<p>This equation and more information of it can be found in <a href="https://en.wikipedia.org/wiki/Expectation%E2%80%93maximization_algorithm#Applications" rel="nofollow noreferrer">Expectation Maximization Wikipedia site</a> and the explanation there was as follows (formula there in two parts):</p>

<p><a href="https://i.sstatic.net/dwJhx.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/dwJhx.png" alt="enter image description here"></a></p>

<p>Some more explanation from same page:</p>

<blockquote>
  <p>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.</p>
</blockquote>

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

CC BY-SA 3.0
2018-01-28T19:55:15.500Z
2018-01-28T19:55:15.500Z
mico
<p>What does the following equation mean? What does each part of the formula represent or mean?</p>

<p><span class="math-container">$$\theta^* = \underset {\theta}{\arg \max} \Bbb E_{x \sim p_{data}} \log {p_{model}(x|\theta) }$$</span></p>

CC BY-SA 4.0
2019-06-14T22:48:20.953Z
Hi Arash. This is a legitimate question. However, next time, please, provide some context, that is, describe where you saw this formula.
nbro
<machine-learning><math><probability><notation><expectation>
What does the argmax of the expectation of the log likelihood mean?
arash moradi
# What does the argmax of the expectation of the log likelihood mean?

(Asked by: username_0 on 2018-01-28)

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

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

**Tags:** machine-learning, math, probability, notation, expectation

> **Comments:**
> **username_1**: Hi Arash. This is a legitimate question. However, next time, please, provide some context, that is, describe where you saw this formula.  

---

## 1 answers

### Answer by username_2 on 2018-01-28. Score: 3

This equation and more information of it can be found in [Expectation Maximization Wikipedia site](https://en.wikipedia.org/wiki/Expectation%E2%80%93maximization_algorithm#Applications) and the explanation there was as follows (formula there in two parts):

[![enter image description here](https://i.sstatic.net/dwJhx.png)](https://i.sstatic.net/dwJhx.png)

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.


---

