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In many applications, objective functions, including loss functions as a particular case, are determined by the problem formulation. In other situations, the decision maker’s preference must be elicited and represented by a scalar-valued function (called also utility function) in a form suitable for optimization — the problem that Ragnar Frisch has highlighted in his Nobel Prize lecture. [4]
These are called margin-based loss functions. Choosing a margin-based loss function amounts to choosing . Selection of a loss function within this framework impacts the optimal which minimizes the expected risk, see empirical risk minimization.
Two very commonly used loss functions are the squared loss, () =, and the absolute loss, () = | |.The squared loss function results in an arithmetic mean-unbiased estimator, and the absolute-value loss function results in a median-unbiased estimator (in the one-dimensional case, and a geometric median-unbiased estimator for the multi-dimensional case).
where x is the instance, [] the expectation value, C k is a class into which an instance is classified, P(C k |x) is the conditional probability of label k for instance x, and L() is the 0–1 loss function:
In this case the set of actions is the parameter space, and a loss function details the cost of the discrepancy between the true value of the parameter and the estimated value. For example, in a linear model with a single scalar parameter θ {\displaystyle \theta } , the domain of θ {\displaystyle \theta } may extend over R {\displaystyle ...
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(Reuters) -The crowd-sourced fact-checking feature of Elon Musk's X, Community Notes, is not countering false claims about the U.S. election, the Center for Countering Digital Hate (CCDH) said in ...
The loss function is a function that maps values of one or more variables onto a real number intuitively representing some "cost" associated with those values. For backpropagation, the loss function calculates the difference between the network output and its expected output, after a training example has propagated through the network.