Is it possible to construct a Bayesian Neural Network without Probability Distributions as dependent Variable for purpose of predictive modeling?
I mean, if id like to Infer on a Specific Value, like y(e.g. y=5), with a vector of explanatory Variables X(e.g. X=[3,5,1.3,(.....)]) The Bayesian Neural Network infers on a distribution of ymean with standard deviation sigma(e.g. ymean =5, sigma =0.5).
Does it even make sense? Is the loss function of the Neural net able to work by comparing y with ymean, without taking simgma into account?
partial answer: I think sigma is the result of the distributions in the weight matrices of the Neural net, and it should work. But I want to be sure and understand.
PS: I work in ecology, so getting a probability distribution as result would serve my goals.