I am reading this paper by Ian Goodfellow. Currently I have an undergraduate knowledge of probability/statistics/linear algebra/calculus/differential equations. I am trying to understand the formula below proposed in the paper but I have no idea it what it means. min G max D V ( D , G ) = E x ∼ p d a t a ( x ) ⁡ [ log ⁡ D ( x ) ] + E z ∼ p z ( z ) ⁡ log ⁡ [ ( 1 − D ( G ( z ) ) ) ]I can see that we have some value function(what is a value function? what topic does this fall under?) and it equals some expectation of x (what is x?) which is (~) similar to the probability of the data of x? I just have no idea how to start interpreting formulas like this when I begin reading papers. Any useful guide on what topics I need to study to understand the math in this paper is very appreciated.

Question

I am reading this paper by Ian Goodfellow. Currently I have an undergraduate knowledge of probability/statistics/linear algebra/calculus/differential equations. I am trying to understand the formula below proposed in the paper but I have no idea it what it means.      min          G            max          D        V  (  D  ,  G  )  =                    E                            x            ∼                        p                          d          a          t          a                    (              x            )        ⁡  [  log  ⁡  D  (      x    )  ]  +                    E                            z            ∼                        p                          z                    (              z            )        ⁡  log  ⁡  [  (  1  −  D  (  G  (  z  )  )  )  ]I can see that we have some value function(what is a value function? what topic does this fall under?) and it equals some expectation of x (what is x?) which is (~) similar to the probability of the data of x? I just have no idea how to start interpreting formulas like this when I begin reading papers. Any useful guide on what topics I need to study to understand the math in this paper is very appreciated.

Savion Stanton · Accepted Answer

You might want to check out Game Theory. Value is the outcome of the game.Consider two players, a discriminator and a generator. The generator tries to create fake data that resembles the real data.The discriminator gets better rewards if it can distinguish real data from the fake data provided by the generator. The discriminator gets rewards if it says it is a real data sample with high probability for every real data sample it encounters and says it is not a real data with high probability if it encounters a fake data set. The discriminator tries to maximize this value.On the other hand, the generator tries to reduce this quantity, hence the minimization term.The notation   ∼ means follows the distribution.

I am reading this paper by Ian Goodfellow. Currently I have an undergraduate knowledge of probabilit

Answered question

Answer & Explanation

New Questions in Pre-Algebra