Transfer Learning on Heterogeneous Feature Spaces for Treatment Effects Estimation
Anonymous Author(s)
AffiliationAddress
Abstract
Consider the problem of improving the estimation of conditional average treatmenteffects (CATE) for a target domain of interest by leveraging related informationfrom a source domain with a different feature space.
This heterogeneous transferlearning problem for CATE estimation is ubiquitous in areas such as healthcarewhere we may wish to evaluate the effectiveness of a treatment for a new patientpopulation for which different clinical covariates and limited data are available.
In this paper, we address this problem by introducing several building blocks thatuse representation learning to handle the heterogeneous feature spaces and a flexible multi-task architecture with shared and private layers to transfer informationbetween potential outcome functions across domains.
Then, we show how thesebuilding blocks can be used to recover transfer learning equivalents of the standard
CATE learners.
On a new semi-synthetic data simulation benchmark for heterogeneous transfer learning we not only demonstrate performance improvements ofour heterogeneous transfer causal effect learners across datasets, but also provideinsights into the differences between these learners from a transfer perspective.
Introduction
Estimating the personalized effects of interventions from observational data is a fundamental problemin causal inference that is crucial for decision-making in many domains: in healthcare, for determiningwhich treatments to give to patients [1], in education, for deciding which school curriculum is best foreach student [2, 3] or in public policy for choosing who would benefit from job training programs [4].
Recently, a large number of machine learning methods have been proposed for estimating conditionalaverage treatment effects (CATE) which enable such personalized policies [5–14].
Nevertheless, the good performance of these methods on a population of interest relies heavily onthe availability of large enough observational datasets for training [15].
In healthcare, for instance,this can be challenging when hospitals with few patients cannot collect enough data (e g. a largeproportion of hospitals in the USA have fewer than 100 beds, which for rare diseases can results in lessthan 80 training examples per year [16]).
Moreover, in situations such as the COVID pandemic, eachhospital will initially have very limited amount of data to learn the effectiveness of interventions from[17].
Compared to the predictive setting, this problem is exacerbated in the treatment effects settingwhere we need to observe both patients who are treated and not treated to be able to reliably train amodel for CATE estimation to obtain personalized treatment recommendations for the intended patientpopulation.
While data from large national registries can be used to build global models for generaluse across hospitals, such models do not take into account the particularities of different patientpopulations (e.g. different conditional outcome distributions ) and consequently can perform poorlyduring deployment [16, 18].
Moreover, various hospitals often record different (but overlapping)sets of patient covariates [16, 19] which makes this transfer problem even more challenging as weneed to account for the heterogeneous feature spaces .
Therefore, it becomes crucial to build methods for heterogeneous transfer learning that can leverage information from large source datasets withpotentially different feature spaces to improve CATE estimation on the target datasets of interest.
We consider the Neyman-Rubin potential outcomes (PO) framework [20, 21], where for each individual we can define two potential outcomes , one with and one without the treatment.
Out of these,we can only observe the factual outcome; the counterfactual outcome is never observed.
Under theidentifiability conditions of overlap and ignorability, observational data can be used to estimate the
PO conditional on the patient’s characteristics, which can then be used to obtain CATE.
In this paper,we address the problem of heterogeneous transfer for CATE estimation, where we aim to leveragerelated data from a source domain with different feature space (e.g. data from another hospital) toimprove CATE estimation on a target domain from which we only have few training examples.
Due to the fundamental problem of causal inference of not being able to observe both PO for a patient[22], heterogeneous transfer learning in the context of CATE estimation becomes significantly morechallenging than for supervised learning.
In addition to the feature mismatch between domains, the
PO may also have different conditional distributions, as covariate relationships and their impacton patients’ response to treatments cannot be expected to stay constant across hospitals/locations[16].
Moreover, as clinicians may use different criteria for assigning treatments for various patientpopulations, this selection bias may create discrepancies in the covariate shift induced by the treatedand control populations in each domain.
Consequently, we need to build an approach that can bothhandle the heterogeneous feature spaces, and also model the similarities and differences betweenboth PO functions and treatment assignment mechanisms across the source and target domains.
For the binary treatment setting in a single patient population, a large number of different approachesfor CATE estimation have been proposed where the main design choices involved modelling the POfunctions and handling the selection bias present in observational datasets [10, 12–14, 23–25].
Wediscuss these in more details in Section 2.
However, note that each different CATE learner has its ownadvantages and disadvantages in terms of the inductive biases they use for modelling the PO functionsand the covariate shift induced by the selection bias, and thus, different learners will achieve betterperformance in various scenarios [13, 26].
Therefore, we propose a flexible approach for transferlearning, that (1) preserves the characteristics of each learner in a single domain, while (2) enablingheterogeneous feature spaces and (3) sharing information between PO functions across domains.
Firstly, we introduce several building blocks that can be used to adapt the most common CATElearners [10, 13] to transfer information from a source to a target domain.
These building blocksinvolve handling the heterogeneous feature spaces, sharing information between PO functions acrossdomains and sharing information between PO functions within a single domain.
Secondly, we showhow these building blocks can be used to build heterogeneous transfer causal effect (HTCE-) learnerequivalents of the most common and popular CATE learners based on neural networks [10, 13].
Contributions.
Our contributions are three-fold (i) we define the problem of heterogeneous transferlearning in the context of CATE estimation and propose several building blocks that can be used toconstruct models to address this problem, (ii) we use these building blocks to construct HTCE-learnerequivalents of the most common CATE learners, and (iii) we propose a new semi-synthetic datasimulation and guidelines for evaluating CATE methods for heterogeneous transfer and performextensive experiments that not only show that our HTCE-learners achieve improved performance, butalso provide new insights into the differences between these learners from a transfer perspective.
Related works
We tackle the problem of heterogeneous transfer learning in the context of CATE estimation.
Thus,our work straddles at the intersection of research in (1) causal inference methods for CATE estimation(2) leveraging multiple datasets for CATE estimation (3) multi-task/transfer learning and domainadaptation.
Refer to Appendix A for further discussion of related works.
CATE learners.
The estimation of CATE has received a lot of attention in the causal inferenceliterature and several methods have been proposed to estimate the effects of binary treatments.
Out ofthese, we consider the most popular approaches that involve using model agnostic learning strategies,also known as meta-learners, for CATE estimation [13, 27] or neural network-based models that buildshared representations between the PO functions followed by outcome specific layers [10, 13, 23, 24].
The CATE meta-learners can be split into (a) one-step plug-in learners (indirect meta-learners) thatestimate the PO from the observational data and then set CATE as the difference in the PO [27] and (b) two-step learners (direct meta-learners) that estimate the PO and/or the propensity scorein the first step on the basis of which they build a pseudo-outcome and obtain CATE directly byregressing the input covariates on the pseudo-outcome in the second step [13, 27–29].
Refer to [13]for a more thorough classification of the different meta-learners.
Alternatively, several methods basedon representation learning with neural networks and multi-task learning have been proposed thatinvolve having shared layers between the PO functions followed by outcome-specific layers.
Themost standard architecture for this is TARNet [10] which has been extended to allow for differenttypes of information sharing between the PO and propensity score in [12, 13, 23].
To account for theconfounding bias present in observational datasets, several approaches have been proposed to extendthis model architecture by building balanced representations (treatment invariant representations)[10, 24] and/or incorporating propensity weighting to obtain unbiased estimates of the PO [25, 30].
These different approaches have their own benefits and drawback, which is why it is important tobuild a heterogeneous transfer learning approach that is general enough to extend all of them.
Transfer and domain adaptation for CATE estimation.
While, the problem of transfer learning for
CATE estimation has also been addressed by [31] the proposed approach considers shared featurespaces and consists of a two-stage training procedure that involves warm-start on the first domainand fine-tuning on the second domain.
Alternatively, [32] proposes a CATE estimation method thatcan generalize to distribution shifts in the patient population in the unsupervised domain adaptationsetting.
However, they do not assume access to label information in the target domain and onlyconsider a shared feature space between the two domains.
In addition, [33] leverages data frommultiple different environments, with shared feature spaces, to learn an invariant representation thatremoves the ‘bad controls’ which induce bias in the CATE estimation.
Then, they use this invariantrepresentation to learn PO functions are shared across the different environments.
Multi-task/transfer learning and domain adaptation .
Methods to address these problems havebeen extensively studied in the predictive (supervised) setting.
We describe here the works mostrelated to ours that consider (a) shared feature space and (b) heterogeneous feature space.
Forshared feature spaces, methods in domain adaptation focus on handling the covariate shift, i.e. thedistribution mismatch between the input features across the different domains and propose variousapproaches of learning domain invariant representations [34, 35] based on which they learn an outcome function shared between domains.
Alternatively, multi-task/transfer learning methods proposevarious approaches for neural networks to learn from related tasks that involve using both shared andtask (domain) specific layers [36, 37] to allow a flexible modelling of the different outcomes.
Tohandle heterogeneous feature spaces, [19] proposes RadialGAN, a method that augments the targetdataset with generated samples from the source datasets.
However, RadialGAN involves trainingseparate generators and discriminators for each domain and consequently also requires access toenough training data in the target domain.
After the data generation, RadialGAN trains separatepredictors in each domain that do not share information between each other.
Alternatively, Wiens etal.
[16] considers the problem of feature mismatch (in a specific healthcare application), but does notaddress the problem of distributional differences in the outcomes.
We are the first to address the problem of heterogeneous transfer for CATE estimation.
We build
HTCE-learners that use representation learning to handle the heterogeneous feature spaces and amulti-task architecture with shared and private layers to transfer information between PO acrossdomains, thus also handling the case when different populations respond differently to treatments.
Problem formalism
Let random variable X i ∈
X denote a vector of pre-treatment covariates (confounders), W i ∈ { 0 , 1 } 136 the assigned binary treatment and Y i a categorical or continuous observed outcome for individuali .
Let π ( x ) =
p ( W = 1 | X = x ) denote the treatment assignment mechanism.
As previouslymentioned, we work in the Neyman-Rubin potential outcomes (PO) framework [20, 21] and weconsider that each individual has two potential outcomes Y i (1) and Y i (0) for receiving and notreceiving the treatment respectively.
However, only one of these outcomes can be observed such that
Y i
=
W i Y
i (1) + (1 − W i )
Y i (0) .
Let µ 1 ( x ) =
E [ Y (1) | X = x ] and µ 0 ( x ) =
E [ Y (0) | X = x ] bethe PO functions.
Our aim is to estimate the conditional average treatment effect (CATE):
[Equation]
which is the difference between expected outcomes for an individual with covariates X = x .
Letη = ( µ 0 ( x ) , µ 1 ( x ) , π ( x )) be the nuisance functions for this CATE estimation problem.
Assume access to a source dataset D R
= { ( X Ri , W i , Y i ) } N R
i
=1 and a target dataset D T
={ ( X Ti , W i , Y i ) } N T
i =1 .
Different domains in applications such as healthcare, have heterogeneous featurespaces such that X Ri ∈ R D R and X Ti ∈ R D T , where D R ̸
= D T are the dimensions of the featurespaces.
We also consider that the source and target domains have different marginal distributionsp ( X R ) ̸
= p ( X T ) , different treatment assignment mechanisms p ( W = 1 | X R ) ̸
= p ( W = 1 | X T )and different conditional distributions for PO, p ( Y ( w ) | X R ) ̸
= p ( Y ( w ) | X T ) .
This results indifferent joint distributions p ( X R , W, Y )
̸
= p ( X T , W, Y ) which is representative of hospitals recording different types of patient data where the relationships between patient covariates, treatments andoutcomes can change across diseases and locations [16, 38].
Nevertheless, we implicitly assume thatthere is a shared structure between these conditional distributions across domains to enable transfer.
Our aim is to estimate conditional average treatment effects (CATE) for the target domain:
[Equation]
by using both the source D R and target dataset D T .
In particular, we want to improve the estimationin the target domain by leveraging information from the source domain.
This is useful in the settingwhere the target dataset is much smaller than the source one N T << N R
and we can leverageshared structure between the source and target outcome response functions: µ R 0 ( x R ) , µ T 0 ( x T ) andµ R 1 ( x R ) , µ T 1 ( x T ) and treatment assignment mechanisms π R ( x R ) , π T ( x T ) .
To be able to identify thecausal effects from observational data, we make the standard assumptions for both domains.
Assumption 1.
(Unconfoundedness)
There are no unobserved confounders, such that the treatmentassignment and PO are conditionally independent given the covariates: Y (0) , Y (1) ⊥⊥ W | X T and
Y (0) , Y (1) ⊥⊥ W | X R .
Assumption 2.
(Overlap) π T ( x T ) =
p ( W = 1 | X T = x T ) > 0 , ∀ x T ∈ X T and π R ( x R ) =
p ( W = 1 | X R = x R ) > 0 , ∀ x R ∈ X R .
Building blocks for CATE transfer learners
In this section, we propose building blocks that enable a flexible transfer approach for CATE learners.
The challenge in this setting is threefold as we need to (1) handle heterogeneous feature spacesbetween the source and target domains (2) share information between PO functions across sourceand target datasets ( µ R 1 , µ T 1 ) and ( µ R 0 , µ T 0 ) as well as (3) share information between PO functionswithin a single domain ( µ R 0 , µ R 1 ) and ( µ T 0 , µ T 1 ) .
We start by addressing (1) and (2) and show how the proposed building blocks can be used to obtaintransfer approaches for the most common meta-learning strategies in the treatment effects literature[13].
Then, we propose a building block for addressing (3) to obtain transfer CATE learners that useshared layers and outcome specific layers for the potential outcome functions in each domain [10].
4.1 Handling heterogeneous feature spaces between source and target domains
[Figure]
x R <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> x s <latexit sha1_base64="(null)">(null)</latexit
[Table]
h p T w,l <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> h sw,l <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> ˆ µ Rw ( x R ) <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> ˆ µ Tw ( x T ) <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> Sharing [Table]
between PO
[Table]
across source and target domains  p T ( x T [Equation] <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit>  p R ( x R ) <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit>
Consider the following split for the source and target covariates X R =(
X s , X p R ) and X T
=
( X s , X p T ) such that we have a set of featuresprivate (specific) to the source dataset X p R ∈ R D pR , a set of featuresprivate to the target dataset X p T ∈ R D pT and a set of shared featuresbetween the two datasets X s ∈ R D S .
To handle the heterogeneousfeatures spaces between the source and target datasets we propose usingseveral encoders to create a common representation that can be usedas input to the different transfer CATE learners.
Let ϕ p R ( x R ) :
R D R → R D p and ϕ p T ( x T ) : R D T → R D p be domainspecific (private) encoders that map the heterogeneous input features toa representation of size D p , such that ϕ p T ( x T ) =
z p T and ϕ p R ( x R ) =
z p R .
Moreover, let ϕ s ( x s ) :
R D S → R D
s be a shared encoder thatmaps the shared features between the source and target domains intoa representation of size D s such that ϕ s ( x s ) =
z s .
As illustrated in
Figure 1, a source example x R is encoded to [ z s || z p R ] and a targetexample x the domain-specific encoders ϕ p only for the private features x p R and x p T .
However, inputting theshared features through both types of encoders allows us to learn relationships between them that areshared across the different domain, as well as interactions which are domain-specific.
To discourageredundancy and ensure that z p and z s encode different information from the input features, wepropose using a regularization loss that enforces their orthogonality [35]:
[Equation]
(3) where ζ p R , ζ p T and ζ s are matrices whose rows are the private z p R , z p T and shared z s representationsfor the source and target examples respectively, and ∥ · ∥ 2 F is the squared Frobenius norm.
4.2 Sharing information between potential outcomes response functions across domains
[Figure]
[Equation]
[Table]
null)</latexit> <latexit sha1_base64="(null)">(null)</latexit>
z p T <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit>
[Table]
p R <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_
[Table]
="
[Table]
null)">
[Table]
null)
<
[Table]
<
[Table]
h p R w,l <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> h p T w,l <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> h sw,l <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(
[Equation]
[Figure]
[Equation]
sharing information between PO across domains.
As treatment responses can vary between differentpatient populations, it is important to build a transferapproach that enables learning target-specific outcomefunctions, while also sharing information from thesource domain.
Thus, we propose a building blockfor sharing information between PO functions acrossdomains that is inspired by the FlexTENet architecture[12] and by works in multitask learning [37] and thatinvolves having private layers (subspaces) for eachdomain as well as shared layers as shown in Figure 2.
For each treatment w ∈ { 0 , 1 } , we consider a model 214 architecture for estimating its PO functions in thesource and target domains µ Rw and µ Tw that consistsof L layers, each having a shared and two privatesubspaces (one for each domain).
For simplicity, weconsider the same number of hidden dimensions foreach shared and private subspace.
Let ˜ h
p R w,l , ˜ h
p T w,l , ˜
h sw,l be the inputs and h p R w,l , h p T w,l , h sw,l the outputsof the l th layer.
For l > 1 , similarly to [12], the inputs to the ( l + 1) th layer are obtained as follows:˜ h p R w,l +
=
[ h sw,l || h
p R w,l ] , ˜ h
p T w,l +1 =
[ h sw,l || h
p T w,l ] , ˜ h sw,l +1 =
[ h sw,l ] .
For l = 1 , we set ˜ h
p R w, 1 = Φ R ( x R ) ,
˜ h
p T w, 1 = Φ T ( x T ) , and ˜ h sw, 1 = ˜ h
p R w, 1 when using an example from the source domain or ˜ h sw, 1 = ˜
h p T w, 1when using an example from the target domain, where Φ R ( · ) and Φ T ( · ) are input representations.
When sharing the encoders from Section 4.1 for both treatments, we set Φ R ( x R ) =
[ z s ||
z p R ] andΦ T ( x T ) =
[ z s ||
z p T ] .
However, as we will see in Section 5.1, this input representation is CATElearner specific and can be extended (see Section 5.2) by adding more representation layers to shareinformation between PO functions within each domain.
Overall, let g Rw , g Tw be the hypothesis functions estimating the potential outcomes in the sourceand target domains respectively, such that g Rw (Φ R ( x R ))
=
ψ ( h p R w,L + h sw,L ) and g Tw (Φ T ( x T ))
=
ψ ( h p T w,L + h sw,L ) , where ψ is the linear function for continuous outcomes and sigmoid function forbinary ones.
This allows us to define the following loss function for estimating the PO:
[Equation]
where l ( · , · ) can be the mean squared error for continuous outcomes and the cross-entropy for binaryoutcomes.
Moreover, to discourage redundancy between the shared and private layers, we apply anorthogonal regularization loss, similar to [12, 37].
Let m sw,l − 1 , m p R w,l − 1 , m p T w,l − 1 be the dimensions ofh sw,l − 1 , h p R w,l − 1 , h p T w,l − 1 respectively, i.e. the outputs of the ( l − 1) th layer.
Let the weights in the l thlayer be θ sw,l ∈ R m [Equation] ,l [Equation]
[Equation]
[Equation]
,l
[Equation]
m
[Equation]
,l and
[Equation]
[Equation]
This allows us to use the following orthogonal regularizer:
[Equation]
A similar approach can be used to share information between the propensity estimation functions( ˆ π ( x ) ) that are used by some of the meta-learners.
See appendix B for details.
Heterogeneous transfer causal effect learners
Using these building blocks of handling the heterogeneous feature spaces and sharing informationabout PO functions across domains, we now propose a transfer learning alternative for the standardmeta-learners and neural networks (NNs) based CATE estimators, which we refer to as Heterogeneous
Transfer Causal Effect (HTCE) learners.
See Appendix C for the pseudo-code for the HTCE-learners.
5.1 Heterogeneous transfer learning for CATE meta-learners
Consider NN-based implementations for the nuisance functions
η = ( µ 0 ( x ) , µ 1 ( x ) , π ( x )) of each
CATE meta-learner.
Based on the taxonomy of meta-learners described in [13] we divide them intoone-step plug-in learners and two-step learners and provide HTCE- equivalents for both.
One-step plug-in learners.
One-step plug-in learners estimate
ˆ µ 1 and ˆ µ
and then compute CATEas ˆ τ ( x ) =
ˆ µ 1 ( x ) − ˆ µ 0 ( x ) .
The most common strategies are the T-learner which does not shareinformation between PO functions and the S-learner which does [27].
Here, we consider the simplest
S-learner that uses the treatment as an additional feature, while in Section 5.2 we explore morecomplex strategies for sharing information between PO functions within a single domain.
For our HTCE-T-learner (Figure 3 (a)), we build a model where there is no parameter sharing between( g R 0 , g R 1 ) and between ( g T 0 , g T 1 ) .
We consider treatment-specific encoders ϕ p R w , ϕ p T w , ϕ sw for the heterogeneous feature spaces, such that Φ Rw ( x R ) =
[ ϕ sw ( x s ) ||
ϕ p R w ( x R )] and Φ Tw ( x T ) =
[ ϕ sw ( x s ) ||
ϕ p T w ( x T )] .
To enable transfer, we use the approach described in Section 4.2 to share information between thehypothesis functions ( g R 0 (Φ R 0 ( x R )) , g T 0 (Φ T 0 ( x T ))) and ( g R 1 (Φ R 1 ( x R )) , g T 1 (Φ T 1 ( x T ))) .
Alternatively,for the HTCE-S-learner (Figure 3 (b)), we propose concatenating the treatment w to the input featuresx and using shared layers to obtain the PO functions in each domain.
Thus, we build input representations Φ R ( x R , w ) =
[ ϕ s ( x s , w ) ||
ϕ p R ( x R , w )] , Φ T ( x T , w ) =
[ ϕ s ( x s , w ) ||
ϕ p T ( x T , w )] and weenable transfer by having private and shared layers between the hypothesis functions g R (Φ R ( x R , w ))and g T (Φ T ( x T , w )) that share parameters for both treatments within a single domain.
[Figure]
Transfer DR-learner ˆ˜ Y RDR, ˆ ⌘ <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> ˆ˜ Y TDR, ˆ ⌘ <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> 2.
Second step x R <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit
[Table]
<latexit sha1_base64="(null)">(null)</latexit> ˆ µ Tw ( x T ) <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> ˆ ⇡ R ( x R ) <latexit sha1_base64="(null)">(null)</latexit>
<latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> ˆ ⇡ T ( x T )
<latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit>
<latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> x R <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> x s <latexit sha1_base64="(null)">(null)</latexit>
<latexit sha1_base64="(null)">(null)</latexit> <latexit sha
[Table]
[Equation]
[Table]
[Equation]
[Table]
[Equation]
[Table]
[Equation]
[Table]
[Equation]
[Table]
null)
<
[Table]
<
[Table]
[Equation]
[Table]
) <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit>
[Table]
) <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit>
[Table]
[Equation]
[Table]
) <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit>
[Table]
[Equation] [Table] ) <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)
[Table] [Table] [Figure] [Figure]
[Figure]
ˆ˜ Y RDR, ˆ ⌘ <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> ˆ˜ Y TDR, ˆ ⌘ <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> 2.
Second step
[Table]
sha1_
[Table]
">
[Table]
null [Table] </ [Table]
sha1_
[Table]
="
[Table]
null)">(null)</
[Table]
> <
[Table]
sha1_
[Table]
="(null)">(null)</latexit> <latexit sha1_
[Table]
="(null)">(null)</latexit
[Table]
<latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_
[Table]
="(null)">(null)</latexit> <latexit sha1_
[Table]
="(null)">(null)</latexit
[Table]
sha1_
[Table]
=" [Table] null)">
[Table]
null)</
[Table]
> [Table] sha1_ [Table]
="
[Table]
null
[Table]
>
[Table]
null
[Table]
[Table]
[Equation]
[Table]
[Equation]
[Table]
[Equation]
[Table]
[Equation]
[Table]
[Equation]
="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> ( x s ,w ) <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> ˆ µ R ( x R ,w ) <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> ˆ µ T ( x T ,w ) <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> x R <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> x s <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> x T <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> ˆ µ Rw ( x R ) <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit>
ˆ µ Tw ( x T ) <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> ˆ ⇡ R ( x R ) <latexit sha1_base64="(null)">(null)</latexit>
<latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null
[Table]
latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit>  p R w <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit>  sw <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> ˜ Y DR,⌘ = ✓ W ˆ ⇡ ( x )  1  W 1  ˆ ⇡ ( x ) ◆ Y + ✓ 1  W ˆ ⇡ ( x ) ◆ ˆ µ 1 ( x )  ✓ 1  1  W 1  ˆ ⇡ ( x ) ◆ ˆ µ 0 ( x )  <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit>  s <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base
[Table]
> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> x R <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> x s <latexit sha1_base64="(null)">(null)</latexit>
<latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> x T <latexit sha1_base64="(null)">(null)</latexit>
<latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit>
Plug-in learner
Transfer propensity estimator
R w ( x R ) <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit>  T w ( x T ) <
latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit>  T ( x T ) <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit>  R ( x R ) <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null) [Figure]
[Figure]
Two-step learners.
The two-step (direct) learners consist of a first stage that involves obtainingplug-in estimates ˆ η of the nuisance parameters η
= ( µ 0 , µ 1 , π ) which are used to compute thepseudo-outcome ˜
Y ˆ η and a second stage that involves regressing ˜ Y
ˆ η on X directly to obtain ˆ τ .
Severalstrategies based on regression adjustment (RA), propensity weighting (PW) or doubly robust (DR)meta-learner [13] have been proposed to compute pseudo-outcomes ˜
Y
ˆ η which result in unbiasedestimates of CATE when η is known: τ ( x )
=
E [ ˜ Y
ˆ η | X
= x ] .
These meta-learners have differenttheoretical properties depending on the sample size and the selection bias present in observationaldatasets [13], which is why it is important to build a transfer approach to extend all of them.
We describe here how to build the HTCE-DR-learner (Figure 4) and note that a similar approach 273 can be used for to obtain the HTCE-RA-learner , and the HTCE-PW-learner which use a subset ofnuissance parameters to compute the pseudo-outcomes.
For the first stage of the HTCE-DR-learner ofestimating the nuisance parameters ˆ η , we use an approach similar to the HTCE-T-learner where each 276 nuisance function has its own parameters.
To handle the heterogeneous feature spaces, we considertreatment-specific feature encoders for the potential outcome functions ϕ p R w , ϕ p T w , ϕ sw and additionalfeature encoders for the propensity estimation ϕ
p R π , ϕ p T π , ϕ sπ such that Φ Rw ( x R ) =
[ ϕ sw ( x s ) ||
ϕ p R w ( x R )] ,Φ Tw ( x T ) =
[ ϕ sw ( x s ) ||
ϕ p T w ( x T )] and Φ Rπ ( x R ) =
[ ϕ sπ ( x s ) ||
ϕ p R π
( x R )] , Φ Tπ ( x T ) =
[ ϕ sπ ( x s ) ||
ϕ p T π ( x T )] .
280 Using the approach described in Section 4.2 and Appendix B, we share information across domainsbetween each nuisance function: ( g Rw (Φ Rw ( x R )) , g Tw (Φ Tw ( x T ))) and ( g Rπ (Φ Rπ ( x R )) , g Tπ (Φ Tπ ( x T )))
to
[Table]
[Equation]
[Table]
[Equation]
<latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> h p T y,l <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> h p R y,l <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> h sy,l <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit>  R y ( x R ) <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit>  T y ( x T ) <latexit sha1_base64="(null)">(null)</
[Figure]
estimate ˆ η .
We then compute the pseudo-outcomes ˜ Y DR, ˆ η as follows [13]:
[Equation]
[Figure] [Equation] [Figure] [Equation]
[Figure]
[Equation]
[Figure]
[Equation]
[Figure]
[Equation]
For the second stage of regressing the input on the pseudo-outcomes ˜ Y R DR, ˆ η , ˜ Y T DR, ˆ η directly, we builda similar transfer architecture with feature encoders ϕ p R y , ϕ p T y , ϕ sy to handle the heterogeneous feature,followed by hypothesis functions with private and shared layers ( g Ry (Φ Ry ( x R )) , g Ty (Φ Ty ( x T ))) , whereΦ Ry ( x R ) =
[ ϕ sy ( x s ) ||
ϕ p R y
( x R )] , Φ Ty ( x T ) =
[ ϕ sy ( x s ) || ϕ p
T y ( x T )] .
5.2 Sharing information between potential outcome functions within each domain
In previous sections, we focused on sharing information between PO functions across domains ( µ R 1 ,µ T 1 ) and ( µ R 0 , µ T 0 ) .
However, many methods in the causal inference literature for estimating treatmenteffects propose different strategies for also sharing information between PO functions within a singledomain ( µ R 0 , µ R 1 ) and ( µ T 0 , µ T 1 ) [10, 13, 23].
The most common one is the TARNet architecture [10]which uses several layers to build a shared representation, followed by outcome-specific layers.
[Equation]
[Figure]
[Equation]
[Table]
sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit>
h s 1 ,l <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> h p T 0 ,l <latexit sha1_base64="(null)">(null)</latexit>
<latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> h p R 1 ,l <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> h p T 1 ,l <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit>  T ( x T ) <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit>  R ( x R ) <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit>
To obtain HTCE-TARNet (Figure 5), we propose usingfeature encoders ϕ p R , ϕ p T , ϕ s that are shared across thedifferent treatments in each domain.
Then, we constructanother building block that involves adding several representation layers on top of the feature embeddings ineach domain using domain-specific encoders Ω p T andΩ p R .
These representation layers are domain specificas their purpose is to share information between the
PO functions within a single domain.
Thus, we obtain Φ R ( x R ) =
Ω p
R
[ ϕ s ( x s ) ||
ϕ
p R ( x R )]) , Φ T ( x T ) =
Ω p T ([ ϕ s ( x s ) ||
ϕ p T ( x T )]) , which are used as input tothe corresponding (treatment-specific) hypothesis functions g Rw (Φ R ( x R )) and g Tw (Φ T ( x T )) .
This approach can be easily extended to recover HTCE- equivalents of other SNet architecture[13] that build additional representation layers to share information between PO (and propensity)estimation within each single domain [23].
Moreover, several methods have been proposed to accountfor the selection bias in the observational dataset by building balancing representations [10, 23, 24].
This can also be achieved for our HTCE-learners by enforcing regularization on top of the learntdomain-specific representations: Ω p R ( · ) and Ω p T ( · ) .
Overall, we have built the HTCE-learners topreserve the characteristics of the different CATE-learners in a single domain, but to handle theheterogeneous feature spaces and to share information between outcome functions across domains.
Evaluation
6.1 Experimental set-up
Semi-synthetic data generation.
Given that counterfactuals, and subsequently ground truth causal 316 effects are never observed in real-datasets, semi-synthetic data is needed to be able to evaluatemethods for estimating CATE.
While several benchmarks have been proposed for the standard CATE 318 estimation problem [13, 15] in a single domain, none exist for the heterogeneous transfer learning setting.
Thus, we propose a new semi-synthetic data simulation to evaluate our HTCE-learnersagainst the benchmarks.
Let X R =
( X s , X p R ) and X T =
( X s , X p T ) be patient features from realsource and target datasets respectively.
We simulate outcomes as follows:
[Equation]
where v sw,j , v p R w,j , v p T w,j , v Rj , v Tj ∼ N ( − 10 , 10) , ϵ R , ϵ T ∼ N (0 , 0 . 1) and the parameters α and β 323 control the amount of sharing between PO across and within domains respectively.
For each domain,we simulate the treatment assignment using W | X
∼ Bernoulli
( Sigmoid ( κ ( Y (1) − Y (0)))) , where 325 for κ = {+
+} there is no selection bias and the treatments are assigned randomly, while a high κ indicateshigh selection bias.
Unless otherwise specified, we set α = 0 .
5 , β = 0 .
5 and κ R = 1 , κ T = 1 .
Datasets.
We perform experiments using patient features from three real datasets with diversecharacteristics (e.g. number of features, proportion of categorical features): Twins [40], TCGA [41]and MAGGIC [42].
From the real patient features, the treatment assignments and correspondingoutcomes are simulated as described.
Refer to Appendix D for details of the datasets and of the waythe source and target domain and the shared and private features are obtained.
Due to space limitation,we report here the results on Twins.
See Appendix E for the results on the other datasets.
CATE learners and benchmark methods.
The following CATE learners are used in our experiments:
S-Learner, T-Learner, DR-Learner and TARNet.
We consider the following benchmarks: (1) trainingthe CATE learners only on the target dataset, (2) using only the shared features between the sourceand target datasets and (3) using RadialGAN [19] to ‘translate’ the source dataset into the targetdomain.
We compare these against our HTCE-learners that leverage the full source and target datasetsfor training.
To ensure a fair comparison, we fixed equivalent hyperparameters in terms of number oflayers and units in each layer for the CATE-learners trained on data from the different benchmarksand our HTCE-learners.
We describe the hyperarameter used and provide implementation details in
Appendix D. We evaluate the different methods using the the Root Mean Squared Error of estimatingτ T ( x T ) , also known as the precision of estimating heterogeneous effects (PEHE) [5].
The results areaveraged across 10 runs for which we report the mean PEHE and its standard error.
6.2 Results and discussion
[Table]
[Figure]
[Table]
[Figure]
[Table]
[Figure]
[Table]
[Figure]
[Table]
[Figure]
[Table]
[Figure]
[Table]
[Figure]
[Table]
[Figure]
[Table]
[Figure]
[Table]
[Figure]
[Table]
[Figure]
[Table]
[Figure]
[Table]
[Figure]
[Table]
[Figure]
[Table]
[Figure]
[Table]
[Figure]
[Table]
[Figure]
[Table]
[Figure]
[Table]
[Figure]
[Table]
[Figure]
[Table]
[Figure]
[Table]
[Figure]
[Table]
[Figure]
[Table]
[Figure]
[Table]
[Figure]
[Table]
Benchmarks comparison and source of gain .
We first evaluate the HTCE-learners against thebenchmarks and perform a source of gain analysis to evaluate the importance of our differentcomponents and loss functions.
We evaluate theimpact of removing the shared and private layersthat enable sharing information between the POfunctions across domains (HTCE - PO sharing),removing the orthogonal regularization loss forthe learnt shared and private feature representations in Equation 3 (HTCE - L orth z ) and removingorthogonal regularization loss from the PO layers in Equation 5 (HTCE - L ortho PO ).
Table 1 reportsresults on the Twins dataset.
Note that our HTCE-learners achieve better performance comparedto the baselines and that each component we propose brings performance improvements.
Whenanalyzing the performance across the different CATE learners we notice that the S-Learner achievesworse performance due to its strong inducting bias of fully-sharing information between PO functionswithin each domains, which becomes even more restrictive in the transfer setting.
Varying the information sharing between domains .
To further gain insights into the differencesbetween the benchmarks under different settings, we vary the parameter α , which controls the amountof information shared between the PO in the source and target dataset.
Figure 6 (top) reports theresults for this analysis on the Twins dataset.
Note that our flexible approach for information sharingbetween PO functions across domains achieves good performance both when the PO functions aresignificantly different between the source and target dataset ( α = 0 .
and also when they have thesame functional form and only depend on the shared features ( α = 1 . 0 ).
As a sanity check, we alsonotice that for ( α = 1 . 0 ) the performance of the HTCE-learners matches the one of the corresponding
P E H E
SLearner 0.2 0.4 0.6 0.8 1.0 0.
TLearner 0.2 0.4 0.6 0.8 1.0 0.
DRLearner 0.2 0.4 0.6 0.8 1.
TARNet
TargetShared features RadialGANHTCE (ours)
[Figure]
[Figure]
P E H E
SLearner
[Figure]
T 0.
[Figure]
T
[Figure] [Figure]
[Figure]
DRLearner
[Figure]
T
[Figure]
[Figure] [Figure] [Figure]
TargetShared
[Figure]
CATE learners trained only on the shared features between the two domains.
Moreover, note that forthis setting of α = 1 .
when the PO only depend on the shared features between the two domains,the different CATE learners trained only on the target dataset have a decrease in performance as theyalso need to perform the task of implicit feature selection with limited amount of data.
Varying the target dataset size.
We also evaluate performance when varying the size of the targetdataset N T .
We report in Figure 6 (bottom) the results on the Twins datasets.
Note that while our
HTCE-learners still bring benefits for all values of N T , the most performance improvements arewhen the target dataset size is small and we get diminishing returns as N T increases.
Moreover, notethat TARNet trained only on the target dataset reaches the performance of the HTCE-TARNet learnerwith less amount of data compered to T-learner trained on the target dataset vs. the HTCE-T-learner.0 2 4 6 8 10 T 0.
P E H E
R =0.
0 2 4 6 8 10 T
R =2.
0 2 4 6 8 10 T
R =10.
Target
Shared features
RadialGAN
HTCE (ours)
Effect of selection bias.
Finally, we investigate howthe selection bias in the source and target datasetsimpact transfer performance.
We consider threesetting for the selection bias in the source datasetκ R = 0 .
for random treatment assignment, κ R =2 . 0 for moderate and κ R = 10 .
for strong selectionbias.
For each setting of κ R , we vary the selectionbias in the target dataset κ T from κ T = 0 .
to κ T =10 .
and report the results on Twins for the DRlearner in Figure 7.
See Appendix E for results onthe other learners and datasets.
Note that our HTCE-DR-learner has consistent performance whenincreasing the selection bias in both datasets and when there are significant discrepancies in thetreatment assignment mechanism between the source and target datasets.
Discussion
We proposed heterogeneous transfer causal effect (HTCE) learners capable of improving the estimation of CATE on a target domain by leveraging data from a related source domain.
This representsthe first work that addresses the heterogeneous transfer learning problem for CATE estimation whichis prevalent in many causal inference application areas where the personalized effects of interventionsfor a new population need to be estimated from small target datasets with different features than theavailable source datasets [3, 16].
We hope that the insights gained from this paper, in terms of theneed for sharing information between PO functions to enable transfer and the differences between
CATE learners in the transfer setting, will help guide further model development for this problem.
In terms of limitations and directions for future work, while we focused on the binary treatment settingwhich is the most common in the causal inference literature, addressing the problem of heterogeneoustransfer learning is equally important for more complex treatment settings such as treatments withdosage [43, 44], treatment combinations [45, 46] and treatments in the temporal setting [47, 48].
Moreover, while we demonstrate the benefits of our HTCE-learners experimentally, future workshould also provide theoretical guarantees on their performance in terms of the similarities betweenthe source and target datasets.
Finally, we acknowledge that in areas such as healthcare, acting basedon incorrect estimates from such causal inference models can have life-threatening implications.
Because of this, it becomes crucial that such models undergo extensive testing through clinical trialsand expert validation and that they are only used for decision support alongside clinicians. Checklist For all authors...
(a) Do the main claims made in the abstract and introduction accurately reflect the paper’s
contributions and scope?
[Yes]
(b) Did you describe the limitations of your work?
[Yes] See Section 7.
(c) Did you discuss any potential negative societal impacts of your work?
[Yes] See
Section 7.
(d) Have you read the ethics review guidelines and ensured that your paper conforms to
them?
[Yes]
If you are including theoretical results...
(a) Did you state the full set of assumptions of all theoretical results?
[N/A]
(b) Did you include complete proofs of all theoretical results?
[N/A]
If you ran experiments...
(a) Did you include the code, data, and instructions needed to reproduce the main experi-
mental results (either in the supplemental material or as a URL)?
[No] Code will be
released upon acceptance.
(b) Did you specify all the training details (e
g., data splits, hyperparameters,
how they
were chosen)?
[Yes] See Appendix D.
(c) Did you report error bars (e
g., with respect to the random seed after running experi-
ments multiple times)?
[Yes] See Section 6 and
Appendix E.
(d) Did you include the total amount of compute and the type of resources used (e.g., type
of GPUs, internal cluster, or cloud provider)?
[Yes] See Appendix D.
If you are using existing assets (e
g., code, data, models) or curating/releasing new assets...
(a) If your work uses existing assets, did you cite the creators?
[Yes] See Section 6 and
Appendix D.
(b) Did you mention the license of the assets?
[Yes]
In addition to two public datasets,
we
use a private heart failure dataset.
We provide details for all datasets in Appendix D.
(c) Did you include any new assets either in the supplemental material or as a URL?
[N/A]
(d) Did you discuss whether and how consent was obtained from people whose data you’re
using/curating?
[Yes] We provide references to the papers introducing the datasets
which discuss how they were obtained and curated.
See Appendix D.
(e) Did you discuss whether the data you are using/curating contains personally identifiable
information or offensive content?
[Yes] See Appendix D.
If you used crowdsourcing or conducted research with human subjects...
(a) Did you include the full text of instructions given to participants and screenshots, if
applicable?
[N/A]
(b) Did you describe any potential participant risks, with links to Institutional Review
Board (IRB) approvals, if applicable?
[N/A]
(c) Did you include the estimated hourly wage paid to participants and the total amount
spent on participant compensation?
[N/A]