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THE PATENTS ACT, 1970
(39 of 1970)
&
THE PATENT RULES, 2003
COMPLETE SPECIFICATION (See Section 10 and Rule 13)
Title of invention:
METHOD AND SYSTEM FOR CAUSAL INFERENCE IN HETEROGENEOUS POPULATION USING META-LEARNING
Applicant
Tata Consultancy Services Limited A company Incorporated in India under the Companies Act, 1956
Having address:
Nirmal Building, 9th floor,
Nariman point, Mumbai 400021,
Maharashtra, India
Preamble to the description
The following specification particularly describes the invention and the manner in which it is to be performed.

TECHNICAL FIELD [001] The disclosure herein generally relates to the field of data mining and, more particular, to a method and system for causal inference in heterogeneous population using meta-learning.
BACKGROUND
[002] Inference on observational data is becoming extremely relevant due to the widespread availability of data in fields like healthcare, education and retail etc. Further, the observational data is accrued from multiple homogeneous subgroups of a heterogeneous population. Often, observational data is scarce, and study-population is heterogeneous. Hence, generalizing the inference mechanism over such data is challenging.
[003] Conventional methods for observational data inference obtain average treatment effect at aggregate level directly rather than at individual level by accounting for the selection bias using propensity scores hence creating unbiased estimators of the averaged treatment effect. Many deep neural network based causal inference approaches, which handle the bias, are randomly initiated. However the conventional methods fails to predict factual and counterfactual response at individual subject level.
SUMMARY [004] Embodiments of the present disclosure present technological improvements as solutions to one or more of the above-mentioned technical problems recognized by the inventors in conventional systems. For example, in one embodiment, a method for causal inference in heterogeneous population using meta-learning is provided. The method includes receiving a structured data, wherein the structured data comprises a plurality of covariates, a factual treatment data and a counterfactual response data of a plurality of subjects under test. Further, the method includes creating a set of tasks from the structured data, wherein each task is associated with a factual data. The method of creating the set of tasks includes the following steps: (i) computing of the Joint Probability

Density Function (JPDF) for the plurality of covariates (ii) segmenting the plurality of subjects under test based on the JPDF of the plurality of covariates to obtain a plurality of disjoint chunks and (iii) creating the set of tasks by combining the plurality of disjoint chunks in a predetermined proportion. Further the method includes training a machine learning network with the set of tasks until the predefined number of iterations, wherein the machine learning network includes a causal inference framework and a meta-learning framework. The causal inference framework includes the representation layer and the hypothesis layer. The representation layer computes the representation layer weight and the hypothesis layer computes the hypothesis layer weight. The representation layer maps the factual and counterfactual population to the space where the imbalance between the two is minimum. The hypothesis layer predicts the factual and counterfactual response for each subject under test. The method of training the machine learning framework includes the following steps: (i) Sampling the first task from the set of tasks using random sampling technique (ii) computing the first set of weights for a first sampled task, wherein the first set of weights comprising a representation layer weight and a hypothesis layer weight (iii) updating weights of the meta-learning framework based on the corresponding first set of weights (iv) predicting a counterfactual response for the first sampled task based on the updated weights of the meta-learning framework (v) Sampling a second task from the set of tasks using random sampling technique (vi) computing a second set of weights for a second sampled task based on the first set of weights (vii) updating weights of the meta-learning framework using the corresponding second set of weights and (viii) predicting a counterfactual response for the second sampled task based on the updated weights of the meta-learning framework. Furthermore the method includes fine-tunes the weights associated the meta-learning framework of the trained machine learning network using a sample of an unseen task.
Finally the method includes predicting a counterfactual response for the unseen task using the trained machine learning technique.

[005] In another aspect, a system for causal inference in heterogeneous population using meta-learning is provided. The system includes at least one memory storing programmed instructions, one or more Input /Output (I/O) interfaces, and one or more hardware processors operatively coupled to the at least one memory, wherein the one or more hardware processors are configured by the programmed instructions to receive a structured data, wherein the structured data comprises a plurality of covariates, a factual treatment data and a counterfactual response data of a plurality of subjects under test. Further, the one or more hardware processors are configured by the programmed instructions to create a set of tasks from the structured data, wherein each task is associated with a factual data. The method of creating the set of tasks includes the following steps: (i) computing the Joint Probability Density Function (JPDF) for the plurality of covariates (ii) segmenting the plurality of subjects under test based on the JPDF of the plurality of covariates to obtain a plurality of disjoint chunks and (iii) creating the set of tasks by combining the plurality of disjoint chunks in a predetermined proportion. Further, the one or more hardware processors are configured by the programmed instructions to train a machine learning network with the set of tasks until the predefined number of iterations, wherein the machine learning network includes a causal inference framework and a meta-learning framework. The causal inference framework includes a representation layer and a hypothesis layer. The representation layer computes a representation layer weight and the hypothesis layer computes a hypothesis layer weight. The representation layer maps the factual and counterfactual population to the space where the imbalance between the two is minimum. The hypothesis layer predicts the factual and counterfactual response for each subject under test. The method of training the machine learning framework includes the following steps: (i) Sampling the first task from the set of tasks using random sampling technique (ii) computing the first set of weights for a first sampled task, wherein the first set of weights comprising a representation layer weight and a hypothesis layer weight (iii) updating weights of the meta-learning framework based on the corresponding first set of weights (iv) predicting a counterfactual response for the first sampled task based on the updated weights

of the meta-learning framework (v) Sampling a second task from the set of tasks using random sampling technique (vi) computing a second set of weights for a second sampled task based on the first set of weights (vii) updating weights of the meta-learning framework using the corresponding second set of weights and (viii) predicting a counterfactual response for the second sampled task based on the updated weights of the meta-learning framework. Furthermore, the one or more hardware processors are configured by the programmed instructions to fine-tune the weights associated the meta-learning framework of the trained machine learning network using a sample of an unseen task. Finally, the one or more hardware processors are configured by the programmed instructions to predict a counterfactual response for the unseen task using the trained machine learning technique.
[006] In yet another aspect, a computer program product including a non-transitory computer-readable medium having embodied therein a computer program for method and system for causal inference in heterogeneous population using meta-learning is provided. The computer readable program, when executed on a computing device, causes the computing device to receive a structured data, wherein the structured data includes a plurality of covariates, a factual treatment data and a counterfactual response data of a plurality of subjects under test. Further, the computer readable program, when executed on a computing device, causes the computing device to create a set of tasks from the structured data, wherein each task is associated with a factual data. The method of creating the set of tasks includes the following steps: (i) computing the Joint Probability Density Function (JPDF) for the plurality of covariates (ii) segmenting the plurality of subjects under test based on the JPDF of the plurality of covariates to obtain a plurality of disjoint chunks and (iii) creating the set of tasks by combining the plurality of disjoint chunks in a predetermined proportion. Further, the computer readable program, when executed on a computing device, causes the computing device to train a machine learning network with the set of tasks until the predefined number of iterations, wherein the machine learning network includes a causal inference framework and a meta-learning framework. The causal inference

framework includes a representation layer and a hypothesis layer. The representation layer computes a representation layer weight and the hypothesis layer computes a hypothesis layer weight. The representation layer maps the factual and counterfactual population to the space where the imbalance between the two is minimum. The hypothesis layer predicts the factual and counterfactual response for each subject under test. The method of training the machine learning framework includes the following steps: (i) Sampling the first task from the set of tasks using random sampling technique (ii) computing the first set of weights for a first sampled task, wherein the first set of weights comprising a representation layer weight and a hypothesis layer weight (iii) updating weights of the meta-learning framework based on the corresponding first set of weights (iv) predicting a counterfactual response for the first sampled task based on the updated weights of the meta-learning framework (v) Sampling a second task from the set of tasks using random sampling technique (vi) computing a second set of weights for a second sampled task based on the first set of weights (vii) updating weights of the meta-learning framework using the corresponding second set of weights and (viii) predicting a counterfactual response for the second sampled task based on the updated weights of the meta-learning framework. Furthermore, the computer readable program, when executed on a computing device, causes the computing device to fine-tune the weights associated the meta-learning framework of the trained machine learning network using a sample of an unseen task. Finally, the computer readable program, when executed on a computing device, causes the computing device to predict a counterfactual response for the unseen task using the trained machine learning technique.
[007] It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention, as claimed.
BRIEF DESCRIPTION OF THE DRAWINGS [008] The accompanying drawings, which are incorporated in and
constitute a part of this disclosure, illustrate exemplary embodiments and, together
with the description, serve to explain the disclosed principles:

[009] FIG. 1 is a functional block diagram of a system for causal inference in heterogeneous population using meta-learning, according to some embodiments of the present disclosure.
[010] FIG. 2 is an exemplary architecture of the system for causal inference in heterogeneous population using meta-learning, according to some embodiments of the present disclosure.
[011] FIG. 3 depicts the Joint Probability Density Function (JPDF) of a plurality of covariates for causal inference in heterogeneous population using meta-learning, according to some embodiments of the present disclosure.
[012] FIG. 4 is an exemplary block diagram of a MetaCI (Meta Causal Inference) framework for causal inference in heterogeneous population using meta-learning, according to some embodiments of the present disclosure.
[013] FIG. 5A and 5B are exemplary flow diagrams for a processor implemented method for causal inference in heterogeneous population using meta-learning implemented by the system of FIG. 1, according to some embodiments of the present disclosure.
DETAILED DESCRIPTION OF EMBODIMENTS
[014] Exemplary embodiments are described with reference to the accompanying drawings. In the figures, the left-most digit(s) of a reference number identifies the figure in which the reference number first appears. Wherever convenient, the same reference numbers are used throughout the drawings to refer to the same or like parts. While examples and features of disclosed principles are described herein, modifications, adaptations, and other implementations are possible without departing from the spirit and scope of the disclosed embodiments. It is intended that the following detailed description be considered as exemplary only, with the true scope and spirit being indicated by the following claims.
[015] Embodiments herein provide a method and system for causal inference in heterogeneous population using meta-learning. The system for causal

inference in heterogeneous population using meta-learning provides a MetaCI (Meta Causal Inference) framework with a goal of answering counterfactual questions in context of causal inference (CI), wherein a plurality of factual observations are obtained from a plurality of homogeneous subgroups of subjects. The MetaCI framework includes a CI (Causal Inference) framework and a meta optimization network. The CI is designed to generalize from factual to counterfactual distribution in order to tackle covariate shift. The meta optimization technique known as “Reptile” optimization technique is built on a causal inference framework. The CI framework includes a representation layer and a hypothesis layer. The representation layer and the hypothesis layer are associated with a representation layer weight and a hypothesis layer weight accordingly. Initially a plurality of tasks are created by using observational data. Further, the MetaCI framework is trained using the plurality of tasks. The trained MetaCI framework is further used to predict a counterfactual response of an unseen task in an efficient manner. The Reptile optimization technique along with the CI framework provides maximum efficiency in prediction of the counterfactual response of an unseen task.
[016] Referring now to the drawings, and more particularly to FIG. 1 through 3B, where similar reference characters denote corresponding features consistently throughout the figures, there are shown preferred embodiments and these embodiments are described in the context of the following exemplary system and/or method.
[017] FIG. 1 is a functional block diagram of a system 100 for causal inference in heterogeneous population using meta-learning, according to some embodiments of the present disclosure. The system 100 includes or is otherwise in communication with hardware processors 102, at least one memory such as a memory 104, an I/O interface 112. The hardware processors 102, memory 104, and the Input /Output (I/O) interface 112 may be coupled by a system bus such as a system bus 108 or a similar mechanism. In an embodiment, the hardware processors 102 can be one or more hardware processors.

[018] The I/O interface 112 may include a variety of software and hardware interfaces, for example, a web interface, a graphical user interface, and the like. The I/O interface 112 may include a variety of software and hardware interfaces, for example, interfaces for peripheral device(s), such as a keyboard, a mouse, an external memory, a printer and the like. Further, the interface 112 may enable the system 100 to communicate with other devices, such as web servers and external databases.
[019] The I/O interface 112 can facilitate multiple communications within a wide variety of networks and protocol types, including wired networks, for example, local area network (LAN), cable, etc., and wireless networks, such as Wireless LAN (WLAN), cellular, or satellite. For the purpose, the I/O interface 112 may include one or more ports for connecting a number of computing systems with one another or to another server computer. The I/O interface 112 may include one or more ports for connecting a number of devices to one another or to another server.
[020] The one or more hardware processors 102 may be implemented as one or more microprocessors, microcomputers, microcontrollers, digital signal processors, central processing units, state machines, logic circuitries, and/or any devices that manipulate signals based on operational instructions. Among other capabilities, the hardware processor 102 is configured to fetch and execute computer-readable instructions stored in the memory 104.
[021] The memory 104 may include any computer-readable medium known in the art including, for example, volatile memory, such as static random access memory (SRAM) and dynamic random access memory (DRAM), and/or non-volatile memory, such as read only memory (ROM), erasable programmable ROM, flash memories, hard disks, optical disks, and magnetic tapes. In an embodiment, the memory 104 includes a plurality of modules 106, a prediction unit 120. The memory 104 also includes a data repository 110 for storing data processed, received, and generated by one or more of the modules 106 and the prediction unit 120. The modules 106 may include routines, programs, objects,

components, data structures, and so on, which perform particular tasks or implement particular abstract data types.
[022] The memory 104 also includes module(s) 106 and the data repository 110. The module(s) 106 include programs or coded instructions that supplement applications or functions performed by the system 100 for causal inference in heterogeneous population using meta-learning. The modules 106, amongst other things, can include routines, programs, objects, components, and data structures, which perform particular tasks or implement particular abstract data types. The modules 106 may also be used as, signal processor(s), state machine(s), logic circuitries, and/or any other device or component that manipulates signals based on operational instructions. Further, the modules 106 can be used by hardware, by computer-readable instructions executed by a processing unit, or by a combination thereof. The modules 106 can include various sub-modules (not shown). The modules 106 may include computer-readable instructions that supplement applications or functions performed by the system 100 for causal inference in heterogeneous population using meta-learning.
[023] The data repository 110 may include observational data of the plurality of subjects under test and other data. Further, the other data may serve as a repository for storing data that is processed, received, or generated as a result of the execution of one or more modules in the module(s) 106 and the modules associated with the prediction unit 120.
[024] Although the repository 110 is shown internal to the system 100, it will be noted that, in alternate embodiments, the repository 110 can also be implemented external to the computing device 100, where the repository 110 may be stored within a database (not shown in FIG. 1) communicatively coupled to the system 100. The data contained within such external database may be periodically updated. For example, new data may be added into the database (not shown in FIG. 1) and/or existing data may be modified and/or non-useful data may be deleted from the database (not shown in FIG. 1). In one example, the data may be stored in an external system, such as a Lightweight Directory Access Protocol (LDAP) directory and a Relational Database Management System (RDBMS).

[025] Learning causal relationships is the heart and soul of several domains including healthcare, advertising, education, economics, etc. For instance, personalized and targeted treatment considering a subject’s health indicators is crucial in healthcare, targeted advertising campaign is essential to achieve higher profit margin in channel attribution. Causal inference (CI) aims to infer unbiased causality effect of a treatment from observational data by factoring impact of the confounding variables of the plurality of subjects under test. In the context of observational studies, confounding variables affect treatment and outcome, and hence, disentangling the effect of the cofounding variables is the key to achieve treatment effectiveness. Here the study-population is heterogeneous, and hence, developing CI-based systems that generalize for new unseen subgroups in data, as provided by the system 102 disclosed herein, is essential in order to provide better targeted interventions.
[026] FIG. 2 is an exemplary architecture of the system for causal inference in heterogeneous population using meta-learning, according to some embodiments of the present disclosure. Now referring to FIG. 2, the exemplary architecture includes a causal inference framework and a meta-learning framework. The causal inference framework includes a representation layer a hypothesis layer. The meta-learning framework is the Reptile optimization framework. The Reptile optimization framework includes a plurality of Reptile model parameters ( Ψ) and the model parameters are adapted for fast learning.
[027] The CI framework is explained as follows: Let T represent a set of treatments, be a set of contexts associated with the set of treatments, and be a set of possible outcomes corresponding to a task. Let the treatment be binary, T G {0,1}, where t = 1 is assigned as ‘treated’ and t = 0 as ‘control’. For a given context one of the observed potential outcomes according
to the treatment provided, i.e., if is observed and if
is observed, and accordingly the optimized Individual Treatment Effect (ITE) value for the context in task ω, xw is given by equation 1.

Further, Average Treatment Effect (ATE) is given by equation 2.


The objective function to minimize an imbalance between the factual and counterfactual population is given by equation 3.

where are hyperparameters that control the strength of the imbalance
penalties, is a model complexity term represents the factual distribution,
and represents the counterfactual distribution, respectively, and disc is
the discrepancy measure
[028] The Reptile framework of the FIG. 2 is explained as follows: Given the plurality of Reptile model parameters Ψ and a randomly sampled task ω, with a corresponding loss the reptile optimization is as given in equation 4.

is an update operator, and L represents the Stochastic Gradient Descent (SGD) epochs.
[029] The Reptile framework sampling task co, followed by learning the plurality of Reptile model parameters using an update operator (e.g., SGD) on the data pertaining to co, and updates these parameters by learning on different tasks. The training phase of the Reptile optimization framework provides a meta-initialization for the plurality of Reptile model parameters Ψ of the network, such that, for a new unseen task, network can be fine-tuned using this meta-initialization by using a small amount of data from a new task.
[030] In embodiments having multiple substructures in the deep neural network model, a ‘multi-Reptile’ framework is used. The ‘multi-Reptile’ framework employs different learning rates for each the plurality of Reptile model parameters of the multiple substructures. A parallel version of the Reptile optimization technique, providing solution for the problem given in equation 1 is given in equation 5.

where ɛ is an adaptive learning rate, and is obtained after applying the update operator on the task data. The objective of the present disclosure is to

learn a model for counterfactual inference. Hence, is used as a stochastic
gradient descent operator which optimizes a cost function pertaining to counterfactual inference. The meta optimization framework to tackle both, the prior shift that occurs due to a drift in the feature distribution across tasks, and the concept shift that occurs due to a drift in probability distribution of the target variables.
[031] The prediction unit 120, executed by the one or more processors of the system 100, receives a structured data. The structured data includes a plurality of covariates, factual treatment data and factual response data of the plurality of subjects under test. For example, the structured data be an observational data associated with a subject undergoing a medical treatment and the present disclosure aims at predicting the counterfactual response for the treatment. For example, the plurality of covariates can be covariates measuring different aspects of mother and infant like age of mother, bilirubin index of mother, number of cigarettes smoked by mother. The factual treatment data can be home visit by a specialist or not. The factual response data can be “future cognitive test score of infant”.
[032] Further, the prediction unit 120, executed by the one or more processors of the system 100, creates a set of tasks from the structured data. Each task is associated with a factual data. The task creation method includes the following steps. (i) compute of a Joint Probability Density Function (JPDF) for the plurality of covariates (ii) segment the plurality of subjects under test based on the JPDF of the plurality of covariates to obtain a plurality of disjoint chunks and (iii) create the set of tasks by combining the plurality of disjoint chunks in a predetermined proportion;
[033] Defining task similarity is the key overarching challenge in meta learning framework. In the presence of heterogeneity in the population, knowledge regarding the features specific to subgroups, which are also the confounding variables are considered in order to define tasks. The tasks are defined by combining a majority of samples from one subgroup, and a few

samples from other subgroups in fixed proportions. Mathematically, it ensured that a subgroup that lies in a given region of the joint distribution is chosen, and mixed with samples from smaller disjoint regions of the same joint probability distribution using the JPDF of the confounding variables, as depicted in FIG. 3. FIG. 3 depicts the JPDF of the plurality of covariates for causal inference in heterogeneous population using meta-learning, according to some embodiments of the present disclosure.
[034] Now referring to FIG. 3, the task T1 is formed by combining the subgroup 302, 304, 306 and 308. Maximum proportion is taken from the subgroup 302 and minimum proportion is taken from other subgroups 304, 306 and 308.
[035] Further, the prediction unit 120, executed by one or more processors of the system 100, a machine learning network with the set of tasks until a predefined number of iterations, wherein the machine learning network comprising a causal inference framework and a meta-learning framework. The causal inference framework includes a representation layer and a hypothesis layer and. The representation layer computes the representation layer weight and the hypothesis layer computes the hypothesis layer weight. The representation layer maps the factual and counterfactual population to the space where the imbalance between the two is minimum. The hypothesis layer predicts the factual and counterfactual response for each subject under test
[036] For example, the machine learning network can be the MetaCI framework. The training of the MetaCI framework includes the following steps: (i) sampling a first task from the set of tasks using random sampling technique (ii) compute a first set of weights for a first sampled task, wherein the first set of weights comprising a representation layer weight and a hypothesis layer weight (iii) update weights of the meta-learning framework based on the corresponding first set of weights (iv) predict a counterfactual response for the first sampled task based on the updated weights of the meta-learning framework (v) sample a second task from the set of tasks using random sampling technique (vi) compute a second set of weights for a second sampled task based on the first set of weights (vii) update weights of the meta-learning framework using the corresponding second

set of weights and (viii) predict a counterfactual response for the second sampled task based on the updated weights of the meta-learning framework.
[037] FIG. 4 is an exemplary block diagram of the MetaCI framework for causal inference in heterogeneous population using meta-learning, according to some embodiments of the present disclosure. Now referring to FIG. 4, the MetaCI framework is explained corresponding to the task ω as given in the MetaCI algorithm. The FIG. 4 includes the CI framework 402 and the multi-Reptile framework 404. The dotted blocks 408 and 410 are intermediate layers of the CI framework. The solid block 408 is the representation layer and the solid block 412 is the hypothesis layer. A task is indicated as ω and indicates the
context of the task ‘t’ in the dotted block indicates the factual data of the
corresponding task, is the intermediate weight before computing the
representation layer weight and is the intermediate weight before
computing the hypothesis layer weight The solid block 414 computes the
loss function of the CI framework as given in equation 3.
[038] In an embodiment, let a pool of train tasks be Initially, a first
task ω from the pool is sampled. Let the sampled task be task T1
corresponding to first iteration. Further, the set of weights of the representation layer 402 and weights for hypothesis layer404 are computed for task
T1. The weight and of reptile framework for representation layer
and the hypothesis layer are updated using weights of representation layer and weights of hypothesis layer learned using T1. Further, a second task ω
from the pool is sampled. Let the second sampled task be task T2. The set of
weights of the representation layer and weights for hypothesis layer
using task T2 are computed. The weights of reptile framework for representation layer hypothesis layer are updated using weights of representation
layer (W˜ Φ) and weights of hypothesis layer learned using T2. This
sampling of task, computation of the set of weights and updating of the weights associated with the Reptile framework is continued for ‘R’ iterations. The weights of the reptile framework and obtained after R iterations are the
desired trained weights of reptile framework.

[039] In an embodiment, the MetaCI algorithm is given below:

[040] In an embodiment, training the MetaCI framework is explained as follows: Let the set of tasks be T1, T2,……,TR. Initially, the task T1 is sampled using the random sampling technique. The representation layer weight and
the hypothesis layer weight (Wh) are computed for the sampled task T1. Further, the weights of the Reptile framework are updated with the
weights and (Wh) corresponding to the task T1. Further, the counterfactual
response for the task T1 is predicted using the updated Reptile framework.
[041] Further, the task T2 is sampled using the random sampling technique. The representation layer weight (WΦ) and the hypothesis layer weight (Wh) are computed for the sampled task T2 using the weights Further, the Reptile framework is updated to weights corresponding to the task T2. Further, the counterfactual response for the task T2 is predicted using the updated Reptile framework.
[042] Further, the task T3 is sampled using the random sampling technique. The representation layer weight and the hypothesis layer weight
(Wh) are computed for the sampled task T3 using the weights Further, the Reptile framework is updated to the weights

corresponding to the task T3. Further, the counterfactual response for the task T3 is predicted using the updated Reptile framework. This iteration is performed until a predefined number of times, for example 500 times.
[043] Further, the prediction unit 120, executed by one or more processors of the system 100, fine-tunes the weights associated the meta-learning framework of the trained machine learning network using a sample of an unseen task.
[044] Further, the prediction unit 120, executed by one or more processors of the system 100, predicts a counterfactual response for the unseen task using the trained machine learning technique.
[045] FIG. 5A and 5B are exemplary flow diagrams for a processor implemented method for causal inference in heterogeneous population using meta-learning implemented by the system of FIG. 1, according to some embodiments of the present disclosure. The method 500 may be described in the general context of computer executable instructions. Generally, computer executable instructions can include routines, programs, objects, components, data structures, procedures, modules, functions, etc., that perform particular functions or implement particular abstract data types. The method 500 may also be practiced in a distributed computing environment where functions are performed by remote processing devices that are linked through a communication network. The order in which the method 500 is described is not intended to be construed as a limitation, and any number of the described method blocks can be combined in any order to implement the method 500, or an alternative method. Furthermore, the method 300 can be implemented in any suitable hardware, software, firmware, or combination thereof.
[046] At 502, the method 500, receives, by a one or more hardware processors, a structured data, wherein the structured data includes a plurality of covariates, factual treatment data and factual response data of the plurality of subjects under test.
[047] At 504, the method 500, creates, by the one or more hardware processors, the set of tasks from the structured data, wherein each task is

associated with a factual data. The method of creating the set of tasks includes the following steps: (i) computing of the Joint Probability Density Function (JPDF) for the plurality of covariates (ii) segmenting the plurality of subjects under test based on the JPDF of the plurality of covariates to obtain a plurality of disjoint chunks and (iii) creating the set of tasks by combining the plurality of disjoint chunks in a predetermined proportion.
[048] At 506, the method 500, trains, by the one or more hardware processors, the machine learning network with the set of tasks until the predefined number of iterations, wherein the machine learning network includes the causal inference framework and the meta-learning framework. The causal inference framework comprises the representation layer and the hypothesis layer. The representation layer computes the representation layer weight and the hypothesis layer computes the hypothesis layer weight. The representation layer maps the factual and counterfactual population to the space where the imbalance between the two is minimum. The hypothesis layer predicts the factual and counterfactual response for each subject under test. The method of training the machine learning framework includes the following steps: (i) Sampling the first task from the set of tasks using random sampling technique (ii) computing the first set of weights for a first sampled task, wherein the first set of weights comprising a representation layer weight and a hypothesis layer weight (iii) updating weights of the meta-learning framework based on the corresponding first set of weights (iv) predicting a counterfactual response for the first sampled task based on the updated weights of the meta-learning framework (v) Sampling a second task from the set of tasks using random sampling technique (vi) computing a second set of weights for a second sampled task based on the first set of weights (vii) updating weights of the meta-learning framework using the corresponding second set of weights and (viii) predicting a counterfactual response for the second sampled task based on the updated weights of the meta-learning framework.
[049] At 508, the method 500, fine-tunes, by the one or more hardware processors, the weights associated the meta-learning framework of the trained machine learning network using a sample of an unseen task.

[050] At 510, the method 500, predicts, by the one or more hardware processors, the counterfactual response for the unseen task using the trained machine learning technique.
[051] In an embodiment, the system 100 is experimented as follows: In an embodiment, the system 100 is tested with two datasets including a synthetically generated advertisement dataset and a semi-synthetic IHDP (Infant Health Development Program) dataset.
[052] Synthetic advertisement dataset: The sample size N = 2000 and number of features/covariates P = 200. Further, the set of features N(0,1), and the basis functions are generated. The treatment T is
restricted as being binary, and the treatment is generated as:
and 0 otherwise. Further, the response is generated as
Here, is assigned set to generate data for demonstrating the effect of
covariate. Further, the response is generated as
Here, set is set to generate data for demonstrating the effect of covariate
shift, and set 0 as 1, 10 and 20 to generate data for demonstrating the effect of concept shift. Note that the features have confounding effects on both the
treatment and the outcome, and the rest of the features contribute to the noise in the model.
[053] Semi-synthetic IHDP dataset: The IHDP dataset includes measurements of mother and children for studying the effect of specialist home visits on future cognitive test scores. The dataset includes 4302 infants having 25 features. Out of these, 8 are selected based on ACIC (Atlantic Causal Inference Conference) challenge to obtain context information X. Specifically, these features form the basis of the meta-learning tasks obtained using the DGP.
[054] Task creation for Reptile: In order to appropriately provide tasks to the MetaCI framework in presence of covariate shift, 2000 users distinguished based on the set of features are generated, for number of tasks defined by cardinality of is disjoint chunks, and mixed with samples from other

chunks in the ratio 3 : 2, i.e., each task consists of 60% of samples from a given chunk, and 40% of samples in equal proportion from k other chunks. For every subgroup, is generated. In the single feature case, the data is split
on the basis of the first feature which is one of the confounding variables. In the case of multiple confounding features, the data is split on the basis of the first two features which are confounding. Here, the tasks are created based on the JPDF of the confounding features.
[055] Tasks in IHDP dataset: Here, the tasks are defined by dividing the entire population of infants, given as a finite number of contexts in the ACIC challenge dataset, 2017, into equal sized chunks. The chunks are created based
on the JPDF of multiple confounding features. Specifically, mother’s age, child’s bilirubin level and mother’s place of birth are considered as cofounding featured. Each chunk is mixed with samples from other chunks in the ratio 3 : 2, i.e., each task dataset, consists of 60% of samples from a given chunk, and 40 % of
samples in equal proportion from k other chunks. For each of the tasks, T and is
generated synthetically using hetroskedastic, additive error DGP. In both the above cases, the number of chunks used for mixing (k) is an experimental variable and lies in range
[056] Concept and covariate shift: Tasks in synthetic and IHDP dataset scenario: In order to demonstrate the performance of MetaCI in the presence of concept shift, two different generation processes which differ in generation of the response variable Y are used and two types of tasks are created accordingly.
1. Case 1- concept shift using 2 DGPs: Based on the confounding features of the datasets, 4 chunks per DGP, and 3 chunks per DGP are considered in synthetic and IHDP datasets, respectively.
2. Case 2- concept shift using 3 DGPs: 3 chunks per DGP and 2 chunks per DGP are considered in synthetic and IHDP datasets, respectively.
[057] In both the above cases, the chunks are mixed within and across groups by retaining 60% of the samples of one chunk, and replacing the remaining 40% with samples from other chunks, to create tasks. The mixed chunks

contribute to generating the responses as dictated by the number of DGPs. Across DGPs, the parameters of the distribution which is used to sample is varied
to demonstrate concept shift.
[058] Training of MetaCI framework: The plurality of tasks |Ω| are splitted into train tasks and a test task. Every train task is divided in the
ratio 1 : 1 corresponding to training and validation and test task is divided in the ratio 2 : 1 : 1 corresponding to training, validation and test sets. The MetaCI framework is trained for 1000 iterations by sampling a train task in each iteration. For each iteration (r), weights (Wr) of causal meta model are computed after L = 64 epochs of mini-batch Stochastic Gradient Descent (SGD) over the batches of train set of train task. These weights during training of MetaCI) are
then used to update the initial weights present at the start of each iteration
using reptile update equation 5.
[059] In an embodiment, a set of best train task hyper-parameters (learning rate, dropout) correspond to the least value of validation loss function averaged across all iterations are chosen. Further, the performance of the system based on the chosen hyper parameters are evaluated on the test set of test task by tuning the meta causal models’ weights for
64 epochs on the test task’s train set. Best hyper-parameters for test task is obtained in the same manner as discussed for training phase. Each experiment is repeated by considering each of tasks as meta test tasks, and report the
averaged MAPE (Mean Absolute Percentage Error).
[060] Metrics: The performance metrics used for evaluating the system 100 is described below: The average treatment effect for r-th test
iteration and test task are used as the performance metric, which is given in
equation 6.

where is the factual response to treatmentis its
corresponding counterfactual response, are the number of samples in

the task ω that are offered treatment 1 (0). In order to eliminate any bias in the test set, report the averaged ATE corresponding to the iteration that has the least averaged validation objective across test set of the meta-test tasks has been reported. The mean absolute percentage error defined on the ground truth ATE and the ATE obtained as above as given in equation 7.

i.e., lower values of MAPE indicate that the obtained ATE values are closer to the ground truth ATE.
[061] The written description describes the subject matter herein to enable any person skilled in the art to make and use the embodiments. The scope of the subject matter embodiments is defined by the claims and may include other modifications that occur to those skilled in the art. Such other modifications are intended to be within the scope of the claims if they have similar elements that do not differ from the literal language of the claims or if they include equivalent elements with insubstantial differences from the literal language of the claims.
[062] The embodiments of present disclosure herein addresses unresolved problem of predicting counterfactual effect from the observational data in an accurate manner. The Reptile optimization technique along with the CI framework provides maximum efficiency. Further, the present disclosure adapts its parameters in the presence of both covariate and concept shift in the dataset, and outperforms the baselines by large margins. Further, MetaCI employs the meta-learning paradigm to tackle the shift in data distributions between training and test phase due to the presence of heterogeneity in the population, and due to drifts in the target distribution, also known as concept shift. The performance of the MetaCI framework is measured using mean absolute percentage error over the average treatment effect as the metric, and demonstrate that meta initialization has significant gains compared to randomly initialized networks and other methods.
[063] It is to be understood that the scope of the protection is extended to such a program and in addition to a computer-readable means having a message

therein; such computer-readable storage means contain program-code means for implementation of one or more steps of the method, when the program runs on a server or mobile device or any suitable programmable device. The hardware device can be any kind of device which can be programmed including e.g. any kind of computer like a server or a personal computer, or the like, or any combination thereof. The device may also include means which could be e.g. hardware means like e.g. an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or a combination of hardware and software means, e.g. an ASIC and an FPGA, or at least one microprocessor and at least one memory with software modules located therein. Thus, the means can include both hardware means and software means. The method embodiments described herein could be implemented in hardware and software. The device may also include software means. Alternatively, the embodiments may be implemented on different hardware devices, e.g. using a plurality of CPUs.
[064] The embodiments herein can comprise hardware and software elements. The embodiments that are implemented in software include but are not limited to, firmware, resident software, microcode, etc. The functions performed by various modules described herein may be implemented in other modules or combinations of other modules. For the purposes of this description, a computer-usable or computer readable medium can be any apparatus that can comprise, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device.
[065] The illustrated steps are set out to explain the exemplary
embodiments shown, and it should be anticipated that ongoing technological
development will change the manner in which particular functions are performed.
These examples are presented herein for purposes of illustration, and not
limitation. Further, the boundaries of the functional building blocks have been
arbitrarily defined herein for the convenience of the description. Alternative
boundaries can be defined so long as the specified functions and relationships
thereof are appropriately performed. Alternatives (including equivalents,
extensions, variations, deviations, etc., of those described herein) will be apparent

to persons skilled in the relevant art(s) based on the teachings contained herein. Such alternatives fall within the scope and spirit of the disclosed embodiments. Also, the words “comprising,” “having,” “containing,” and “including,” and other similar forms are intended to be equivalent in meaning and be open ended in that an item or items following any one of these words is not meant to be an exhaustive listing of such item or items, or meant to be limited to only the listed item or items. It must also be noted that as used herein and in the appended claims, the singular forms “a,” “an,” and “the” include plural references unless the context clearly dictates otherwise.
[066] Furthermore, one or more computer-readable storage media may be utilized in implementing embodiments consistent with the present disclosure. A computer-readable storage medium refers to any type of physical memory on which information or data readable by a processor may be stored. Thus, a computer-readable storage medium may store instructions for execution by one or more processors, including instructions for causing the processor(s) to perform steps or stages consistent with the embodiments described herein. The term “computer-readable medium” should be understood to include tangible items and exclude carrier waves and transient signals, i.e. non-transitory. Examples include random access memory (RAM), read-only memory (ROM), volatile memory, nonvolatile memory, hard drives, CD ROMs, DVDs, flash drives, disks, and any other known physical storage media.
[067] It is intended that the disclosure and examples be considered as exemplary only, with a true scope and spirit of disclosed embodiments being indicated by the following claims.

WE CLAIM:
1. A processor implemented method, the method comprising:
receiving a structured data, wherein the structured data comprises a plurality of covariates, a factual treatment data and a factual response data of a plurality of subjects under test;
creating a set of tasks from the structured data, wherein each task is associated with a factual data, comprising:
computing a Joint Probability Density Function (JPDF) for the plurality of covariates;
segmenting the plurality of subjects under test based on the JPDF of the plurality of covariates to obtain a plurality of disjoint chunks; and
creating the set of tasks by combining the plurality
of disjoint chunks in a predetermined proportion;
training a machine learning network with the set of tasks until a
predefined number of iterations, wherein the machine learning network
comprising a causal inference framework and a meta-learning framework,
comprising:
sampling a first task from the set of tasks using random sampling technique;
computing a first set of weights for a first sampled task, wherein the first set of weights comprising a representation layer weight and a hypothesis layer weight;
updating weights of the meta-learning framework based on the corresponding first set of weights;
predicting a counterfactual response for the first sampled task based on the updated weights of the meta-learning framework;
sampling a second task from the set of tasks using a random sampling technique;

computing a second set of weights for a second sampled task based on the first set of weights;
updating weights of the meta-learning framework using the corresponding second set of weights;
predicting a counterfactual response for the second sampled task based on the updated weights of the meta-learning framework; fine-tuning the weights associated the meta-learning framework of the trained machine learning network using a sample of an unseen task; and
predicting a counterfactual response for the unseen task using the trained machine learning technique.
2. The method as claimed in claim 1, wherein the causal inference framework comprises a representation layer and a hypothesis layer and, wherein the representation layer computes the representation layer weight and the hypothesis layer computes the hypothesis layer weight.
3. The method as claimed in claim 1, wherein the representation layer maps the factual and counterfactual population to the space where -an imbalance between the two is minimum.
4. The method as claimed in claim 1, wherein the hypothesis layer predicts the factual response data and the counterfactual response for each subject under test.
5. The method as claimed in claim 1, wherein the meta-learning framework is updated by using a reptile transfer learning technique.
6. A system (100), the system (100) comprising:
at least one memory (104) storing programmed instructions;

one or more Input /Output (I/O) interfaces (112); and one or more hardware processors (102) operatively coupled to the at least one memory (104), wherein the one or more hardware processors (102) are configured by the programmed instructions to:
receive a structured data, wherein the structured data comprises a plurality of covariates, a factual treatment data and a factual response data of a plurality of subjects under test;
create a set of tasks from the structured data, wherein each task is associated with a factual data, comprising:
computing a Joint Probability Density Function (JPDF) for the plurality of covariates;
segmenting the plurality of subjects under test based on the JPDF of the plurality of covariates to obtain a plurality of disjoint chunks; and
creating the set of tasks by combining the plurality
of disjoint chunks in a predetermined proportion;
train a machine learning network with the set of tasks until a
predefined number of iterations, wherein the machine learning network
comprising a causal inference framework and a meta-learning framework,
comprising:
sampling a first task from the set of tasks using random sampling technique;
computing a first set of weights for a first sampled task, wherein the first set of weights comprising a representation layer weight and a hypothesis layer weight;
updating weights of the meta-learning framework based on the corresponding first set of weights;
predicting a counterfactual response for the first sampled task based on the updated weights of the meta-learning framework;

Sampling a second task from the set of tasks using random sampling technique;
computing a second set of weights for a second sampled task based on the first set of weights;
updating weights of the meta-learning framework using the corresponding second set of weights;
predicting a counterfactual response for the second sampled task based on the updated weights of the meta-learning framework; fine-tuning the weights associated the meta-learning framework of the trained machine learning network using a sample of an unseen task; and
predicting a counterfactual response for the unseen task using the trained machine learning technique.
7. The system as claimed in claim 6, wherein the causal inference framework comprises a representation layer and a hypothesis layer and, wherein the representation layer computes the representation layer weight and the hypothesis layer computes the hypothesis layer weight.
8. The system as claimed in claim 6, wherein the representation layer maps the factual and counterfactual population to the space where the imbalance between the two is minimum.
9. The system as claimed in claim 6, wherein the hypothesis layer predicts the factual response data and the counterfactual response for each subject under test.

10. The system as claimed in claim 6, wherein the meta-learning framework is updated by using a reptile transfer learning technique.