4 ms·
That’s an interesting thought, about windowing. I think it is clear that O(n) vs O(n^2) is really just an analogy so we shouldn’t over-formalize it. But it is
by bee_rider 1y ago
That’s an interesting thought, about windowing.
I think it is clear that O(n) vs O(n^2) is really just an analogy so we shouldn’t over-formalize it. But it is interesting to note that a sigmoid could be thought of as looking like either one, depending on when you look at it.
It makes me wonder if there’s some sampling bias that is accidentally being applied. Because, another way of looking at it could be: assume I observe companies only after they hit a particular size. The companies that are still in the exponential growth phase when I notice them; due to the shape of a sigmoid, those are likely heading much a higher carrying capacity. Those that have hit the linear phase before they are large enough for me to see them are not on as good a trajectory.
- godelski 1y agoSure sampling bias is probably a factor. But I'm sure it's also a factor in nearly every one of these discussions that isn't a serious and meticulous study. For wondering, I believe this might help. If we parametrize sigmoid to be 1/(1+e^{-ax}) then our a factor is at play. We're interested in x<=0. When a < 1 then the function becomes flat and much more linear like. The larger a becomes the more quadratic it looks at near the origin (but still x<=0) I still think the model is naive. Even just a sigmoid is. You need the composition of them and further parameterization. They are good for approximating as you originally suggested but this is similar to using fourier series. It's the fact that you have the three classes of second derivatives allowing you to strongly control the composite function through minimal parameterization and complexity. But that's also why I immediately understood this to be being using in an illustrative way rather than a serious one. I mean realistically so are you.