I am trying to enhance the learning capabilities of my regression task with the help of active learning. I decided to use variance reduction using the Fisher information matrix as a query strategy as explained in Settles' popular survey "Active learning literature survey, 2010" (https://www.cs.cmu.edu/~10701/slides/Settles_notes.pdf). According to it the output variance of an input x can be approximated by
where F is the Fisher information matrix.
It appears like in this equation y is expected to be a scalar output. I am working with a neural network that has 3 output nodes and I am not sure if the equation can still be applied without modification. Of course I would get a covariance matrix instead of a scalar variance.
Unfortunately I could not find any literature regarding active learning using the Fisher information matrix for regression tasks with multiple outputs.
Can I still use this equation for estimating the output variance of my inputs? Is there any literature that goes into more detail regarding my problem?