Can learning algorithms take in data along with their uncertainty? (chaining ML algorithms along with errors) How to chain statistical methods (estimators or classifiers) taking into account the uncertainty (error) of the previous step?
Ex: Consider a pipeline, where housing prices are estimated from census and geographical data and are fed into another algorithm to estimate credit scores. How does the error in estimating housing prices fed into credit scores estimator and factor in the overall error?
I think that if you just consider the output values and not the error of the previous step, the error of the current estimator will be lesser and will be misleading. The uncertainty is not being propagated forward in this pipeline, hence the uncertainty at the end is only because of the last step.
I'm new to Machine Learning and in the introductory books or courses I didn't come across any discussion about this topic. If anyone can point me to good resources to learn more about this, I'll be happy.
One option is to use Bayesian methods in machine learning.
Assume the input to any stage in a machine learning pipeline is a prior distribution and the output of any stage is a posterior distribution. Then it would be possible to chain stages together with uncertainty propagated through the system through the distributions.