pytorch-ts/pts/model/causal_deepar

Causal DeepAR

Causal DeepAR model augments the DeepAR model by incorporating a causal structure via a control time-dependent signal.

The main assumption of this model is that the target at time t depends not only on the covariates up till time t and but also on control till time t. Thus we encode this structure via a model which now adds a control_output distribution layer. The main assumption we have is that at training time our dataset of time series now have an additional control key with the corresponding 1-d control-variate values (with the array being as large as target).

We translate this structure into the following schematics of Causal-DeepAR at time t:

┌─────────┐             ┌────────┐ 
│control_t│──────┐      │target_t│ 
└─────────┘      │      └────────┘ 
     ▲           │           ▲     
     │           │           │     
 log-prob/       │       log-prob/ 
   sample        │         sample  
     │      ground-truth/    │     
┌────────┐     sample/   ┌───────┐ 
│control │       do      │target │ 
│  dist  │       └──────▶│ dist  │ 
└────────┘               └───────┘ 
     ▲                       ▲     
     └────────────┬──────────┘     
                  │                
               ┌────┐              
     ───h_t-1─▶│RNN │───h_t──▶     
               └────┘              
                  ▲                
            ┌─────┴────┐           
            │target_t-1│           
            └─────┬────┘           
            ┌─────┴─────┐          
            │control_t-1│          
            └─────┬─────┘          
              ┌───┴──┐            
              │cov_t │            
              └──────┘  

The model is trained as per the DeepAR assumption, which mainly implies that the covariates and control are known for all the time points while training and only the covariates are known for all the time points that we wish to forecast for.

In terms of the control at inference time, we now have two choices:

1. We can predict by setting the control array to np.Nan for the duration of the prediction length in which case the model will sample values from the control_output.distribution and feed it auto-regressively to the target head and RNN.

2. On the other hand we can in the prediction window "do" an intervention by setting the values of control to some fixed value of our choosing for the time steps in the future we are interested in. In this case this model will "break" the causal connections and just use the supplied values and feed those to the target head and RNN at the appropriate time points.

Possible uses

• target can be sales and control can be discounts
• target can be sales and control can be the temperature