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I found the following equation:

enter image description here

This is on the explanation of batch normalization on a book titled "Hands-On Machine Learning with Scikit-Learn and TensorFlow", published by O'Reilly. The author writes the following explanation:

The algorithm uses exponential decay to compute the running averages, which is why it requires the decay parameters. Given a new value v, the running average is updated through the equation [the equation of the image inserted here].

A good decay value is typically close to 1—for example, 0.9, 0.99, or 0.999 (you want more 9s for larger datasets and smaller mini-batches).

What is the arrow pointed to the left (but it is not used on the lim)?

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Blaszard
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1 Answers1

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It's probably an assignment statement in an algorithm. It means "the new value of $\hat v$ is computed from the old value using the formula on the right of the arrow".

Ethan Bolker
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  • Ah, that makes sense! Thanks. Is this arrow used to point only to left? – Blaszard Aug 08 '17 at 15:04
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    @Blaszard The left pointing arrow is a common pseudocode convention for an assignment statement. There are even languages where <- is the actual code for assignment. – Ethan Bolker Aug 08 '17 at 15:11
  • I know it (say, R). I just wanted to make sure that it is only used to point to left, but not right? So is it true that you can use the arrow to point to right side as well, but conventionally not used? – Blaszard Aug 08 '17 at 15:17
  • @Blaszard It is strictly a left-pointing arrow, and made this way because it is much easier to read when the object is on the left, and the huge calculation determining what it is is on the right. It's like a label for a cabinet being on the front of it rather than in the back corner, due to the fact we read left-to-right. – LloydTao Aug 08 '17 at 15:27