Multivariate Regression task where some variables are easy, some hard and some impossible to predict

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I am trying to create a multivariate regression model in keras, but the model always ends up predicting a single value regardless if the input.

I tried fixing the learning rate, batch size and model architecture, but so far I can’t fix it.

Upon further inspection, I know that some values in the output vector will be hard or impossible for the model to predict (say the height of a man deduced from the car brand he likes), but due to the nature of the problem, I don’t know which these hard or impossible to predict variables.

I am currently using MSE loss. I suspect I have to use or create a custom loss function that deals with this kind of problem.

Chatgpt proposed a Heteroscedastic loss, but I can’t understand what it means.

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