Evaluating Predicted Sequences

Assessing Predictive Text Systems

A researcher is developing a system that predicts the next five words in a sentence. After the system generates a sequence of five words, denoted as $\hat{y}_{i+1}, \hat{y}_{i+2}, \hat{y}_{i+3}, \hat{y}_{i+4}, \hat{y}_{i+5}$, the researcher wants to use a probabilistic evaluation model, $p(\cdot)$, to assess the quality of the entire generated sequence as a whole. Which of the following expressions correctly represents this evaluation?

When using a probabilistic framework to assess the quality of a predicted sequence of five future values, $\hat{y}_{i+1}, \hat{y}_{i+2}, \dots, \hat{y}_{i+5}$, the most comprehensive approach is to calculate the probability of each value separately and then average the results.

Diagram of an Evaluation Model Assessing a Predicted Sequence