#conditional-likelihood

Four classifiers are trained by maximum likelihood on the same 100 two-class examples: GaussI, one Gaussian per class with both covariances fixed to $I$; GaussX, one Gaussian per class with unrestricted covariances; LinLog, logistic regression on linear features; QuadLog, logistic regression on all linear and quadratic features. The Gaussian models maximize the joint likelihood of inputs and labels, the logistic ones the conditional likelihood of labels. Using the average training value of $\log p(y \mid x)$, which statements must always hold? Select all that apply.