Smoothing frequencies without count data

Question

I have frequency data for different events under two conditions, resulting in sets of frequencies F1 and F2. I would like to normalize the frequencies of events under condition 1 by their frequencies under condition 2. However, there are events that occur in condition 1 but not condition 2, resulting in divide-by-zero problems when I attempt to normalize.

For raw count data, I understand that there are a number of smoothing techniques (e.g. Witten-Bell) that can help sort this out, but I only have the frequencies, not the individual counts. In other words, I have frequencies like {0, 0.1, 0.2, 0.7} which could correspond to counts of {0, 1, 2, 7}, {0, 10, 20, 70}, etc. Are there any algorithms that are able to smooth this type of frequency data?

Answer 1

Yes. $\:$ Assume that the counts have the smallest sum that would produce your frequency data. $\:$ (How to do that depends on whether the frequencies were calculated and stored as doubles or something else.)