I have a true value y that I'd like to predict with a regression, but I'm interested in the probabilities that y will be different values. Y is theoretically continuous but in the dataset it is rounded to integers. Let's say y could be 0-9. I want 10 probabilities, one for each possible value. I tried doing this categorically, with a neural network having 10 output nodes, this hurts the predictions since we lose the relationships between categories, 1 is closer to 2 than it is to 10.
Example toy problem:
y is the weight of an object in pounds. The dataset has Y values rounded s.t. y can be from 0 to 9 pounds. Predict the probabilities that y will be 0-9 pounds based on the features X.
[0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1,] (ten # summing to 1)
I'd like to be able to accomplish this with Keras.