Fix: MultivariateQExponential.log_prob ignores power when fast log-prob is off

[richardcsuwandi]

Problem

When gpytorch.settings.fast_computations.log_prob is off, MultivariateQExponential.log_prob falls back to torch.distributions.MultivariateNormal.log_prob. That path is Gaussian-only, so it ignores power and always returns the q = 2 log-density.

This matters in practice because BoTorch turns that setting off on import, and QePyTorch reuses gpytorch.settings. So any BoTorch-style Exact QEP fit via

mll = ExactMarginalLogLikelihood(likelihood, model)
loss = -mll(output, target)

quietly does ordinary Gaussian MLE, even when power != 2.

I hit this with a BoTorch-style SingleTaskQEP wrapper: same data and init, q ∈ {2, 1.5, 1, 0.5}, but output.log_prob(...) and the MLL stayed identical for every q (matching the Gaussian value). output.power itself was set correctly; only the numerical log-prob / MLL was wrong.

Why it happens

MultivariateQExponential.log_prob currently does:

if settings.fast_computations.log_prob.off():
    return super().log_prob(value)  # Gaussian-only; ignores power

That early return is copied from GPyTorch's MultivariateNormal, where a Gaussian fallback is fine. Here super() is still torch.distributions.MultivariateNormal, which has no power, so the fallback is wrong for q != 2.

The Q-Exponential formula in the rest of the method is correct. A plain MultivariateQExponential(...).log_prob(y) with fast log-prob left on is q-dependent as expected. The bug only appears once the fast-log-prob-off path is taken (e.g. after importing BoTorch).

On a small ExactQEP / SingleTaskQEP example, the broken MLL was about -12.25 for all four q values. Recomputing the QED formula from the same loc, covariance, and power gave the correct sequence: about -12.25, -13.68, -15.65, -18.17.

Implications

• Hyperparameter learning through ExactMarginalLogLikelihood under BoTorch (or any code with fast log-prob off) fits a GP, not a QEP, whenever q != 2.
• Code that only reads .power (e.g. some acquisition logic) is unaffected.
• The failure is silent: no error, just the wrong objective.

Fix

Only use the Gaussian super().log_prob fallback when power == 2. For power != 2, always evaluate the Q-Exponential log-density via inv_quad_logdet, even if fast_computations.log_prob is off.

After the fix, the same BoTorch / SingleTaskQEP setup recovers the q-dependent MLL values above.

Checklist (from CONTRIBUTING.md)

• Code change
• No new public API / docs objects required
• Ran python -m unittest locally before opening the PR