# Intuition behind variance of Gaussian Process Classification

Looking at the last figure in the post, I'm puzzled by the variances of the latent logit variables. I assumed the variances would be highest near the decision 0.5 line. However, this is where the uncertainty is the smallest. Why is this?

A related question. I believe the implementation in the post assumes noise free inputs. How do can I add that the outcome (0 or 1) is noisy? The goal is to prevent overfitting. I tried including a white noise kernel but not sure if it's doing anything.

• there are two types of uncertainty to look out for here: one is the uncertainty we see on the Gaussian process in logit space, which is high far from data and low close to data. Since we have data near the boundary, this type of variance, which you are asking about, is low there (as that figure shows). However, even if we are 100% sure the logodds is 0 (as it is at the boundary), the variance of the outcome variable $y$ is the variance of a bernoulli variable with $p=0.5$, which has variance $0.25$, which is maximal. It is this second variance your intuition was leading you towards. Commented Sep 14, 2022 at 22:50
• Indeed, I think we could argue that your confusion is evidence that the author plotted the wrong variance. Commented Sep 14, 2022 at 22:51

The confusion regarding the variances of the latent logit variables in Gaussian Process Classification (GPC), as illustrated in the last figure of the blog post, arises from the difference between two types of uncertainty: the uncertainty in the Gaussian Process (GP) in the logit space versus the uncertainty in the outcome variable $$y$$.