System and method for learning disentangled representations for temporal casual inference

1. A processor implemented method, comprising:

processing, via one or more hardware processors, a plurality of historical observants h t and treatment a t at a timestep t specific to each patient i using an encoder network, wherein the encoder network comprises of a recurrent network with an LSTM (Long short-term memory) unit, wherein the plurality of historical observants h t for each patient i is derived from an observational dataset D={{x t i , a t i , y t+1 i } t=1 T i ∪{v i }} i=1 N for N patients containing a plurality of time dependent patient covariates x t i for each patient i, the treatment a t i received by each patient i, corresponding response y t+1 i to the treatment a t i obtained from each patient i and a plurality of static covariates v for each patient i and wherein, the plurality of historical observants h t is represented by a sequence of the patient's time-varying covariates x 1,t-1 =[x 1 , . . . , x t−1 ], a sequence of treatments ā 1,t-1 =[a 1 , . . . , a t−1 ] and the plurality of static covariates v as h t =[ x 1,t-1 , ā 1,t-1 , v];

obtaining, via the one or more hardware processors, a state representation s t using the processed plurality of historical observants h t ;

learning, via the one or more hardware processors, a first set of disentangled representations comprising an outcome representation (Φ γ E (s t )), a confounding representation (Φ Δ E (s t )) and a treatment representation (Φ Γ E (s t )) by passing the obtained state representation s t at each timestep t through a plurality of disentangled-two-layered Exponential Linear Unit (ELU) Multi-Layer Perceptrons (MLPs) ( 306 );

passing, via the one or more hardware processors, the outcome representation (Φ γ E (s t )), the confounding representation (Φ Δ E (s t )) and the treatment a t through a set of layers (W γ E ) comprising the plurality of disentangled-two-layered Exponential Linear Unit (ELU) Multi-Layer Perceptron's (MLPs) at the timestep t to predict an outcome t+1 one timestep ahead of the timestep t;

concatenating, via the one or more hardware processors, the outcome representation (Φ γ E (s t )), the confounding representation (Φ Δ E (s t )) and the treatment representation (Φ Γ E (s t )) from the encoder network to obtain a unified representation Ψ t for each timestep t for each patient i;

initializing, via the one or more hardware processors, a state of a decoder network comprising a LSTM (Long short-term memory) unit using the unified representation Ψ t to obtain a state representation s t+m specific to each patient i m-timestep ahead of the timestep t, wherein the decoder network is trained by splitting the observational dataset D of trajectory of each patient i into shorter sequences of τ timestep represented as {{Ψ t }∪{ t+m , a t+m , t+m+1 } m=1 τ-1 ∪{v}} t=1 T-τ and wherein, t+m denotes the predicted outcome m timestep ahead of the timestep t, a t+m denotes the treatment at each m timestep ahead of the timestep t and t+m+1 denotes the predicted outcome m+1 timestep ahead of the timestep t;

learning, via the one or more hardware processors, a second set of disentangled representations comprising an outcome representation (Φ γ D (s t+m )), a confounding representation (Φ Δ D (s t+m )) and a treatment representation (Φ Γ D (s t+m )) by passing the obtained state representation s t+m for each m timestep ahead of the timestep t through the plurality of disentangled-two-layered Exponential Linear Unit (ELU) Multi-Layer Perceptron's (MLPs); and

concatenating, via the one or more hardware processors, the outcome representation (Φ γ D (s t+m )), the confounding representation (Φ Δ D (s t+m )) and the treatment a t+m at each m timestep ahead of the timestep t and passing through a set of layers (W γ D ) comprising the plurality of disentangled-two-layered Exponential Linear Unit (ELU) Multi-Layer Perceptron's (MLPs) to predict outcome t+m+1 m+1 timesteps ahead of the timestep t and proceeding iteratively for all values of m up to τ−1 ahead of the timestep t.

2. The method of claim 1 , wherein the encoder network further comprises of weights of LSTM unit, weights of Exponential Linear Unit (ELU) and weights of Multi-Layer Perceptron's (MLP's) wherein, weights of LSTM unit, weights of Exponential Linear Unit (ELU) and weights of Multi-Layer Perceptron's (MLP's) are used to compute a set of loss functions comprising a prediction loss, a treatment loss, an imbalance loss, and a weighting loss, and wherein, the set of loss functions are used to learn the first set of disentangled representations comprising the outcome representation (Φ γ E (s t )), the confounding representation (Φ Δ E (s t )) and the treatment representation (Φ Γ E (s t )).

3. The method of claim 1 , wherein the decoder network further comprises of weights of LSTM unit, weights of Exponential Linear Unit (ELU) and weights of Multi-Layer Perceptron's (MLP's), wherein, weights of LSTM unit, weights of Exponential Linear Unit (ELU) and weights of Multi-Layer Perceptron's (MLP's) are used to compute a set of loss functions comprising a prediction loss, a treatment loss, an imbalance loss, and a weighting loss, and wherein the set of loss functions are used to learn the second set of disentangled representations comprising the outcome representation (Φ γ D (s t+m )), the confounding representation (Φ Δ D (s t+m )) and the treatment representation (Φ Γ D (s t+m )).

4. The method of claim 1 , further comprising processing a plurality of historical observants h t and treatment a t at a timestep t specific to a patient using the encoder network to obtain a state representation s t .

5. The method of claim 4 , further comprising initializing the state of the decoder network comprising the LSTM (Long short-term memory) unit using the unified representation Ψ t to obtain a state representation s t+1 specific to the patient one timestep ahead of timestep t, wherein an input to the decoder network comprises the predicted outcome t+1 one timestep ahead of the timestep t and treatment a t+1 to obtain a predicted outcome t+2 , two timestep ahead of the timestep t, wherein the predicted outcome t+2 serves as an input to the subsequent LSTM unit of the decoder network to predict an outcome t+3 for the treatment a t+2 and proceeding autoregressively till t+τ .

6. A system, comprising:

a memory storing instructions;

one or more communication interfaces; and

one or more hardware processors coupled to the memory via the one or more communication interfaces, wherein the one or more hardware processors are configured by the instructions to:

process a plurality of historical observants h t at a timestep t specific to each patient i using an encoder network, wherein the encoder network comprises of a recurrent network with an LSTM (Long short-term memory) unit, wherein the plurality of historical observants for each patient i is derived from an observational dataset D={{x t i , a t i , y t+1 i } t=1 T i ∪{v i }} i=1 N for N patients containing a plurality of time dependent patient covariates x t i for each patient i, the treatment a t i received by each patient i, corresponding response y t+1 i to the treatment a t i obtained from each patient i and a plurality of static covariates v i for each patient i and wherein, the plurality of historical observants h t is represented by a sequence of the patient's time-varying covariates x 1,t-1 =[x 1 , . . . , x t−1 ], a sequence of treatments ā 1,t-1 =[a 1 , . . . , a t−1 ] and the plurality of static covariates v as h t =[ x 1,t-1 , ā 1,t-1 , v];

obtain a state representation s t using the processed plurality of historical observants h t ;

learn a first set of disentangled representations comprising an outcome representation (Φ γ E (s t )), a confounding representation (Φ Δ E (s t )) and a treatment representation (Φ Γ E (s t )) by passing the obtained state representation s t at each timestep t through a plurality of disentangled-two-layered Exponential Linear Unit (ELU) Multi-Layer Perceptrons (MLPs);

pass the outcome representation (Φ γ E (s t )), the confounding representation (Φ Δ E (s t )) and the treatment at through a set of layers (W γ E ) comprising the plurality of disentangled-two-layered Exponential Linear Unit (ELU) Multi-Layer Perceptron's (MLPs) at the timestep t to predict an outcome t+1 one timestep ahead of the timestep t;

concatenate the outcome representation (Φ γ E (s t )), the confounding representation (Φ Δ E (s t )) and the treatment representation (Φ Γ E (s t )) from the encoder network to obtain a unified representation Ψ t for each timestep t for each patient i;

initialize a state of a decoder network comprising a LSTM (Long short-term memory) unit using the unified representation Ψ t to obtain a state representation s t+m specific to each patient i m-timestep ahead of the timestep t, wherein the decoder network is trained by splitting the observational dataset D of trajectory of each patient i into shorter sequences of τ timestep represented as {{Ψ t }∪{ t+m , a t+m , t+m+1 } m=1 τ-1 ∪{v}} t=1 T-τ and wherein t+m denotes the predicted outcome m timestep ahead of the timestep t, a t+m denotes the treatment at each m timestep ahead of the timestep t and t+m+1 denotes the predicted outcome m+1 timestep ahead of the timestep t;

learn a second set of disentangled representations comprising an outcome representation (Φ γ D (s t+m )), a confounding representation (Φ Δ D (s t+m )) and a treatment representation (Φ Γ D (s t+m )) by passing the obtained state representation s t+m for each m timestep ahead of the timestep t through the plurality of disentangled-two-layered Exponential Linear Unit (ELU) Multi-Layer Perceptron's (MLPs); and

concatenate the outcome representation (Φ γ D (s t+m )), the confounding representation (Φ Δ D (s t+m )) and the treatment a t+m at each m timestep ahead of timestep t and passing through a set of layers (W γ D ) comprising the plurality of disentangled-two-layered Exponential Linear Unit (ELU) Multi-Layer Perceptron's (MLPs) to predict outcome t+1+1 m+1 timesteps ahead of the timestep t and proceeding iteratively for all values of m up to τ−1 ahead of the timestep t.

7. The system as claimed in claim 6 , wherein the encoder network further comprises of weights of LSTM unit, weights of Exponential Linear Unit (ELU) and weights of Multi-Layer Perceptron's (MLP's) wherein, weights of LSTM unit, weights of Exponential Linear Unit (ELU) and weights of Multi-Layer Perceptron's (MLP's) are used to compute a set of loss functions comprising a prediction loss, a treatment loss, an imbalance loss, and a weighting loss, and wherein, the set of loss functions are used to learn the first set of disentangled representations comprising the outcome representation (Φ γ E (s t )), the confounding representation (Φ Δ E (s t )) and the treatment representation (Φ Γ E (s t )).

8. The system as claimed in claim 6 , wherein the decoder network further comprises of weights of LSTM unit, weights of Exponential Linear Unit (ELU) and weights of Multi-Layer Perceptron's (MLP's), wherein, weights of LSTM unit, weights of Exponential Linear Unit (ELU) and weights of Multi-Layer Perceptron's (MLP's) are used to compute a set of loss functions comprising a prediction loss, a treatment loss, an imbalance loss, and a weighting loss, and wherein, the set of loss functions are used to learn the second set of disentangled representations comprising the outcome representation (Φ γ D (s t+m )), the confounding representation (Φ Δ D (s t+m )) and the treatment representation (Φ Γ D (s t+m )).

9. The system as claimed in claim 6 , wherein a plurality of historical observants h t and treatment a t are processed at a timestep t specific to a patient using the encoder network to obtain a state representation s t .

10. The system as claimed in claim 9 , wherein the state of the decoder network comprising the LSTM (Long short-term memory) unit is initialized using the unified representation Ψ t to obtain a state representation s t+1 specific to the patient one timestep ahead of the timestep t, wherein an input to the decoder network comprises the predicted outcome t+1 one timestep ahead of the timestep t and treatment a t+1 to obtain a predicted outcome t+2 , two timestep ahead of the timestep t, wherein the predicted outcome t+2 serves as an input to the subsequent LSTM unit of the decoder network to predict an outcome t+3 for the treatment a t+2 and proceeding autoregressively till t+τ .

11. One or more non-transitory machine-readable information storage mediums comprising one or more instructions which when executed by one or more hardware processors cause:

processing a plurality of historical observants h t at a timestep t specific to each patient i using an encoder network, wherein the encoder network comprises of a recurrent network with an LSTM (Long short-term memory) unit, wherein the plurality of historical observants for each patient i is derived from an observational dataset D={{x t i , a t i , y t+1 i } t=1 T i ∪{v i }} i=1 N for N patients containing a plurality of time dependent patient covariates x t i for each patient i, the treatment a t i received by each patient i, corresponding response y t+1 i to the treatment a t i obtained from each patient i and a plurality of static covariates v i for each patient i and wherein, the plurality of historical observants h t is represented by a sequence of the patient's time-varying covariates x 1,t-1 =[x 1 , . . . , x t−1 ], a sequence of treatments ā 1,t-1 =[a 1 , . . . , a t−1 ] and the plurality of static covariates v as h t =[ x 1,t-1 , ā 1,t-1 , v];

obtaining a state representation s t using the processed plurality of historical observants h t ;

learning a first set of disentangled representations comprising an outcome representation (Φ γ E (s t )), a confounding representation (Φ Δ E (s t )) and a treatment representation (Φ Γ E (s t )) by passing the obtained state representation s t at each timestep t through a plurality of disentangled-two-layered Exponential Linear Unit (ELU) Multi-Layer Perceptrons (MLPs);

passing the outcome representation (Φ γ E (s t )), the confounding representation (Φ Δ E (s t )) and the treatment a t i through a set of layers (W γ E ) comprising the plurality of disentangled-two-layered Exponential Linear Unit (ELU) Multi-Layer Perceptron's (MLPs) at the timestep t to predict an outcome t+1 one timestep ahead of the timestep t;

concatenating the outcome representation (Φ γ E (s t )), the confounding representation (Φ Δ E (s t )) and the treatment representation (Φ Γ E (s t )) from the encoder network to obtain a unified representation Ψ t for each timestep t for each patient i;

initializing a state of a decoder network comprising a LSTM (Long short-term memory) unit using the unified representation Ψ t to obtain a state representation s t+m specific to each patient i m-timestep ahead of the timestep t, wherein the decoder network is trained by splitting the observational dataset D of trajectory of each patient i into shorter sequences of τ timestep represented as {{Ψ t }∪{ t+m , a t+m , t+m+1 } m=1 τ-1 ∪{v}} t=1 T-τ and wherein t+m denotes the predicted outcome m timestep ahead of the timestep t, a t+m denotes the treatment at each m timestep ahead of the timestep t and t+m+1 denotes the predicted outcome m+1 timestep ahead of the timestep t;

learning a second set of disentangled representations comprising an outcome representation (Φ γ D (s t+m )), a confounding representation (Φ Δ D (s t+m )) and a treatment representation (Φ Γ D (s t+m )) by passing the obtained state representation s t +m for each m timestep ahead of the timestep t through the plurality of disentangled-two-layered Exponential Linear Unit (ELU) Multi-Layer Perceptron's (MLPs); and

concatenating the outcome representation (Φ γ D (s t+m )), the confounding representation (Φ Δ D (s t+m )) and the treatment a t+m at each m timestep ahead of timestep t and passing through a set of layers (W γ D ) comprising the plurality of disentangled-two-layered Exponential Linear Unit (ELU) Multi-Layer Perceptron's (MLPs) to predict outcome t+m+1 m+1 timesteps ahead of the timestep t and proceeding iteratively for all values of m up to τ−1 ahead of the timestep t.

12. The one or more non-transitory machine readable information storage mediums of claim 11 , wherein the encoder network further comprises of weights of LSTM unit, weights of Exponential Linear Unit (ELU) and weights of Multi-Layer Perceptron's (MLP's) wherein, weights of LSTM unit, weights of Exponential Linear Unit (ELU) and weights of Multi-Layer Perceptron's (MLP's) are used to compute a set of loss functions comprising a prediction loss, a treatment loss, an imbalance loss, and a weighting loss, and wherein, the set of loss functions are used to learn the first set of disentangled representations comprising the outcome representation (Φ γ E (s t )), the confounding representation (Φ Δ E (s t )) and the treatment representation (Φ Γ E (s t )).

13. The one or more non-transitory machine readable information storage mediums of claim 11 , wherein the decoder network further comprises of weights of LSTM unit, weights of Exponential Linear Unit (ELU) and weights of Multi-Layer Perceptron's (MLP's), wherein, weights of LSTM unit, weights of Exponential Linear Unit (ELU) and weights of Multi-Layer Perceptron's (MLP's) are used to compute a set of loss functions comprising a prediction loss, a treatment loss, an imbalance loss, and a weighting loss, and wherein the set of loss functions are used to learn the second set of disentangled representations comprising the outcome representation (Φ γ D (s t+m )), the confounding representation (Φ Δ D (s t+m )) and the treatment representation (Φ Γ D (s t+m )).

14. The one or more non-transitory machine readable information storage mediums of claim 11 , wherein the one or more instructions which when executed by the one or more hardware processors cause processing a plurality of historical observants h t and treatment a t at a timestep t specific to a patient using the encoder network to obtain a state representation s t .

15. The one or more non-transitory machine readable information storage mediums of claim 14 , wherein the one or more instructions which when executed by the one or more hardware processors cause initializing the state of the decoder network comprising the LSTM (Long short-term memory) unit using the unified representation Ψ t to obtain a state representation s t+1 specific to the patient one timestep ahead of timestep t, wherein an input to the decoder network comprises the predicted outcome t+1 one timestep ahead of the timestep t and treatment a t+1 to obtain a predicted outcome t+2 , two timestep ahead of the timestep t, wherein the predicted outcome t+2 serves as an input to the subsequent LSTM unit of the decoder network to predict an outcome t+3 for the treatment a t+2 and proceeding autoregressively till t+τ .