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An optimization problem seeks to minimize a loss function. An objective function is either a loss function or its opposite (in specific domains, variously called a reward function, a profit function, a utility function, a fitness function, etc.), in which case it is to be maximized. The loss function could include terms from several levels of ...
Cross-entropy can be used to define a loss function in machine learning and optimization. Mao, Mohri, and Zhong (2023) give an extensive analysis of the properties of the family of cross-entropy loss functions in machine learning, including theoretical learning guarantees and extensions to adversarial learning. [3]
The sole minimizer of the expected risk, , associated with the above generated loss functions can be directly found from equation (1) and shown to be equal to the corresponding (). This holds even for the nonconvex loss functions, which means that gradient descent based algorithms such as gradient boosting can be used to construct the minimizer.
As defined above, the Huber loss function is strongly convex in a uniform neighborhood of its minimum =; at the boundary of this uniform neighborhood, the Huber loss function has a differentiable extension to an affine function at points = and =. These properties allow it to combine much of the sensitivity of the mean-unbiased, minimum-variance ...
The plot shows that the Hinge loss penalizes predictions y < 1, corresponding to the notion of a margin in a support vector machine. In machine learning, the hinge loss is a loss function used for training classifiers. The hinge loss is used for "maximum-margin" classification, most notably for support vector machines (SVMs). [1]
In Taguchi's view tolerance specifications are given by engineers and not by customers; what the customer experiences is 'loss'. This equation is true for a single product; if 'loss' is to be calculated for multiple products the loss function is given by L = k[S 2 + (¯ – m) 2], where S 2 is the 'variance of product size' and ¯ is the ...
The cross-entropy (,) is itself such a measurement (formally a loss function), but it cannot be thought of as a distance, since (,) =: is not zero. This can be fixed by subtracting H ( P ) {\displaystyle H(P)} to make D KL ( P ∥ Q ) {\displaystyle D_{\text{KL}}(P\parallel Q)} agree more closely with our notion of distance, as the excess loss.
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.