# compute the KL divergence between two datasets

I have two datasets $$D1$$ and $$D2$$ in two different feature spaces $$\mathcal{X}_{1} \in \Re^{m}$$ and $$\mathcal{X}_{2} \in \Re^{n}$$. Further assume that the datasets have different number of data points.

I also do not have any idea about the distribution that each of the above datasets are coming from. Can I still compute the KL divergence between the two datasets ?

I came across the fact that unless we know the distribution of the datasets (or fit a distribution to the datasets), it is not possible for us to compute the KL divergence.