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The title says it all: I have seen three functions so far, that seem to be the same / similar:

  • error function
  • criterion function
  • cost function
  • objective function

I am currently working on classification problems.

$$E(W) = \frac{1}{2} \sum_{x \in E}(t_x-o(x))^2$$

where $W$ are the weights, $E$ is the evaluation set, $t_x$ is the desired output (the class) of $x$ and $o(x)$ is the given output. This function seems to be commonly called "error function".

But while reading about this topic, I've also seen the terms "criterion function" and "objective functin". Do they all mean the same for neural nets?

edit:

  • Geoffrey Hinton called cross-entropy for softmax-neurons and $E(W) = \frac{1}{2} \sum_{x \in E}(t_x-o(x))^2$ a cost function.
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