Why is ScaleToBounds scaling to an interval multiplied by 0.95?

[andreimargeloiu]

Looking at the source code for ScaleToBounds, I noticed that it scales to an interval multiplied by 0.95. For example ScaleToBounds(1, 2) will output numbers between 0.95 and 1.9.

What's the rationale behind the decision to multiply by 0.95?

[andreimargeloiu]

Any thoughts?

[wjmaddox]

I think to prevent edge case errors of hitting exactly [0.95].

[jacobrgardner]

I believe the reason we do this is because SKI ends up with some pretty weird boundary conditions whenever you have data that's really close to the boundary, because you end up with fewer inducing points than expected on either side. Our goal in scaling is to always avoid left_boundary_pts from every actually having data here:

gpytorch/gpytorch/utils/interpolation.py

Lines 117 to 120 in f06004e

	# Find points who's closest lower grid point is the first grid point
	# This corresponds to a boundary condition that we must fix manually.
	left_boundary_pts = (lower_grid_pt_idxs < 0).nonzero(as_tuple=False)
	num_left = len(left_boundary_pts)

because the "fix" for the boundary condition involved ends up having pretty low fidelity. Similarly we don't want the right side condition to ever trigger either:

gpytorch/gpytorch/utils/interpolation.py

Lines 135 to 138 in f06004e

	right_boundary_pts = (lower_grid_pt_idxs > num_grid_points - num_coefficients).nonzero(as_tuple=False)
	num_right = len(right_boundary_pts)
	if num_right > 0:

[gpleiss]

To build upon what @jacobrgardner mentioned here - SKI is a lot faster if we can avoid triggering the edge cases (or at least this was the case when we first implemented it!).