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General Form of a Loss Function

Description

To get an idea on the performance of a prediction model a loss function is typically used. The loss function can quantify how good or bad a model is based on the prediction a model makes and the target output or 'ground truth', these inputs need to be of the same dimension. A loss function compares these two inputs and maps them to a non-negative real number using some kind of operation. Well known loss functions include the Counting loss and Mean Squared Error Loss (MSE)

\[\htmlClass{sdt-0000000072}{L} : \htmlClass{sdt-0000000045}{\mathbb{R}}^{\htmlClass{sdt-0000000117}{n}} \times \htmlClass{sdt-0000000045}{\mathbb{R}}^{\htmlClass{sdt-0000000117}{n}} \rightarrow \htmlClass{sdt-0000000045}{\mathbb{R}}_{\geq 0}\]

Symbols Used:

This is the symbol for a loss function. It is a function that calculates how wrong a model's inference is compared to where it should be.

\( n \)

This symbol represents any given whole number, \( n \in \htmlClass{sdt-0000000014}{\mathbb{W}}\).

\( \mathbb{R} \)

This is the symbol for the set of real numbers.

Example

Examples of well known loss function:

  1. Counting loss
  2. Mean Squared Error Loss (MSE)
  3. Quadratic

References

  1. Jaeger, H. (n.d.). Neural Networks (AI) (WBAI028-05) Lecture Notes BSc program in Artificial Intelligence. Retrieved April 14, 2024, from https://www.ai.rug.nl/minds/uploads/LN_NN_RUG.pdf