1. It's within the model family of the true distribution.
2.The true distribution $p_{data}$ must correspond to exactly one value of $\theta$.

University of Michigan - Ann Arbor

Under appropriate conditions, as the number of training examples approaches inﬁnity, the maximum likelihood estimate of a parameter converges to the true value of the parameter.

The property of consistency of maximum likelihood

Goodfellow, I., Bengio, Y., & Courville, A. (2016). $\mathit{Deep \ Learning.}$ MIT Press. Retrieved from [www.deeplearningbook.org](https://www.deeplearningbook.org) 

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