Understanding max_lag_sources parameter

[Sirish Gambhira]

Hello Everyone,

I am trying to calculate the effective connectivity in brain when motor imagery task is performed. I have few queries and I would be grateful if anyone could make some time and clarify them.

 

1. I read  " Transfer entropy—a model-free measure of effective connectivity for the neurosciences" paper, where it is mentioned that the time series is mapped into higher dimensions based on embedding dimension and delay parameters to calculate transfer entropy. I wanted to know if the max_lag_source parameter in bi variate TE analysis is performing the same job as that of the embedding dimension (mapping it to higher dimension), and tau_sources as that of delay.

2. Kindly correct me if I am wrong. If we want to identify all the hidden connections in the network, then we need to select max_lag_sources = 1, as we increase max_lag_sources parameter we get smaller and  equivalent circuit.

3. Since the max_lag_source parameter changes the effective connections in the network, how can I know the value at which I can get the optimized network.

[Patricia W]

Hi,

thanks for your interest in the toolbox! Regarding your questions:

1. max_lag_sources is related to the embedding as described in the paper you cite, however, IDTxl uses a different embedding method than the one described there. IDTxl doesn't perform a delay embedding with a fixed dimension and tau, but uses a non-uniform embedding as described here or here. The non-uniform embedding considers all past samples up to a maximum lag. That maximum lag is specified by max_lag_sources. If you don't want to test every sample up to max_lag_sources, the max_lag_tau parameter tells the algorithm to test only every nth parameter. For example, if you set the max_tau to 2 and max_lag to 10, the algorithm will test every second sample up to a maximum lag of 10 and will include it if it adds significant information about the current value. 

2. I am not sure, I understand your question. If you want to find all connections in a network, make sure to use the analyse_network function, which will test all possible combinations of source processes in the network. The max_lag parameter just tells the algorithm which time horizon to consider in each source processes' past. 

3. The max_lag parameter should consider the following things (note that it is set in samples): 

• the expected dynamics in your network (e.g., the memory that is to be expected in individual processes in the system you are analyzing, there may be evidence from the literature), this requires to consider the sampling rate to make sure the algorithm covers an appropriate time horizon when constructing the embedding
• the expected delay between source processes (there is also the option to set a min_lag, this way samples are skipped when constructing the non-uniform embedding)
  
• you may have a look at auto-correlation or the auto-mutual information if you have no idea what to expect in your data 

Hope this helps, let me know if something is unclear or needs further explanation.

Best,

Patricia

[Sirish Gambhira]

I am grateful for your clarification. It really helped me.

[Sirish Gambhira]

Hello,

As per your kind advice, I plotted the auto-correlation to observe the memory of time-series with 9 channels. The following is its plot:

 

As per the plot, I am choosing the max_lag_sources parameter to be max_lag till which auto correlation is >=0. For example, in the above case 7. Can you please guide me if I am doing it right way?

Regards,

Sirish Gambhira.

[Patricia W]

Hi Sirish,

Yes, that looks good. To be on the safe side, you can also do the same plot using mutual information instead of correlation, to also capture non-linear dependencies. 

Best, Patricia