[Python] Is there an efficient approach in PyTorch for multi-output regression where inputs...

I'm looking for the fastest way to essentially predict a rotating n values using, effectively, the other n-1 features. I can conceptualize a way of doing this with a for loop and will explain it below. There very well may be a matrix operation I'm unaware of that does this and I just don't know the name for it.

Say you have a toy dataset:

# Training Data
users, item1, item2, item3
one , 1 , 2 , 1
two , 1 , 4 , 3
thr , 1 , 2 , 5

# Prediction example
pred , x , y , z


In this example, I'm trying to predict n=3 classes; n being the number of features. One way I could approach this is by making a traditional feedforward NN with input_size = n and then use a mask.

toy_data = ... # what you see up there
model = model(input_size=num_of_cols) # traditional Torch NN

for epoch in epochs:
for col_index in num_of_cols:
mask_toy_data = mask_col_at_idx(toy_data, col_index)

# Basically, make prediction without nth col features
pred = model.forward(mask_toy_data)

# Loss is only on predictions on nth column
mask_pred = mask_cols_at_all_other_idx(pred, col_index)
mask_toy_data_for_loss = mask_cols_at_all_other_ix(toy_data, col_index)

loss = mask_pred - mask_toy_data_for_loss
... # backprop, etc.

def mask_col_at_idx(data, col_idx):
# 0 out every value in the column idx

def mask_cols_at_all_other_idx(data, col_idx):
# 0 out every other col, besides the given one



This approach would be totally fine if you only had three columns. But how could I approach this if I have hundreds or thousands? A for loop over each column does not seem feasible.

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