Hi @jpchen, re my comment "multiply the inputs by each weight / distribution".
sample test data
feature_1, feature_2, feature_3
12, 0, 19
2, 15, 0
Least squares regression
In a regular regression problem once the model is trained and to make a prediction on new inputs you would multiply each feature by the corresponding weight and sum the values to output the final prediction for a given sample input.
weights (after training a model): w1=7, w2=18, w3=17
Multiplying the the weights by the the features for each input data sample will output a prediction (without any uncertainty information)
Probabilistic Linear Regression
weights (after training a model - linear model so only one set of weights):
Now that you have the mean value of each weight and standard deviation can you use this information to calculate the uncertainty of a prediction on the test data? i.e w2 has a large standard deviation so any input data with high values for this feature would result in high uncertainty in the prediction.
The second sample test input above has a value of 15 for feature_2 so maybe this would result in high uncertainty in the test prediction.
The first sample has a value of 0 for feature_2 so maybe this would result in a more confident prediction as the other two features effecting the prediction have a low standard deviation?
This is what I mean by using the mean and std of each weight to calculate the uncertainty specific to each new test input.
Does this make sense?