What does the following equation mean? What does each part of the formula represent or mean?

$$\theta^* = \underset {\theta}{\arg \max} \Bbb E_{x \sim p_{data}} \log {p_{model}(x|\theta) }$$

  • 2
    $\begingroup$ Hi Arash. This is a legitimate question. However, next time, please, provide some context, that is, describe where you saw this formula. $\endgroup$
    – nbro
    Jun 14, 2019 at 22:48

1 Answer 1


This equation and more information of it can be found in Expectation Maximization Wikipedia site and the explanation there was as follows (formula there in two parts):

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Some more explanation from same page:

In statistics, an expectation–maximization (EM) algorithm is an iterative method to find maximum likelihood or maximum a posteriori (MAP) estimates of parameters in statistical models, where the model depends on unobserved latent variables. The EM iteration alternates between performing an expectation (E) step, which creates a function for the expectation of the log-likelihood evaluated using the current estimate for the parameters, and a maximization (M) step, which computes parameters maximizing the expected log-likelihood found on the E step. These parameter-estimates are then used to determine the distribution of the latent variables in the next E step.

Mathematically, E in your equation stands for Expectation Value, x|theta is conditional probability and x~data and model are sub-titles of source of probability in either case. The arg max theta is argument theta that maximizes the equation.


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