Hi @tbhaxor,
here is my take on this matter:
No, a sin^2(x), where x as a any really number is not suitable to model a probability. Besides the obvious periodic structure (as a problem) also an other point should be mentioned:
To give you some guidance: usually to model probabilistic characteristics we use a probability density function (PDF). If you integrate over this PDF for the whole possible range per definition it should be equal to 1. So this isn’t the case in my sin^2(x) example or at least such a PDF is not possible to construct in a useful manner.
However it possible is for a logistic / sigmoid function: For a logistic function at least in approximation for a normally distributed feature, this characteristics is given as shown in the link I sent in my previous post above:
A (fitted well) logistic function can also serve as an „easy to compute“ approximation of the integrated gaussian probability distribution function (which describes a normally distributed feature)
- Decision boundary vs prediction f_wb in logistic regression - #9 by Christian_Simonis
- https://www.public.asu.edu/~gwaissi/papers/A%20Sigmoid%20Approximation%20of%20the%20Standard%20Normal%20Integral%201996.pdf
If you are interested in generalising so much, I strongly suggest to carefully read the literature. Hope that helps!
Best regards
Christian