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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.

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  • $\begingroup$ Why do you need bayesian neural net? Did you try other methods before like (Bayesian) Linear regression, GLM... which are simpler than Bayesian neural network and would still give you probability distribution $\endgroup$ – Robin Nicole Jan 13 '19 at 12:27
  • $\begingroup$ If I understand correctly, you are asking if the inputs can be defined without variance? In this case the answer is yes, you only need the variances (sigma) on the weights $\endgroup$ – Vincenzo Lavorini Jan 13 '19 at 15:52
  • $\begingroup$ Ye, Bayesian Regression is on the List; regarding the weights, this was helpfull vincenzo $\endgroup$ – Alexander Vocaet Jan 14 '19 at 20:35
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It is possible to predict a single value from a Bayesian Neural Network. Given a set of input data, conduct the forward pass to generate the resulting probability distribution. Then convert that probability distribution to a single specific value in one of the following common ways:

  1. Sample - Take a random sample. That random sample will automatically be weighted by the posterior probability distribution. This type of sampling is similar to Thompson sampling.

  2. Use a measure of central tendency. Given that posterior probability distribution, calculate the most useful measure of central tendency (e.g., mean, median, or mode).

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