The likelihood of θ is the probability of the full data set according to the model, viewed as a function of θ, and the maximum-likelihood criterion instructs us to choose the parameter settingsθ that maximize likelihood, or equivalently, log-likelihood: represents the truth value of the proposition Φ; it is one if Φ is true and zero otherwise.)
let us define Note that φ x satisfies the formal requirements of a probability distribution over labels j: it is a point distribution with all its mass concentrated on Y x .