US 2022/0093249 A1Published application

Method and system for causal inference in presence of high-dimensional covariates and high-cardinality treatments

AssigneeTata Consultancy Services Limited

InventorsANKIT SHARMA, GARIMA GUPTA, RANJITHA PRASAD, ARNAB CHATTERJEE, LOVEKESH VIG, GAUTAM SHROFF

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Abstract

In presence of high-cardinality treatment variables, number of counterfactual outcomes to be estimated is much larger than number of factual observations, rendering the problem to be ill-posed. Furthermore, lack of information regarding the confounders among large number of covariates pose challenges in handling confounding bias. Essential is to find lower-dimensional manifold where an equivalent problem of causal inference can be posed, and counterfactual outcomes can be computed. Embodiments herein provide a method and system for CI in presence of high-dimensional covariates and high-cardinality treatments using Hi-CI DNN architecture comprising Hi-CI DNN model built by concatenating a decorrelation network and a modified regression network for jointly generating low-dimensional decorrelated covariates from the high-dimensional covariates, and predicting a set of outcomes for the input data set having the high-cardinality treatments comprising of the plurality of dosage levels by generating per-dosage level embedding to learn representation of the high-cardinality treatments.

Claims9

Dependent claims

A processor implemented method for Causal Inference (CI) in presence of high-dimensional covariates and high-cardinality treatments, the method comprising:

building, via one or more hardware processors, a High-dimensional Causal Inference Deep Neural Network (Hi-CI DNN) model executed by the one or more hardware processors, for Causal Inference (CI) from an input data set comprising the high-dimensional covariates that are processed for the high-cardinality treatments (tn (k), for a plurality of samples (n) of the input data set, with cardinality (k), wherein each of the high cardinality treatments comprising a plurality of dosage levels (e), and wherein building the Hi-CI DNN model comprises:
concatenating a decorrelation network and a modified regression network for jointly (i) generating low-dimensional decorrelated covariates from the high-dimensional covariates, and (ii) predicting a set of outcomes for the input data set having the high-cardinality treatments comprising of the plurality of dosage levels by generating per-dosage level embedding to learn representation of the high-cardinality treatments, wherein
a) the decorrelation network, executed by the one or more hardware processors, comprises an autoencoder employing a first loss function based on (i) a first component (Φ,Ψ) that minimizes a mean-squared loss between the low-dimensional decorrelated covariates and the high-dimensional covariates, where Φ represents encoder of the autoencoder and Ψ represents decoder of the autoencoder and (ii) a second component (Φ), which is a cross entropy measure and a third component 2,1(MD) enabling confounding bias compensation to minimize disparity between factual treatments and counter factual treatments among the plurality of treatments, wherein MD is a matrix representing mixed norm on difference of means, and wherein the first loss function of the decorrelation network is represented by:
(Φ,Ψ,βγ)=(Φ)+β(Φ,Ψ)+γ2,1(MD), where β,γ are values obtained by hyperparameter tuning on validation datasets;
and
b) the modified regression network, executed by the one or more hardware processors, comprising a plurality of embeddings Ωe corresponding to the plurality of dosage levels and employing a second loss function comprising a root mean square error (RMSE) loss function and represented by:
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wherein yn(ke) is groundtruth and ŷn(ke) is the set of outcomes predicted by the Hi-CI model, and wherein ŷn=Ωe([Φ(xn),tn]T);
and
training, via the one or more hardware processors, the Hi-CI DNN model for predicting the set of outcomes for the input data set in accordance to an overall loss function of the Hi-CI DNN model, wherein the overall loss function jointly employs the first loss function and the second loss function and is represented by:
(Φ,Ψ,Ωe,β,γ,λ)=(Φ,Ψ,β,γ)+λ(y,ŷ)

58 more elements

A system for Causal Inference (CI) in presence of high-dimensional covariates and high-cardinality treatments, the system comprising:

a memory storing instructions;
one or more Input/Output (I/O) interfaces;
and
one or more hardware processors coupled to the memory via the one or more I/O interfaces, wherein the one or more hardware processors are configured by the instructions to:
build a High-dimensional Causal Inference Deep Neural Network (Hi-CI DNN) model for Causal Inference (CI) from an input data set comprising the high-dimensional covariates that are processed for the high-cardinality treatments (tn(k)), for a plurality of samples (n) of the input data set, with cardinality k, wherein each of the high cardinality treatments comprising a plurality of dosage levels, wherein the Hi-CI DNN model comprises:
concatenating a decorrelation network and a modified regression network for jointly (i) generating low-dimensional decorrelated covariates from the high-dimensional covariates, and (ii) predicting a set of outcomes for the input data set having the high-cardinality treatments comprising of the plurality of dosage levels by generating per-dosage level embedding to learn representation of the high-cardinality treatments, wherein
a) the decorrelation network, executed by the one or more hardware processors, comprises an autoencoder employing a first loss function based on (i) a first component (Φ,Ψ) that minimizes a mean-squared loss between the low-dimensional decorrelated covariates, where Φ represents encoder of the autoencoder and Ψ represents decoder of the autoencoder and the high-dimensional covariates, and (ii) a second component (Φ), which is a cross entropy measure and a third component 2,1(MD) enabling confounding bias compensation to minimize disparity between factual treatments and counter factual treatments among the plurality of treatments, wherein MD is a matrix representing mixed norm on difference of means, and wherein the first loss function of the decorrelation network is represented by:
(Φ,Ψ,β,γ)=(Φ)+β(Φ,Ψ)+γ2,1(MD), where β,γ are values obtained by hyperparameter tuning on validation datasets;
and
b) the modified regression network, executed by the one or more hardware processors, comprising a plurality of embeddings Ωe corresponding to the plurality of dosage levels and employing a second loss function comprising a root mean square error (RMSE) loss function and represented by:
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wherein yn(ke) is groundtruth and ŷ(ke) is set of outcomes predicted by the Hi-CNN model, and wherein ŷn=Ωe([Φ(xn),tn]T);
and
train the Hi-CI DNN model for predicting the set of outcomes for the input data set in accordance to an overall loss function of the Hi-CI DNN model, wherein the overall loss function jointly employs the first loss function and the second loss function and is represented by:
(Φ,Ψ,Ωe,β,γ,λ)=(Φ,Ψ,β,γ)+λ(y,ŷ).

62 more elements

One or more non-transitory machine-readable information storage mediums comprising one or more instructions, which when executed by one or more hardware processors causes a method for causal inference (CI) in presence of high-dimensional covariates and high-cardinality treatments, the method comprising:

building a High-dimensional Causal Inference Deep Neural Network (Hi-CI DNN) model executed by the one or more hardware processors, for Causal Inference (CI) from an input data set comprising the high-dimensional covariates that are processed for the high-cardinality treatments (tn(k)), for a plurality of samples (n) of the input data set, with cardinality (k), wherein each of the high cardinality treatments comprising a plurality of dosage levels (e), and wherein building the Hi-CI DNN model comprises:
concatenating a decorrelation network and a modified regression network for jointly (i) generating low-dimensional decorrelated covariates from the high-dimensional covariates, and (ii) predicting a set of outcomes for the input data set having the high-cardinality treatments comprising of the plurality of dosage levels by generating per-dosage level embedding to learn representation of the high-cardinality treatments, wherein
a) the decorrelation network, executed by the one or more hardware processors, comprises an autoencoder employing a first loss function based on (i) a first component (Φ,Ψ) that minimizes a mean-squared loss between the low-dimensional decorrelated covariates and the high-dimensional covariates, where Φ represents encoder of the autoencoder and W represents decoder of the autoencoder and (ii) a second component (Φ), which is a cross entropy measure and a third component 2,1(MD) enabling confounding bias compensation to minimize disparity between factual treatments and counter factual treatments among the plurality of treatments, wherein MD is a matrix representing mixed norm on difference of means, and wherein the first loss function of the decorrelation network is represented by:
(Φ,Ψ,β,γ)+(Φ)+β(Φ,Ψ)+γ2,1(MD), where β,γ are values obtained by hyperparameter tuning on validation datasets;
and
b) the modified regression network, executed by the one or more hardware processors, comprising a plurality of embeddings Ωe corresponding to the plurality of dosage levels and employing a second loss function comprising a root mean square error (RMSE) loss function and represented by:
ℒ
ℛℳ𝒮ℰ
⁡
(
y
,
y
^
)
=
1
N
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∑
n
=
1
N
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∑
k
=
1
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∑
e
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1
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(
k
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y
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k
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2
,
wherein yn(ke) is groundtruth and ŷn(ke) is the set of outcomes predicted by the Hi-CI model, and wherein ŷn=Ωe([Φ(xn), tn]T);
and
training the Hi-CI DNN model for predicting the set of outcomes for the input data set in accordance to an overall loss function of the Hi-CI DNN model, wherein the overall loss function jointly employs the first loss function and the second loss function and is represented by:
(Φ,Ψ,Ωe,β,γ,λ)=(Φ,Ψ,β,γ)+λ(y,ŷ).

58 more elements

Dependencies are inferred from the claim text.