Machine Learning - Empirical Error

[YoshiMoshi]

Homework Statement

See Below

Relevant Equations

See below

I understand everything in this equation except for the summation. I understand it's the average error over the sample. But why do we need the "1"? Moreover wouldn't the error be the absolute value of the hypothesized value minus the concept value? Meaning
| h( x_i ) - c( x_i ) |
because you have to take the difference between the two to get the error? The original statement in the summation is just saying that the two are not equal. How is this an error?

The above snipping came from a book titled Foundations of Machine Learning by M. Mohri, Afshin Rostamizadeh, Ameet Talwalkar. It's for free on semantic scholar, and this is the beginning of chapter 2.

https://www.semanticscholar.org/pap...e9239469aba4bccf3e36d1c27894721e8dbefc44?p2df

 

[Office_Shredder]

I think the notation $1_{h(x)\neq c(x)}$ means it takes the value 1 if the subscript is true, i.e. $h(x) \neq c(x)$, and 0 otherwise.

I guess as long as for each data point it's either an error or not, without further quantification, this calculates the average error rate in your sample.

 

[YoshiMoshi]

Hey thanks, that would make perfect sense.

 

[Mark44]

I think the notation $1_{h(x)\neq c(x)}$ means it takes the value 1 if the subscript is true, i.e. $h(x) \neq c(x)$, and 0 otherwise.

That's in agreement with what's in the whitepaper. The author calls $1_\omega$ the "indicator function of the event $\omega$."