Understanding the equation of the empirical error

2

The empirical error equation given in the book Understanding Machine Learning: From Theory to Algorithms is

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My intuition for this equation is: total wrong predictions divided by the total number of samples $m$ in the given sample set $S$ (Correct me if I'm wrong). But, in this equation, the $m$ takes $\{ 1, \dots, m \}$. How is this actually calculated, as I thought it should be one number (the size of the sample)?

user30381

Posted 2019-10-11T02:47:47.147

Reputation: 35

Answers

1

This is a commonly used notation in theoretical computer science.

$[m]$ is not the variable $m$, but is instead the set of integers from $1$ to $m$ inclusive. The empirical error equation thus reads in English:

The cardinality of a set consisting of the elements $i$ of the set of integers $[m]$ such that the hypothesis given input $x_i$ disagrees with label $y_i$, normalized by $m$.

John Doucette

Posted 2019-10-11T02:47:47.147

Reputation: 7 904