I was reading the book Deep Learning by Ian Goodfellow. I had a doubt in the Maximum likelihood estimation section (Pg 131). I understand till the Eq 5.58 which describes what is being maximized in the problem.
$$ \theta_{ML} = argmax_{\theta} \sum_1^m log(p_{model}(x^{(i)};\theta)) $$$$ \theta_{\text{ML}} = \text{argmax}_{\theta} \sum_1^m \log(p_{\text{model}}(x^{(i)};\theta)) $$
However the next equation 5.59 restates this equation as:
$$ \theta_{ML} = argmax_{\theta} E_{x \sim p_{data}^{hat}}(log(p_{model}(x;\theta)) $$$$ \theta_{\text{ML}} = \text{argmax}_{\theta} E_{x \sim \hat{p}_{\text{data}}}(\log(p_{\text{model}}(x;\theta)) $$
where $$p_{data}^{hat}$$$$\hat{p}_{\text{data}}$$ is described as the empirical distribution defined by the training data. Could someone explain what is meant by this empirical distribution? It seems to be different from the distribution parametrized by theta as that is described by $$ p_{model} $$$$ p_{\text{model}} $$
