Choi et al., 2016).
Finally, we use the combined features C(l) c(2)
C(T) which contain temporal dependencies among tasks, for prediction for each task d. We use an attention mechanism:
B = tanh (c w +b.)
VI E {1,2, 1I., T).
5

---

Under review as a conference paper at ICLR 2020
(6.0) (i S 1) is the knowledge transfer weight from task timestep i task d at timestep t. Then the model can perform prediction follows,
where w R and by IR, and ji
p(yal x)) Sigmoid 1og @ (1) = 2 (2) + .... + + +B8 O
w +2
(13)
for classification tasks, where @ denotes the clement-wise multiplication between attention (a and shared input embedding vlO (from Eq. 1), Wa E R and bg RR. Predictions for other tasks are done similarly.
It should be noted that our model does not require each instance to have the labels for every tasks. We can just maximize the likelihood p(ya|x) whenever the label ya is available for input æ for task d. Furthermore, is not required that all the instances to have the same number of time-steps T.. But in practice, we can use zero-padding to make the training easier.
4 EXPERIMENTS
We validate our model on multiple clinical risk prediction tasks against relevant baselines.
4.1 TASKS AND DATASETS
We experiment on two clinical time-series datasets. For all datasets, we randomly split the data into training. validation, and test set. For more details on the datasets and tasks, including explanations for dataset MIMIC III- Infection, the base network configurations and hyperparameters, and more experimental results on an additional dataset (MIMIC III Heart Failure), please see the appendix.
1) MIMIC III- Infection (Figure 6). We compiled dataset out of the MIMIC III dataset (Johnson et al., 2016), which contains electronic health records (EHR) of 53,423 distinct hospital admissions between 2001 and 2012 to the intensive care unit (ICU) of hospital. We use records of patients over age 15, from the first 48 hours after the admission, in 48 timesteps. Following clinician's 's guidelines, we select 12 infection-relatee rate, arterial blood pressure, and Glasgow Coma Scale(GCS). Tasks we consider for this dataset are the ones that are necessary for the diagnostic process of patient's 's infectious status; The first task, body temperature elevation (Task 1) provides the signs of infection, and Infection (Task 2) as the confirmation of infection by the result of microbiology tests. We also added Mortality (Task 3) as a possible outcome of infection. After pre-pu me-processing the data, we were able select approximately 2000 data points (that have sufficient amount of features). We use random split of approximately 1000 1000/500/550 50//5000055 /500 for vaaning/validationn//
variables for the features at each timestep, including heart
2) PhysioNet. This dataset (Citi & Barbieri, 2012) contains 4,000 medical records from ICU. Each record contains 48 hours of records, each of which contains 31 physiological signs including heart rate, respiratory rate, temperature, etc. Task used in the experiment includes four binary classifica- tion tasks, namely, 1) Mortality prediction, 2) Length-of-ste less than 3 days: whether the patient would stay in ICU for less than three days. 3) Cardiac Surgery is recoveing from cardiac surgery, and 4) Recovery in Surgical ICU(Recovery):: whether the patient is staying in Surgical ICU to recover from surgery. We use a random split of 2800/400/800 for rrainingvvllidationnesss
whether the patient
4.2 BASELINES
Now we describe the baseline single-task and multi-task models for time-series prediction, along with our models.
1) STL-LSTM. The base single-task Long Short- Memory Network for time-series prediction.
2) RETAIN. The attentional RNN proposed in (Choi et al., 2016) which focuses on interpretability, for clinical prediction with electronic health records.
3) UA. The uncertainty-awart probabilistic attention model proposed in (Heo et al., 2018) for inter- pretable time-series prediction.
4) MTL-LSTM. The naive hard-sharing multi-task learning method where all tasks share the same
network except for the separate output layers for prediction, with LSTM the base network. 5) -TL.-TTTTaa Tran-frranformer. The same as MTL-LSTMM, but with Transformer (Vaswani et al., 2017) as
'The full detail of the variables be found in the supplementary file

---

Under review as a conference paper at ICLR 2020
Table 1: MIMIC-III Infection
Models
Tasks
Fever
Infection
Mostality
Average
LSTM
0.6738 0.02
0.686011
0.02
0.63731: 0.02
0.665711 0.02
STT.
RETAIN (Choi al., 2016)
0.6826+ 0.01
0.6655+t
0.01 0.6504# 0.02
0.6054+ 0.02
0.651 0.01
LA (Heo et al., 2018)
0.6987= 0.02
0.6168# 0.05
0.6553=0.02
LSTM
0.7006 0.03
0.668611
0.02
0.62611 0.03
0.6651 10.02
TRANS (Vaswani et al., 2017)
0.7025+ 0.01
0.6479+
0.02
0.6420+ 0.02
0.6641=0.02
MTL
RETAIN (Choi al., 2016)
0.7059: 0.02
0.6635
0.01
0.6198 0.05
0.663011 0.02
CA (Ileo et al., 2018)
0.712411 0.01
0.648911
0.02
0.63251 0.04
0.664610.02
-ETAAll-Kendll (Kendall et al., 2018)
0.6938+ 0.01
0.6182+
0.03
0.5974+ 0.02
0,6364+ 0,02
AMIL-LSIM (Lee et al., 2016)
0.6858 0.01
0.67734:
0.01
0.6765 0.01
0.6798=0.01
TP-AMTL (our model)
0.7156 0.01
0.7131 0.01
0.7098
0.01
Table 2: PhysioNet
Models
Tisks
Stay <
Cardiac
Recuvery
Mortality
Average
LSTM
0.7673.1 0.09
0.9293.1 0.01
0.8587.
0.01
0.7100.1 0.01
0.8163.1 0.03
STL.
RETAIN (Choi et al. 2016)
0.7407= 0.04
0.9236+
0:01 0.9335# 0.01
0.8148++
0.04
0.7080+-
0.02
0.7968- 0.03
UA (Heo et al., 2018)
0.8556= 0.02
0.8712= 0.01
0,7283+ 0.01
0.8471 0.01
LSTM
0.7418= 0.09
0.9233+
0.01
0.8472:4 0.02
0.72284
0.01
0,8088
0.03
TRANS (Vaswani al., 2017)
0.8532= 0.03
0.9291
0.01
0,8770
0.01
0,7358:
0.01
0.8488#
0.01
MIL
RETAIN (Choi et al., 2016)
0.761332 0.03
0.9064:1: 0.01
0.8160:: 0.04
0.6944::
0.03
0.7945: 0.03
UA (Hen et al., 2018)
0.8573.1 0.03
0.9348 1: 0.01
0.8860:1 0.01
0.7569
0.02
0.85871 0.02
RETAIN-Kendall (Kendall et al., 2018)
0.7418:: 0.02
0.9219-::
0.02
0.7883:1 0.03
0.6787-t
0.02
0.7827 = 0.02
AMTL-LSTM (Lee et al., 2016)
0.7600=
0.9254: 0.01
0 0,80662: 0.01
0.7167:: 0.01
0,8022 0.03
TP-AMTL (our model)
0.9012:: 0.01
0.9368 0.01
0,89231: 0.01
0.75711 0.01
0,8719 0.01
the base network.
6) MTL-RETAIN. The same as MTL-LSTM, but with RETAIN as the base network.
7) MTL-UA. The same as MTL-LSTM, but with UA (Heo et al., 2018) as the base network.
8) AMTL-LSTM. Asymmetric multi-task learning (Lee et al., 2016) adopted for our time-series
prediction framework, where we learn the knowledge transfer graph between task-specific parame- ters, for asymmetric knowledge transfer based on the task loss. Since the parameters for each task are shared across all timesteps, this will result static asymmetric transfer between tasks.
9) RETAIN-KKedall
This is the uncertainty -bseed leighneig scheme proposed in Kendall et al. (2018) with MTL-RETAIN as the base MTL model.
10) TP-AMTL. Our probabilistic temporal asymmetric multi-task learning model that performs both intra-task and inter-task knowledge transfer.
For more details about the baselines, please refer the appendix.
4.3 QUANTITATIVE EVALUATION ON CLINICAL TIME-SERIES PREDICTION TASKS
We first evaluate the prediction accuracies of the bascline STL and MTL models and ours the two clinical time-series datasets, by measuring Area Under the ROC curve (AUROC). Table 1,2 show the result for the MIMIC-III Infection dataset and Physionet dataset respectively. We observe that hard- sharing MTL models outperform STL on some tasks, but suffers from performance degeneration on other tasks, which could be the effect of negative transfer. MTL models especially work poorly on MIMIC-III Infection, which has clear temporal relationships between tasks. Probabilistic models (e.g. UA) generally outperform their deterministic counterparts (e.g. RETAIN). However, AMTL- LETAIN-Kendall which learns the weight for each task loss based on uncertainty, significantly underperforms even the STL-LSTM, which may be due to the fact that losses in our settings are at almost similar scale unlike with the task losses in Kendall et al. (2018) that have largely different scales. AMTL--LSTM improves on some tasks, but degenerates the performance on the others, which attribute the fact that it does not consider inter-timestep transfer. On the other hand, our model, AM-AMT,, obtains significant improvements over all STL and MTL baselines on both datasets. also does not show performance degeneration on any of the tasks, suggesting that it has successfully dealt away with negative transfer in multi-task learning with time-series prediction models.
For further analysis of the relationships between uncertainty and knowledge transfer, we visualize knowledge transfer from multiple sources (Figure 4a) normalized over the number of tagets, and to multiple targets (Figure 4b) normalized over the number of sources, along with their uncertainties.
7

---

Under review as a conference paper at ICLR 2020
Knowledge Transfer from Ca Cardia: to Mortality:
Krowledge Transfer from Cardiac: to Stayc3:
Uncertainiyy of Source features vs Normalized Total Krowledge transfer
Uncertaintyy Target Features Normalized Total Knowledge transfer
Uncertainty of Source
Uncertainty of Target
Transfer Armunt
(a) Outgoing Transfer from different Sources
(b) Incoming Transfer to different Targets
Figure 4: Examples showing the relationship between the amount of knowledge transfer and the uncertainty of source and target features. (a) The sources with low uncertainty transfer more knowledge. (b) The targets with high uncertainty receive morc knowledge.
Specifically, the uncertainty of a task at a certain timestep is represented by the average of the variance of all feature distributions. The normalized amount of knowledge transfer from task j time step ? to task is computed as (af.2 (6.0 +a + (6.7) >/(T---- Similarly, the normalized j.a
amount of knowledge transfer to task d at time step / from task j is (aft.)) +o. (2.9 +...ta.. (//
We observe that source features with low uncertainties transfer knowledge more, while at the tar- get, features with high uncertainties receive more knowledge transfer. However, note that they are not perfectly correlated, since the amount of knowledge transfer is also affected by the pairwise similarities between the source and the target features well.
4.4 INTERPRETATION OF THE LEARNED KNOWLEDGE GRAPHS
With the help of physician, we further analyze how generated transfer weights and uncertainties are related with the patient's actual medical conditions and how we can interpret temporal rel relationships between tasks with our model (see Table and Figure 5). We first consider an example record of a patient from the MIMIC-III Infection dataset who
suspected of infection having fever as an initial symptom, which was diagnosed be caused by bacterial infection later. Figure 5a shows the amount of knowledge transfer from task fever 3:00 all later timesteps of task infection. At this timestep, the patient's condition changes significantly. In Table 6, we see that the patient had fever and the white blood cell count increased the state of leukocytosis, and both the systolic and diastolic blood pressure decrease over time. Most importantly, the patient is diagnosed to have infection, as the bacterial culture test result turns out to be positive 2:57. With the drop of uncertainty of the task infection around the time window where the event happens, the amount of knowledge transfer from fever to infection drops as well, as the knowledge from the source task becomes less useful.
admission
Table 3: Clinical Events selected medical records for case studies. MechVent Mechanical Ventilation, Fi02 Fractional inspired Oxygen, SBP Systolic arterial blood pressure, DBP Diastolic arterial blood pressure, HR Heart Rate, Temp Body Temperature, Urine Urine output, GCS Glasgow Coma Score, WBC White Blood Cell Count, Culture Culture Results.
Mech
SBP
DBP
Tomp
WBC
Culture Results
Vent
Fi02
SBP
DBP
MAP
HR
Temp
Utine
GCS
138
NIA
1:00
100
40.1
12500
N/A
31"
0.7
106
70
74
NIA
2:57
89
46
N/A
NIA
(+jAlebriella Pnenmonine
30' 31
0.6
109
57
73
75
39.1
Knowledge Tranafer from Task Fever from 3:00 to Task Infection
Knowlodge Transfer from Task Recovery to 30'31" Task Mortality
0.12
0.5
6:6%
033
0.34
0:58
0.32
Trensfer Amount
Transfor Amount
Uncertalitty of Source
0.23
00800
Uncortainty
0.022
2220
1031" cert a'c sess Wir 322 32127
(a) MIMIC-III Infection
(b) PhysioNet
Figure 5: Visualizations of the amount of uncertainty and normalized knowledge transfer for example
cases where the changes the amount uncertainty certain timesteps are correlated with clinical events. We denote the timesteps with noticeable changes in uncertainty and knowledge transfer with blue boxes.
8

---

Under review as a conference paper at ICLR 2020
For another case study, we considered record of patient from PhyisoNet dataset who recovered from surgery and passed away during admission (See Figure 5b) for mortaility prediction at 30'31". We observe that at this timestep. the uncertainty of the source task drops, the amount of knowledge transfer increases, since the knowledge from the source task becomes more reliable. From Table 6, observe that at this time step, the patient is applied mechanical mechanical ventilation and the GCS score declined from 15 to 7, and the body temperature increased from 37.7 to 39.9. This patient recovering from surgery, and the changes in features that are vital to survival means that general condition of this patient has altered, needing physician's 's attention. Based on this change in the patient's condition, the model may have predicted that the patient is recovering from surgery, which explains why the uncertainty on recovery decreased, and knowledge transfer to mortality increases to transfer this reliable knowledge.
For more example cases, please see the appendix. These interpretations suggest that by analyzing the learned knowledge graph using our model, we could identify timesteps where interesting interac- tions occur between tasks. This interpretability may become even more useful in large-scale settings where both the number of time-series data instances and the number of timestep is extremely large, on which manual analysis becomes impractical.
4.5 ABLATION STUDY
Effectiveness of the inter-task and inter-timestep knowledge transfer. To show the effective- ness of the inter-task and inter-timestep knowledge transfer, we further compare our model on the PhysioNet dataset against several variations of our model which describe below:
1) AMTL-intratask: The probabilistic AMTL model with uncertainty-awart knowledge transfer, but performs knowledge transfer only within the same task at the transfer layer. Note that, however, this model can still share inter-task knowledge in symmetrical manner since it stilll has shared lower layers (the embedding and the LSTM layers).
2) -samessttt The probabilistic model with uncertainty- knowledge transfer, which performs knowledge transfer only between the features at the same timestep, at the transfer layer. Again, note that this model can still capture the temporal dependencies among the timesteps to cer- tain degree, as it has shared lower layers.
3) TD-AMTL: The deterministic version of the temporal asymmetric multi-tast learning model that does not make use of feature-level uncertainty when performing knowledge transfer.
Table Ablation Study Physionet
Tasks
Model
Stay<3
Cardiac
Recovery
Mortality
Average
AMTL-intratask
0.8829+: 0.01
0.9338 : 0.01
0.88124:
0.01
0.7521 0.01
0.8625
AMTL-samest
0,86691 0.01
0.9273
0.01
0.8902:1
0.01
0.7382+
0,8557
TD-AMTL
0.7381 0.06
0.9155
0.01
0.8629
0.01
0.7365:1.00
0,8133
TP-AMTL (unconstrained)
0.89991: 0.01
0.9186
0.01
0.88921
0.01
0.7610
0.01
0,8672
TP-AMTL (epistemic)
0.8940 0.01
0.9358
0.01
0.8920+
0.01
0.7557+
0.01
0.8694
TP-AMTL (alcatoric)
0.7939+ 0.03
0.9176
0.01
0,8529+
0.02
0.7372+ 0.03
0.8254
TP-AMTL (full model)
0.9012.1 0.01
0.9368.1 0.01
0.892311 0.01 0.7571. 0.01
0,8719
Table 4 shows that our model outperforms the "intratask" and "samestep" variants, which demon- strates the effectiveness of inter-task and inter-step knowledge transfer. Moreover, the deterministic counterpart largely underperforms any variants, which may be due to overfitting of the knowledge transfer graph, that can be effectively prevented by our Bayesian framework.
Future-to-pase transfer. We also compare our model against a variation of our method with no temporal constraint on the inter-step knowledge transfer (TP-AMTL (unconstrained)), such that the knowledge transfer can happen from the later timestep to earlier ones. Table 4 shows that the constrained model outperforms the unconstrained model, while having lower time complexity for each update (O(T) than the unconstrained model (TT))
Two kinds of uncertainty. Furthermore, we examine the effect of two kinds of uncertainty with two variants of the model: TP-AMTL (epistemic) uses only MC-dropout to model epistemic uncer- tainty and (z,) w) is simplified into N (zæ; Mad 0) (i.e. its pdf becomes the dirac delta function at pa and z is always pa); TP-AMTL (aleatoric) uses only po (z. |x, w) to model the alcatoric uncertainty, withouth MC-dropout.

---

Under review as a conference paper at ICLR 2020
Table 4 shows that, for this dataset, epistemic uncertainty attributes more to the performance gain. However, should be noted that the impacts of two kinds of uncertainty vary from dataset to dataset. By modelling both kinds of uncertainty, the model is guaranteed to get the best performance.
CONCLUSION
We proposed novel probabilistic asymmetric multi-task learning framework that allows asymmet- ric knowledge transfer between tasks different timesteps, based on the uncertainty. While existing asymmetric multi-task learning methods consider asymmetric relationships between tasks as fixed, with time-series data, the task relationship may change at different timesteps. Morcover, knowledge obtained for task specific timestep could be useful for other tasks in later timesteps. Thus, to model varying direction of knowledge transfer and across-timester knowledge transfer, we proposed novel probabilistic multi-tast learning framework that performs knowledge transfer based on the uncertainty of the latent representations for each task and timestep. We validated our model on clinical time-series prediction tasks on datasets, which our model significantly outperforms the baseline symmetric and asymmetric multi-task learning models. We further studied the learned knowledge graphs to show that our model can be used to provide useful interpretations on how the model made certain predictions, which is crucial in building a safe AI system.
REFERENCES
Andreas Argyriou, Theodoros Evgeniou, and Massimiliano Pontil. Convex multi-task feature learn- ing. Machine Learning, 73(3):243-21) 27,- 2008
Rich Caruana. Multitask learning. Machine learning, 28(1):41-75, 1997.
Edward Choi, Mohammad Taha Bahadori, Jimeng Sun, Joshua Kulas, Andy Schuetz, and Walter Stewart. Retain: An interpretable predictive model for healthcare using reverse time attention mechanism. In Advances in Neural Information Processing Systems, pp. 3504-3512, 2016.
Luca Citi and Riccardo Barbieri. Physionet 2012 challenge: Predicting mortality of icu patients using cascaded svm-glm paradigm. 2012 Computing in Cardiology, pp. 257-260. IEFE, 2012.
Long Duong, Trevor Cohn, Steven Bird, and Paul Cook. Low resource dependency parsing: Cross- lingual parameter sharing neural network parser. In Proceedings of the 53rd Annual Meeting of the Association for Computational Linguistics and the 7th International Joint Conference Natural Language Processing (Volume 2: Short Papers), volume 2, pp. 845-850, 2015.
Yarin Gal and Zoubin Ghahramani. Dropout as bayesian approximation: Representing model uncertainty in deep learning. In international conference on machine learning, pp. 1050-1059, 2016.
Jay Heo, Hae Beom Lee, Saehoon Kim, Juho Lee, Kwang Joon Kim, Eunho Yang, and Sung Ju Hwang. Uncertainty-aware attention for reliable interpretation and prediction. In Advances in Neural Information Processing Systems, pp. 909-918, 2018
Alistair EW Johnson, Tom J Pollard, Lu Shen, H 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: 3:100535, 2016.
Zhuoliang Kang, Kristen Grauman, and Fei Sha. Learning with whom to share in multi task feature learning. In ICML, volume 2. pp. 4, 2011.
Alex Kendall and Yarin Gal. What uncertainties do we need in bayesian deep learning for computer vision? In I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus. S. Vishwanathan, and R. Garnett (eds.), Advances in Neural Information Processing Systems 30, pp. 5574-5584. 2017.
Alex Kendall, Yarin Gal, and Roberto Cipolla. Multi-task learning using uncertainty to weigh losses for scene geometry and semantics. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 7482-7491, 2018.
Abhishek Kumar and Hal Daume III. Learning task grouping and overlap in multi-task learning. arXiv preprint arXiv: 1206.6417, 2012.
10

---

Under review as a conference paper at ICLR 2020
Giwoong Lee, Eunho Yang, and Sung Hwang. Asymmetric multi-task learning based on task relat-
edness and loss. In International Conference on Machine Learning, pp. 230-238, 2016.
Hae Beom Lee, Eunho Yang, and Sung Ju Hwang. Deep asymmetric multi-task feature learning. arXiv preprint 1080000708.00260, 2017.
Andreas Maurer, Massi Pontil, and Bernardino Romera-Paredes. Sparse coding for multitask and
transfer learning. In International conference machine learning, pp. 343-351, 2013.
Ishan Misra, Abhinav Shrivastava, Abhinav Gupta, and Martial Hebert. Cross-stitch networks for multi-task learning. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 1994-4003. 2016.
Tobias Reichlin, Willibald Hochholzer, Stefano Bassetti, Stephan Steuer, Claudia Stelzig, Sabine Hartwiger, Stefan Biedert, Nora Schaub, Christine Buerge, Mihael Potocki, et al. Early diag- nosis of myocardial infarction with sensitive cardiac troponin assays. New England Journal of Medicine, 361(9):55-8677 2009.
Sebastian Ruder12, Joachim Bingel, Isabelle Augenstein, and Anders Søgaard. Learning what to share between loosely related tasks.
Kihyuk Sohn, Honglak Lee, and Xinchen Yan. Learning structured output representation using deep conditional generative models. In Advances in neural information processing systems, pp- 3483-3491, 2015.
Huan Song, Deepta Rajan, Jayaraman J Thiagarajan, and Andreas Spanias. Attend and diagnose: Clinical time series analysis using attention models. Thirty-Second AAAI Conference on Arti- ficial Intelligence, 2018.
Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention is all you need. Advances in neural information processing systems, pp. 5998 6008, 2017.
Yongxin Yang and Timothy Hospedales. Deep multi-task representation learning: A tensor factori- sation approach. arXiv preprint urXiv:1605.0639) 2016a.
Yongxin Yang and Timothy M Hospedales. Trace norm regularised deep multi-task learning, arXiv preprint /606 04038, 2016b.

---

Under review as a conference paper at ICLR 2020
A DETAILED DESCRIPTION OF DATASETS AND EXPERIMENTAL SETUP
A.1 FEATURES AND TASKS
Dataset used in this experiment was custon-constucted from whole MIMIC III dataset to represent temporal dependencies between tasks. We use the first 48 hours after admission for each patients to only consider the patient condition on admission, as infection occurring after 48 hour is more likely to be acquired at the ICUs. However, our method can be further applied to time-series prediction tasks with longer time steps. Following clinician's guidelines, we select 15 infection-related variables including Heart rate, Systolic Blood Pressure, Diastolic Blood Pressure, Glasgow Coma scale(GCS), invasive procedures: this includes endoscopic procedure, in- tubation, dialysis, chest tube placement, Lumbar drainage, and biopsy etc., serum albumin and total protein which represents nutritional status of patients, and intravenous steroids, for the features at each timestep (see Table 7).
1) MIMIC II-Infection
Symptoms and Signs result of infection
Evidence & Proof infection
One probable result of infection
Body Temperature
Elevation [p37.7 99
Diagnostic Test
Positive Bactoria Fungus/ / Virus
Mortality
Task 1 Fever
Task 2 Infection
Task 3 Mortality
Figure 6: Task overview. Tasks used the experiment included the diagnostic process of patient's infectious status (see Figure 6). When a patient ICU infected to any the pathogen, body temperature elevates (Fever (Task 1)) as a sign of infection. Next, when physician prescribe diagnostic test such as blood culture, Infection (Task 2) is confirmed when the culture result turns out to be positive with bacteria, fungus, or virus. Lastly, Mortality (Task 3) can be resulted from infection.
2) PhysioNet We select 29 physiological signs as listed in this section: : age, gender, height, weight, Systolic Blood Pressure, Diastolic Blood Pressure, mean arterial pressure, heart rale, respiratory rate, body temperature, glucose, bilirubin, serum electrolytes (sodium, potassium, magnesium, bi- carbonate), lactate, pH. Hematocrit, platelets, Partial Pressure of Oxygen(Padee (PaO2). Partial Pressure of carbon dioxide(PaCO.,) Oxygen Saturation(SaO) Fraction of inspired Oxygen( FiO2), Glasgow Coma seale(GCS), blood urea BBUN) Creatinine, Urine, mechanical ventilation status
3) MIMIC III - Heart Failure To test the generalizability of our model, we compiled this additional task set out of the MIMIC III dataset (Johnson et al., 2016). We were able to collect 3, 577 of distinct data instances where adult(age between 18 to 100) patients have admitted to the intensive care unit (ICU) of a hospital. This dataset contains 15 features which are associated to the risk of heart failure occurrence, including Heart rate(HR), Systolic Blood Pressure(SBP), Diastolic Blood Pressure(DBP) Body Temperature(BT), Fraction of inspired oxygen (FiO2), Mixed venous oxygen saturation (2). Oxygen Saturation of arterial blood (2)),), Brain natriuretic peptide(BNP)) Ejection Fraction (EF), Glaagow Coma scale(GCS) Verbal, Motor, Eye. Tasks we consider for this dataset the ones that might lead the development of heart failure. Total tasks selected, and the first task, Ischemic (Task 1) is the patient condition where a patient is diagnosed with ischemic heart disease. The second task Valvular (Task 2) is related to the diagnosis of valvular heart disease, and the third task Heart Failure contains the condition where patient is diagnosed with various types of heart failure. Lastly, Mortality (Task 4) can be a possible outcome of heart failure. We use a random split of approximately 1850/925/925 for trainingvvlldaationness.
A.2 BASELINES
Here describe the baselines with more details.
12

---

Under review as a conference paper at ICLR 2020
1) STL-LSTM. The single-task learning method which uses RNNs to capture the temporal depen- dencies.
(v (T) = Va= x xWd
emb E R Txk
(14)
(h (()) L.T Ma Vd 1..., vdd (T) (2)
(15)
p(ya xx) Sigmoid
7 (lanb (h2)) o v()) tanh (h2 v(2) + tanh (h² @ (T)
W + 0g
(16)
4) MTL-LSTM. The naive hard-sharing multi-task learning method where all tasks share the same network except for the separate output layers for prediction, whose base network is Long Short-Term Memory Network (LSTM).
xW emb E IR" R (h h(2) ..... h(²) LSTM(y(!), v22)) ,,.,,...ve
(v (2) v(T)
(17)
(18)
p((a(x) Sigmoid
T (tanh (1 @ v(1) tanh (h ()) v(2) + tanh (h (T) C v (T) WW +
(19)
5) MTL-Transformer. The same as MTL-LSTM, but with Transformer (Vaswani et al., 2017) as the base network.
xWen embb + POS BON_EENCC- E T f TRANS BLOCK(U) E Tx
(20)
(21)
C 7 (P + (2) +... + p(()
(22)
p(ūa)) = Sigmoid (c, W + bg)
(23)
where DAS_ENCCii is the positional encoding used in Transformer, TRANS BLOCK is also the architechture used in the paper, which consists of sublayers: MULTI LELTHEEEDDD (with 4 heads) and FFW. We also used residual connection and layer norm after each sublayer as the original paper.
6) MTL-RETAIN, The same as MTL-LSTM, but with RETAIN (Choi et al., 2016) as the base network. Specifically, after getting the shared context vector G, separated output layers will be applied to form the prediction for each task.
C₁ context vector from RETAIN
(24)
P( x) = Sigmoid (c, W + 8g)
(25)
7) MTL-UA. The same as MTL-LSTM, but with UA (Heo et al., 2018) as the base network. Specif- ically, after getting the shared context vector c, separated output layers will be applied to form the prediction for each task. This can be seen as the probabilistic version of MTL-RETAIN.
C; context vector from UA
(26)
p(5a(x) Sigmoid (c, W + 62)
(27)
8) AMTL-ISTM. This is asymmetric multi-task learning (Lee et al., 2016) adopted for our time- series prediction framework, where we learn the knowledge transfer graph between task-specific parameters, which is learned to perform asymmetric knowledge transfer based on the task loss. Since the parameters for each task is shared across all timesteps, this will result in static asymmetric transfer between tasks.
9) MTL-RETAIN Kendall --eddall This the work proposed by (Kendall al., 2018). The base model we use is MTL-RETAIN. However, when combining the losses, we followed the work by (Kendall al., 2018):
03 La + log(oa)
(28)
10) TP-AMTL. Our probabilistic temporal asymmetric multi-task learning model that performs both intra-task and inter-task knowledge transfer.
13

---

Under review as a conference paper at ICLR 2020
A.3 DETAILS OF MODELS IN ABLATION STUDY
AMTL-intratask. C Ff +
Ladd
(.tt)
Ga (r.) W (1.2...,;))
add
D -aTe-samestep. c = E + GG (1,,
TD-TAMTL. The deterministic version of our model that does not make use feature-level uncertainty when performing knowledge transfer.
V x W emb E IR TXk
(1 h (
(T) = RNN(((()) v(2) v(T))
hd = o((..o(o((WW by)
+ b/)) E Tx
(C))
hd
C f
ΣΣ j=l
(1.)
G (1,5)) 4A (1.2....,
jjd
/ tanh W WE 21,2,
x() Sigmoid (10 vv + 3 v2)) + ... + + @ Dy +62
(1.4) where az jjdd Fo(tfo, .((0)
TP-TAMTL constraints. C 1(()
6.0 jdd
Gjjd (1)) Vt (1,2...,77
j=1i=1
A.4 CONFIGURATION AND PARAMETERS
We trained all the models using Adam optimizer with dropout regularization. We set the maximum iteration for Adam optimizer 100,000, and for other hyperparameters, searched for the optimal values by cross-validation, within predefined ranges as follows: Hidden units: {8, 16, 32, 64), num- ber of layers: (2,3,6), mini batch size: (32, 64, 128, 256), learning rate: (0.01, 0.001, 0.0001 regularization: [0.02, 0.002, 0.0002,0.00), and dropout rate (0.1, 0.15, 0.2, 0.25, 0.3, 0.4, 0.5).
B QUANTITATIVE EVALUATION ON CLINICAL TIME-SERIES PREDICTION TASK : MIMIC I1l-HEART FAILURE
Here, we provide the experimental results of our model and other baselines on the additional dataset: MIMIC Il-Heart Failre. Table 5 shows that model still outperforms other baselines, which indicates that our method can generalize well on a variaty of time-series datasets.
C CLINICAL INTERPRETATION OF GENERATED UNCERTAINTY AND KNOWLEDGE TRANSFER BETWEEN TASKS
In this section, we further describe the interpretation of several example patients using generated uncertainty and knowledge transfer across timesteps.
The example patient in Figure 5 had a fever on admission and was confirmed to be positive with bacterial infection culture study in this specific timestep 2:57. The patient continued to have
14

---

Under review as a conference paper at ICLR 2020
Table 5: MIMIC-III Heart Failure
Models
Tasks
Ischemic
Valvular
Heart Failure
Mortality
Average
LSTM
0.7072:: 0.01
0.7700= 0.02
0.6899: 0.02
0.7169: 0.03
0,7210:: 0.01
STL
RETAIN (Choi et al. 2016)
0.6573# 0.03
0.7875= 0.01
0.6850 0.01
0.7027+ 0.02
0.7081 0.01
UA (Heo et ul., 2018)
0.6843= 0.01
0,7728= 0.02
0.7090 0.01
0.71914 0.01
0.7213# 0.01
LSTM
0.6838 0.02
0,7808
0.02
0.6965-2 0.01
0.7093+
0.02
0.7254+ 0.02
TRANS (Vaswani et al., 2017)
0.6801 0.01
0.7693= 0.01
0.7098: 0.02
0.7008:: 0.02
0.7150=: 0.02
RETAIN
016644
0.7532 +
0.6868+
0.7023++
0.7018+ 0.02
UA RETAIN-Kendall
0.6917= 0.01
0.7868= 0.01
0,7073 0.01
0.7029:: 0.01
0.7222 + 0.01
0.6476:2 0.03
0.7712= 0.02
0.6826:: 0.01
0.7017#: 0.02
0.7008:: 0.01
AMTI-LSTM et al., 2016)
0.6963-4
0.7006+ 0.01
0.7108
0.7268+
TP-AMTI (our model)
0.7113 0.01
0.7979 0.01
0.7103+ 0.01
0.7185+ 0.02
0.7345-t 0.01
fever, and white blood cell count increased to the state of leukocytosis. Also, both systolic and diastolic blood pressure declined over time. We can see that uncertainty of target task drops when the model can confidently infer to the patient status from feature values, and aids from source target can decrease in that case. Figure 5a represent knowledge transfer from one timestep of source task to multiple time steps in the target task. We examine how multiple time steps of the source task transfers knowledge to certain time steps in the target task from the same example patient of MIMIC- III Infection dataset used in Figure 5a. On the vicinity of the same timepoint where this patient was confirmed have bacterial infection, increase, and knowledge reversely flows to source task fever. This happens in accordance with the drop of knowledge transfer from fever to infection in Figure 5a. We can infer that the knowledge from task infection becomes more useful to predict source fever in this timestep as patient condition related to this task is happening around this time step.
can see that the uncertainty of source target starts to
Knowledge Transfer from Task Fever to 5:00 Task Infection
Knowledge from fever Task Mortality
Uncortainty Source Features
0.:0
(020)
014
0.1
Trensfer Amount
Transfer Amouune
Uncortainty Spurce
0.30
008
0.0
0.31
0.82
006
000
0.0
0.75
2602
1992) (0AR)
02.0 00:00 04:0 25:00 07
06.00
(a) Infection Fever
(b) Fever to Mortality
Figure 7: Visualizations of the amount of uncertainty and knowledge transfer for example cases The changes in the amount uncertainty certain timesteps are correlated with clinical events. We denote the timesteps with noticcable changes in uncertainty and knowledge transfer with blue boxcs.
Additionally, we select other example patient from MIMIC-III Infection dataset (Figure 7a 7b). This patient had fever and leukocytosis (elevation of white blood cell as a result of bacterial intrusion, implies infectious status of patient) the earlier timepoint of admission but was not confirmed to have infection afterwards. The first timepoint highlighted with the blue box is when this patient had fever and started recover from fever. At 19:00 when this patient had fever, the uncertainty of source task fever decreases and this task transfers more to target task mortality. As the patient recov- ers from fever, the uncertainty of task fever increases and knowledge transfer from fever mortality drops accordingly. The second blue box on the right denotes the time step when the complete blood count lab result showed this patient has leukocytosis, which implies the high propensity of infection. Knowledge transfer starts to drop the knowledge from source task fever is less important as the uncertainty of target task mortality drops.
Interpretation another example patient from MIMIC III-heart failure dataset is plotted Figure 8. This example patient is finally diagnosed with congestive heart failure on Chest X-ray. During admission period, troponin level of this patient was elevated, which is not diagnostic (Reichlin et al., 2009), but implying that this patient had cardiac event. Given cardiac events, hypotension occured in 1:21 (Table ??, Figure 8) be explained to be related final diagnosis heart failure. As
15

---

Under review as a conference paper at ICLR 2020
Table 6: Clinical Events selected medical records for case studies. Mech Mechanical Ventilation,
FIO2 Fractional inspired Oxygen, SBP Systolic arterial blood pressure, DBP Diastolic arterial blood
pressure HR Heart Rate, Temp Body Temperature, Urine Urine output. GCS Glasgow Coma Score, WBC- White Blood Cell Count, Culture Culture Results.
HR
SBP
Troponin-c
RR
SBP
DBP
16:21
93
18
139
59
1.26
23:21
120
13
97
36
18:21
84
21
98
38
0:21
113
23
102
36
19:21
81
21
95
36
1:21
128
26
91
30
Knowledge
Knowledge Transfer Task
1:21 Task HF
0.0922
0.0375
0.85
0.901
0.302
0.8
Unceteiity Sourea
0.0008
0.2
Unvertastty Target
0.0015
0.75
0.0006
0.89
(a) KT from single timestep and Target Uncertainty
(b) KT to single timestep and Source Uncertainty
Uncertainty and Knowledge Transfer(KT) Example case of MIMIC III Heart Failure dataset where the changes in the amount of uncertainty at certain timesteps are correlated with clinical events. We denote the timesteps with noticeable changes in uncertainty and knowledge transfer with blue boxes.
Figure 8:
the patient's SBP decreases to 90 and DBP to 30 around 1:21 (Table ??), the uncertainty of target task Heart Failure decreases Figure 8a. Knowledge transfer starts to drop as the knowledge from target task becomes more important than that of source task. We can also see that the trend of knowledge transfer follows the trend of target uncertainty. Furthermore, troponin increased in 16:21 implies ongoing myocardial stress, which can be expressed constantly lowered uncertainty of source task ischemic heart disease among the window period we plotted on Figure 8b. As uncertainty of source task decreases, knowledge transfer target task heart failure kept increasing till 23:21. However, as patient condition related to heart function, especially blood pressure starts to decrease and knowledge from target task gets important, knowledge transfer starts decrease after 23:21.
16

---

Under review as a conference paper at ICLR 2020
Table 7: Feature information of MIMIC Infection dataset
Features
Item-ID
Name of Item
initime
Age
NA
dob
Sex
NA
gender
Heart Rate
Heart Rate
22045
Heart Rate
51
Systolic Blood Pressure
442
Systolic Blood Pressure
Systolic Blood Pressure
Systolic Blood Pressure
6701
Systolic Blood Pressure
220179
Systolic Blood Pressure
220050
Systolic Blood Pressure
8368
Diastolic Blood Pressure
8440
Diastolic Blood Pressure
8441
Diastolic Blood Pressure
Diastolic Blood Pressure
8555
Diastolic Blood Pressure
220051
Diastolic Blood Pressure
220180
Diastolic Blood Pressure
223900
GCS- Verbal Response
Glasgow Coma Scalc
223901
GCS- Motor Response
220739
GCS- Eye Opening
225433
Chest Tube Placed
5456
Chest Tube
225445
Paracentesis
225446
PEG Insertion
225399
Lumbar Puncture
5939
Lumbar drain
225469
OR Received
Invasive procedures
225442
Liver Biopsy
224264
PICC Line
224560
PA Catheter
225430
Cardiac Cath
225315
Tunneled (Hickman) Line
226475
Intraventricular Drain Inserted
Bladder cath
225434
Colonoscopy
Endoscopic Procedure
225439
Endoscopy
227550
ERCP
224385
Intubation
225448
Percutaneous Tracheostomy
225468
Unplanned Extubation (patient-initiated)
Intubation/ Unplanned Extubation
225477
Unplanned Extubation (non-patient initiated)
226237
Open Tracheostomy
225792
Invasive Ventilation
772
Albumin (>3.2)
1521
Albumin
227456
Albumin
Albumin
3727
Albumin (3.9-4.8)
226981
Albumin ApachelV
226982
AlbuminScore ApachelV
220650
Total Protein(6.5-33
849
Total Protein(6_5-88)
Total Protein
3807
Total Protein
1539
Total Protein(6.5-8)
220650
Total Protein(6.5.4
17

---

Under review as a conference paper at ICLR 2020
Features
Item-ID
Name of Item
225441
Hemodialysis
225805
Peritoncal Dialysis
226477
Temporary Pacemaker Wires Inserted
Dialysis
224270
Dialysis Catheter
225802
Dialysis CRRT
225805
Peritoneal Dialysis
4929
Prednisolone
7772
Predisolone
6753
Prednisilone gits
6111
prednisone
8309
prednisolone gits prednisolone methy/prednisolone
5003
1878
2656
SOLUMEDROI MG/KG/HR
2657
SOLUMEDROL CC/H
2629
SOLUMEDROL DRIP solumedrol mg/hr
2983
Intravenous Steroid
7425
Solu-medrol mg/hr solumedol
6323
7592
Solumedrol ca/h
30069
Solumedrol
2959
Solumedrolmg/kghhrr
1878
methylprednisolone
5395
Beclamethasone
4542
Tobradex
5612
Dexamethasone gits
3463
Hydrocortisone
8070
dexamethasone gtts
18

---

Under review as a conference paper at ICLR 2020
Table 8: Feature information of MIMIC IIII Heart Failure dataset
Features
Item-ID
Name of Item
initime
Age
NA
dob
Sex
NA
gender
211
Heart Rate
Heart Rate
22045
Heart Rate
618
Respiratory Rate
619
Respiratory Rate
220210
Respiratory Rate
Respiratory Rate
224688
Respiratory Rate
224689
Respiratory Rate
224690
Respiratory Rate
51
Systolic Blood Pressure
442
Systolic Blood Pressure
455
Systolic Blood Pressure
Systolic Blood Pressure
6701
Systolic Blood Pressure
220179
Systolic Blood Pressure
220050
Systolic Blood Pressure
8368
Diastolic Blood Pressure
8440
Diastolic Blood Pressure
8441
Diastolic Blood Pressure
Diastolic Blood Pressure
8555
Diastolic Blood Pressure
220051
Diastolic Blood Pressure
220180 80
Diastolic Blood Pressure
676
Body Temperature
Body Temperature
Body Temperature
8537
Body Temperature
223762
Body Temperature
226329
Body Temperature
FiO,
190
FiO2
2981
FiO2
Fraction inspired oxygen (FiO2)
3420
FiO2
3422
FiOz
223835
FiOz
823
8,Oz
2396
S,O2
2398
S,0₂
2574
S,O,
2842
S,O₂
2933
5,O₂
2955
S,O₂
3776
S.Oz
Mixed venous Oxygen Saturation (S,02)
5636
S,O,
6024
8,0z
7260
S,0₂
7063
S,0₂
7293
S,O₂
226541
S.O₂
227685
8,0z
225674
S.0²
227686
8,0²
834
S.0²
3288
S,Oz
Oxygen Saturation arterial blood (S,0,)
8498
S.O²
220227
S.Oz
7294
BNP
Brain Natriuretic Peptide (BNP)
227446
BNP
225622
BNP
Ejection Praction (EF)
227008
EF
Glasgow Coma Scale (GCS) Verbal Response
223900
GCS Verbal Response
Glasgow Coma Scale (GCS)- Motor Response
223901
GCS-Motor Response
Glasgow Coma Scale (GCS) Eye Opening
220739
GCS Eye Opening
19


Reviews:
[{"review_id": "H1eb9eT2Yr", "reviewer": "AnonReviewer2", "summary": "", "questions": "", "limitations": "", "rating": 6, "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 submission proposes a probabilistic method for multitask learning for sequence data focusing on the use of uncertainty to control the amount of transfer between tasks. In comparison to prior work, the approach directly models uncertainty by parametrising Gaussian distributions and dropout variational inference. The approach additionally models transfer between features from different time-steps. The evaluation shows that the method outperforms recent state-of-the-art models on two medical benchmarks.\n\nThe paper is overall well written but includes some vagueness regarding the proposed method as well as the experimental setup. While describing techniques to model two kinds of uncertainty the aspect of the model which adapts transfer to the amount of uncertainty in source and target features is not described in detail (F_theta). It is described as if it only received samples for both features without any additional information regarding uncertainty. This makes it improbable that the model is able to take the feature’s uncertainty into account when modelling transfer.\n\nThe paper follows in section 3.3 with an argument for the lower computational complexity of only transferring from previous time-steps. I might misunderstand the description but having every time-step’s features be influenced only by previous timesteps should still result in complexity O(T^2) (even though the amount of computation is reduced by a constant factor). \n\nMy background is not in machine learning with clinical data (so I do not know common datasets) but it is unclear to me why the datasets evaluated on only consist of a very small section of the overall dataset they’re taken from (in case 1). Looking at table 4 the main factor seems to be probabilistic modelling so additional ablations with either version of uncertainty would be interesting.\n\nBy introducing probabilistic modelling to control the amount of transfer between tasks the paper provides an interesting perspective and is able to show strong performance. However it is also quite vague on important aspects such as the exact modelling of transfer and limited regarding evaluation.\n\nMinor aspects:\n- V from the final equation on page 5 is never described.\n- After describing modelling both kinds of uncertainty in the method section, the reader is uninformed which uncertainty is shown in plots ⅘\n- Table 4 does not have the two highest results in bold (see AMTL samestep)\n- Very limited multitask and transfer learning references pre 2016.\n- Some descriptions are unclear including the mention of ‘attention allocation’\n", "extra_scores": {"experience_assessment": "I have read many papers in this area.", "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_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": "Bkg9636aFB", "reviewer": "AnonReviewer3", "summary": "", "questions": "", "limitations": "", "rating": 6, "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": "In this paper, the authors proposed an asymmetric multi-task learning method on temporal data, and applied it to clinical risk prediction.\n\nOverall, the problem studied in this paper is interesting, the proposed method looks reasonable, and the application is also interesting. However, there are also some concerns.\n\n1. The details on how to construct F_\\theta to generate the hyper-parameter of a in (10) are missing. As the proposed MTL method is asymmetric, F_\\theta(f, g) is supposed to be different from F_\\theta(g, f), right? Otherwise, the transfer weight \\alpha from f to g would be the same as the one from g to f. What is the design of F_\\theta.  Moreover, the authors mentioned that \"the network F can learn a meaningful distribution of the transfer weight, such that it sets the value of \\alpha high when f and g are related, with low uncertainty on f and high uncertainty on g.\" However, only based on (8), (9) and (10), it is quite difficult to understand why the claim can be implemented. More details are needed.\n\n2. The complexity analysis is only focused on the relation to the number of timestamps T, without taking the number of tasks D into consideration. As the proposed method is asymmetric across tasks and across time, when the number of tasks is large, the scalability may be an issue. In real-world applications, e.g., in a big hospital, the number of patients can be very large. In this case, is the proposed method practical? \n\n3. Though the proposed method looks reasonable, it contains many components or networks. I guess to train such a composition network precisely needs a lot of tricks in practice.\n ", "extra_scores": {"experience_assessment": "I have published one or two papers in this area.", "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_experiments": "I assessed the sensibility of the experiments.", "review_assessment:_checking_correctness_of_derivations_and_theory": "N/A"}, "extra_text": {}}, {"review_id": "B1lz_JB7qB", "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": "This paper proposes a temporal probabilistic asymmetric multi-task learning model for sequential data. The asymmetric property lies in the feature level.\n\nThis paper criticize that the task loss used in previous works may be unreliable as a measure of the knowledge from the task. However, the feature uncertainty used in the proposed model can also be unreliable and I cannot see any reliable guarantee. \n\nThe organization of Section 3 is not good. The logics in different subsections are not so clear. Some notations seem undefined.\n\nEq. (4) defines p(z_d|x,\\omega). But later it defines z_d is from p(z_d|x,y_d,\\omega). The difference between these two distributions lies in y_d. I don’t know which one is used. What is p_\\theta(z_d|x,\\omega)? The notations need to be properly defined.\n\nBased on Section 3.3, the proposed model seems to require different tasks have the same total time step T and this requirement is a bit strong.\n\nIt seems that there is no Figure 2c.", "extra_scores": {"experience_assessment": "I have published in this field for several years.", "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_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": {}}]

Author rebuttal:

Meta-review: The authors propose a method for multi-task learning with time series data. The reviewers found the paper interesting, but the majority found the description of the method in the paper confusing and several technical details missing. Moreover, the reviewers were not convinced that the technique used for uncertainty quantification of the features at each stage of the time series is well founded.
Decision: Reject