In probabilistic models, the goal is to determine the best output sequence, $\hat{\mathbf{y}}$, for a given input sequence, $\mathbf{x}$. This is accomplished by identifying the possible output sequence, $\mathbf{y}$, that has the highest conditional probability. The formal expression for this predictive rule is: $\hat{\mathbf{y}} = \underset{\mathbf{y}}{\text{arg max}} \ \text{Pr}^w(\mathbf{y}|\mathbf{x})$ This equation states that the prediction $\hat{\mathbf{y}}$ is the argument (arg max) that maximizes the conditional probability $\text{Pr}(\mathbf{y}|\mathbf{x})$. The probability distribution is parameterized by the model's weights, denoted by the superscript w.