# Jensen-Shannon divergence for finite samples

I have two finite samples $s_1$ and $s_2$ and two distributions $p_1(s_1)$ and $p_2(s_2)$ that are associated to these samples. I'm essentially interested to measure the distance or similarity between these two distributions. I'm currently using the Jensen-Shannon (JS) distance, which involves in calculating the entropies of the two distributions separately and jointly. I need to bin the data for calculating the basic entropy functions and it looks like the resulted JS distance is also a function of the data binning strategy that I use. It sounds quite arbitrary and I don't know how much I can trust the results. Is there any way around this? How can I measure the distance between $p_1(s_1)$ and $p_2(s_2)$ in a more rigorous way that needs no data binning or any other sort of arbitrariness?