I don't know a distribution $P_{XY}$. However, I can randomly get some samples (X,Y) from this distribution. Based on $n$ samples, I approximated the distribution as $P'_{XY}$. How can I bound the total variation distance between $P_{XY}$ and $P'_{XY}$?

  • $\begingroup$ Do you assume that $P_{XY}$ is discrete? Otherwise, the total variation distance is just $1$. $\endgroup$
    – user140541
    Feb 12, 2020 at 7:51
  • $\begingroup$ Sorry for replying late. Yes, $P_{XY}$ is discrete $\endgroup$
    – Bikas
    Feb 12, 2020 at 17:44
  • 1
    $\begingroup$ This paper may be useful. $\endgroup$
    – user140541
    Feb 12, 2020 at 18:03


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