Language Models

Choose an appropriate formula for the N-gram LM probability calculation from the options below.

1)

$$P(y_t|y_1, \dots, y_{t-1}) = \frac{N(y_1, \dots, y_{t-1}, y_t)}{N(y_1, \dots, y_{t-1})},$$

2)

$$P(w_i|h_i) = 1 / Z(h_i) * exp(\sum_j \lambda_j f_j (h_i w_i))$$

3)

$$P(w_1, ..., w_m) = \prod_{i=1}^m P(w_i | w_1, ..., w_{i-1}) = \prod_{i=1}^m P(w_i | w_{i-(n-1)}, ..., w_{i-1})$$