# Predicting object by features probabilities

I have the definition of an object provided as features probability. Each object has it's own feature importance and probabilities. For example for object "X", I have "color" feature (with the weight of 0.8) - the object can be blue in 80% of cases and black in 20% of cases. And "shape" feature (with the weight of 20%) - square in 30% and round in 70%.

I'm trying to create a "predictor", so if I'm observing something blue and round - (0.8 x 0.8) x (0.2 x 0.7) - probability for object X.

1. Does it make any sense mathematically?
2. If this method sounds reasonable enough, how should I handle really small numbers (I can have a really long vector of features, the final number will be really small)?
• It's not clear what weight means here. It's also not clear what you mean to predict - probability of object X being what? Commented Jul 8, 2018 at 14:30
• @SeanOwen I guess he is attempting to refer to a kind of similarity measure. Commented Jul 8, 2018 at 14:32
• @Media yes sort of similarity based on feature importance
– Alex
Commented Jul 8, 2018 at 14:36
• @Alex as I've referred you can use Bayes decision theory Commented Jul 8, 2018 at 14:41
• HI @alex, did you find a way of dealing with this other than Bayes Decision Theory ? , I have the same question but Bayes does not seem to help since I only have features and their probabilities not prior or posterior. Commented Oct 19, 2021 at 13:18