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There's data which is hidden from the exchanges called "non-display data"? For a standard stock day trader, is there an advantage to get that type of data? Can I be in the first people to see the big gap up from the beginning of the day? Be aware that I am a trader as well as a C++/Python programmer, and I know very well ML learning.

Here is a SE question which might help you to understand the concept of "non-display data": https://money.stackexchange.com/questions/29621/display-vs-non-display-limit-orders

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You question seems to me to in two parts.

Is there an advantage to knowing the full state of (publicly displayed and hidden) orders on a security / derivative? Answer: yes my instinct tells me this is likely an advantage to some algorithms. For a standard trader who does not perform HFT trading and in depth statistical and mathematical analysis answer: no.

Can you know the full state of the orders on a security / derivative? Answer: no.

And I answer no to that second question for two reasons;

1) If the data is hidden but known by the exchange they must surely be legally obliged or for their own self interest obliged not to dislose it to you.

2) There are different levels of non-display data;

  • Data sent to an exchange on a hidden basis (the controlling exchange is aware of it)
  • Sent to an intermediary broker on a hidden basis and not passed to exchange (only the intermediate broker is aware of it)
  • Inherent to one's trading intent or private algorithm (only the end trader is aware of it)

So your non-display data seems to be a mix of all of the above which you either can't (shouldn't be allowed) access, or cannot possibly find out in aggregate across all participants.

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