You definitely need a number of data at least exponential in the number of parameters, since the number of “bins” is exponential. (It’s not so simple as to say that exponential is enough because it depends on the distributional overlap. If there are cases where one group never hits a given bin, then even an infinite amount of data doesn’t save you.)
So you just need enough data that the events involving entities is much greater than the number of parameters.
You definitely need a number of data at least exponential in the number of parameters, since the number of “bins” is exponential. (It’s not so simple as to say that exponential is enough because it depends on the distributional overlap. If there are cases where one group never hits a given bin, then even an infinite amount of data doesn’t save you.)