Answer: (ii) Parameters that maximize data likelihood

Explanation:

Maximum Likelihood Estimation (MLE):

$\hat{\theta}_{MLE} = \arg\max_{\theta} L(\theta) = \arg\max_{\theta} p(D|\theta) = \arg\max_{\theta} \prod_i p(x_i|\theta)$

• Finds parameter values that make observed data most probable under assumed model.
• Example: For Gaussian, MLE gives sample mean $\hat{\mu}= \bar{x}$ and sample variance (biased) $\hat{\sigma}^2 = \frac1n\sum(x_i-\bar{x})^2$.
• Contrast MAP: $\arg\max p(\theta|D) \propto p(D|\theta)p(\theta)$ includes prior.

It does NOT find priors (i), decision boundaries (iii) directly, or cluster centroids (iv) — those are consequences after estimation.

So (ii) is correct.