Function which measures "error"

In summary, the conversation discusses the properties of an error function denoted as e(x,y), which is not a norm and not symmetric. The speaker then questions if this function is a good choice, to which the response is that it depends on the purpose of the function. The speaker clarifies that the goal is not to show boundedness, but to determine if it is a good measure of error despite being non-symmetric. The conversation then shifts to defining what is considered "good" and the context of the function, with the example of comparing two positions and orientations of a drill. The variables x and y represent elements of SE(3). The conversation concludes that asymmetry may not be an issue if the purpose is to compare expected and
  • #1
hunt_mat
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I have an error, denoted [itex]e(x,y)[/itex] for example. It's not a norm and it isn't symmetric, that is to say: [itex]e(x,y)\neq e(y,x)[/itex].

My question is simply this: With such properties, is the choice of such a function a good one?
 
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  • #2
I suppose that depends on what you want to do with it.
If your goal is to show that the error is bounded, then you should not need the properties of norms and symmetry, although those properties can simplify your proof.
 
  • #3
I'm not worried about showing it's bounded but if it's a good measure of error with it being non-symmetric.
 
  • #4
What defines "good"? What do you want to do with this number?
Also, what are x and y?
 
  • #5
Okay, I am trying to compare two different positions and orientations of a drill. The x and y are elements of SE(3).
 
  • #6
Something like expected and real position? Then I don't see anything wrong with an asymmetry - as an example, "drill too low" could be much worse/better than "drill too high".
 

FAQ: Function which measures "error"

What is a function that measures error?

A function that measures error is a mathematical tool used to quantify the difference between a predicted value and the actual value of a variable. It is used extensively in fields such as statistics, machine learning, and data analysis to evaluate the accuracy of predictive models or data analysis techniques.

Why is measuring error important?

Measuring error is important because it allows us to assess the performance of a model or method and identify areas for improvement. It also helps us understand the reliability and validity of our data and predictions.

How is error typically measured?

Error is typically measured using a variety of metrics such as mean squared error, mean absolute error, root mean squared error, and many others. The choice of metric depends on the type of data and the specific problem being addressed.

What factors can influence the amount of error in a model?

The amount of error in a model can be influenced by a variety of factors, including the complexity of the model, the quality and quantity of the data, the assumptions and limitations of the model, and the chosen metrics for measuring error.

Can error ever be completely eliminated?

No, it is not possible to completely eliminate error in a model or analysis. However, by understanding and minimizing sources of error, we can improve the accuracy and reliability of our predictions and conclusions.

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