Open azev77 opened 4 years ago
In MLJ the plan is to view fitting a distribution as probabilistic supervised learning where the input is X=nothing
- a single point with no information. The data you have above would be the target, labelled y
, and the prediction yhat
is a single (probabilistic) prediction. The API is set up for this already - see https://alan-turing-institute.github.io/MLJ.jl/dev/adding_models_for_general_use/#Models-that-learn-a-probability-distribution-1 - but no-one has contributed a model yet.
Is this what you are after?
Yes, that is.
Btw, this case w/ X=nothing
can be generalized.
For example: y= x*\beta + e, where e ~_{iid} F(\theta)
for a large class of probability distributions for the error term.
Suppose I got a new dataset in the mail today & wanna see which brand-name distribution in Distributions.jl best fits it.
Basically this is predicting Y given X=constant, except the prediction here is not a number but a (unconditional) distribution.