How we do regression when output in a matrix?

I want to do a regression with input is a matrix and output is a vector. Dimension: Input - 132x32 and output 1024x1. output values is just small integer (0 … 15)

I know how to do the regression when output is a scalar but not sure we have a method when output is a matrix.

I find in the thread below that we can make a network for each variable in output. However I need to reduce the computational complexity as much as possible so I’m not sure this is a good approach.

I’m thinking maybe I can do a autoencoder to reduce the dimension. But anyway, i’m new in this topic so there might have a better approach.

I’m very appreciated if someone can help me on this problem. Thank you a lot

Hello ! I’m also trying to predict a matrix as a regression problem. Did you manage to find a way to solve your problem?