negative log-likelihood
log-liklihood
cross entropy
residual sum of square
Answer is Right!
Answer is Wrong!
The correct answer is A. negative log-likelihood.
The negative log-likelihood is a measure of how well a model fits the data. It is defined as follows:
$$-\log \mathcal{L}(\theta|x) = -\sum_{i=1}^n \log \phi(x_i|\theta)$$
where $\theta$ is the model parameters, $x$ is the data, and $\phi(x_i|\theta)$ is the probability density function of the Gaussian distribution with parameters $\theta$.
The negative log-likelihood is minimized when the model parameters are the true parameters of the data. Therefore, it is a natural choice for the objective function to minimize during parameter estimation in a Gaussian distribution model.
The other options are incorrect for the following reasons:
- Option B, log-likelihood, is the opposite of the negative log-likelihood. It is not minimized during parameter estimation.
- Option C, cross entropy, is a measure of how well two probability distributions are related. It is not used in parameter estimation for Gaussian distribution models.
- Option D, residual sum of squares, is a measure of the error between the model predictions and the data. It is not minimized during parameter estimation.