A language model is being trained on a small dataset for a classification task. You are evaluating two different sets of model parameters, $\theta_A$ and $\theta_B$. For a batch of two examples, the models produce the following probabilities for the correct target classes:

Example 1:

• Model A: $P(y^{(1)}|x^{(1)};\theta_A) = 0.7$
• Model B: $P(y^{(1)}|x^{(1)};\theta_B) = 0.9$

Example 2:

• Model A: $P(y^{(2)}|x^{(2)};\theta_A) = 0.6$
• Model B: $P(y^{(2)}|x^{(2)};\theta_B) = 0.4$

Calculate the total conditional log-likelihood for the batch for each set of parameters. Based on your calculation, which set of parameters ($\theta_A$ or $\theta_B$) is considered a better fit for this data? Use the natural logarithm (ln) for your calculations.