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 $P'_{XY}$?
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$\begingroup$ Do you assume that $P_{XY}$ is discrete? Otherwise, the total variation distance is just $1$. $\endgroup$– user140541Feb 12, 2020 at 7:51
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$\begingroup$ Sorry for replying late. Yes, $P_{XY}$ is discrete $\endgroup$– BikasFeb 12, 2020 at 17:44
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1$\begingroup$ This paper may be useful. $\endgroup$– user140541Feb 12, 2020 at 18:03
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