Answers.Body: <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>
  
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2018-01-28T19:55:15.500Z
Answers.LastActivityDate: 2018-01-28T19:55:15.500Z
Answers.UserDisplayName: mico
Body: <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>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2019-06-14T22:48:20.953Z
Comments.Text: Hi Arash. This is a legitimate question. However, next time, please, provide some context, that is, describe where you saw this formula.
Comments.UserDisplayName: nbro
Tags: <machine-learning><math><probability><notation><expectation>
Title: What does the argmax of the expectation of the log likelihood mean?
UserDisplayName: arash moradi
ThreadText: # 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 username_0. 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.
  
  
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