Standardization of output data

[MJeong19]

I am trying to code the multi-objective Bayesian algorithm with SingleTaskGP.
And an error occured concerned about standardizing the output data.
When I multiplied 10000 to second column, this error didn't occur.
I would like to know why this error occured,
and how can I print the output data after standardization.
Here is the code I used,

import numpy as np
import matplotlib
from pyDOE import *
import os
import torch
from gpytorch.kernels import MaternKernel
from botorch.models import SingleTaskGP
from botorch.models.transforms import Normalize, Standardize

num=5
dat=lhs(5,samples=num, criterion='center')

t = torch.from_numpy(dat)
obj=torch.from_numpy(result)

iteration = 10
trainx = t
trainy = obj
covar_module = MaternKernel(nu=2.5, ard_num_dims=6)
print(trainy)

model = SingleTaskGP(train_X = trainx, train_Y = trainy, covar_module = covar_module, 
                     input_transform=Normalize(d=5), outcome_transform=Standardize(m=6))
print(trainy)

and this figure contains output data before standardization and error occured.

[saitcakmak]

Hi @MJeong19. For some outcomes, the range of outcomes is extremely small. For example, the second outcome is on the order of 1e-9. The BoTorch standardization utilities will not do anything for these dimensions, since untransforming the covariance matrix with a coefficient of 10^9 will itself lead to numerical issues elsewhere. It is generally a good practice to pre-transform the data to avoid it from being on a scale that is too small or too large.