Mathematical relation assigning a probability event to a cost
In mathematical optimization and decision theory, a loss function or cost function (sometimes also called an error function) [1] is a function that maps an event or values of one or more variables onto a real number intuitively representing some "cost" associated with the event. 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 the hierarchy.
In statistics, typically a loss function is used for parameter estimation, and the event in question is some function of the difference between estimated and true values for an instance of data. The concept, as old as Laplace, was reintroduced in statistics by Abraham Wald in the middle of the 20th century.[2] In the context of economics, for example, this is usually economic cost or regret. In classification, it is the penalty for an incorrect classification of an example. In actuarial science, it is used in an insurance context to model benefits paid over premiums, particularly since the works of Harald Cramér in the 1920s.[3] In optimal control, the loss is the penalty for failing to achieve a desired value. In financial risk management, the function is mapped to a monetary loss.
^Hastie, Trevor; Tibshirani, Robert; Friedman, Jerome H. (2001). The Elements of Statistical Learning. Springer. p. 18. ISBN 0-387-95284-5.
^Wald, A. (1950). Statistical Decision Functions. Wiley.
^Cramér, H. (1930). On the mathematical theory of risk. Centraltryckeriet.
optimization and decision theory, a lossfunction or cost function (sometimes also called an error function) is a function that maps an event or values of...
learning and mathematical optimization, lossfunctions for classification are computationally feasible lossfunctions representing the price paid for inaccuracy...
statistics, the Huber loss is a lossfunction used in robust regression, that is less sensitive to outliers in data than the squared error loss. A variant for...
The Taguchi lossfunction is graphical depiction of loss developed by the Japanese business statistician Genichi Taguchi to describe a phenomenon affecting...
context of control theory. Backpropagation computes the gradient of a lossfunction with respect to the weights of the network for a single input–output...
mutations, are a form of loss-of-function mutations that completely prohibit the gene's function. The mutation leads to a complete loss of operation at the...
Triplet loss is a lossfunction for machine learning algorithms where a reference input (called anchor) is compared to a matching input (called positive)...
In machine learning, the hinge loss is a lossfunction used for training classifiers. The hinge loss is used for "maximum-margin" classification, most...
fiber Dielectric loss, a dielectric material's inherent dissipation of electromagnetic energy Lossfunction, in statistics, a function representing the...
comparisons of treatment means. However, lossfunctions were avoided by Ronald A. Fisher[clarification needed - lossfunctions weren't explicitly mentioned yet]...
other methods by allowing optimization of an arbitrary differentiable lossfunction. The idea of gradient boosting originated in the observation by Leo...
128-dimensional Euclidean space. The system used the triplet lossfunction as the cost function and introduced a new online triplet mining method. The system...
between the hinge loss and these other lossfunctions is best stated in terms of target functions - the function that minimizes expected risk for a given...
central tendency; because a biased estimator gives a lower value of some lossfunction (particularly mean squared error) compared with unbiased estimators...
as the dysfunction or loss of motor and/or sensory function in the cervical area of the spinal cord. A loss of motor function can present as either weakness...
(x_{i},\;y_{i})} . In order to measure how well a function fits the training data, a lossfunction L : Y × Y → R ≥ 0 {\displaystyle L:Y\times Y\to \mathbb...
predefined lossfunction on given independent data. The objective function takes a tuple of hyperparameters and returns the associated loss. Cross-validation...
values and the actual value. MSE is a risk function, corresponding to the expected value of the squared error loss. The fact that MSE is almost always strictly...
value of a lossfunction (i.e., the posterior expected loss). Equivalently, it maximizes the posterior expectation of a utility function. An alternative...
likelihood function (often simply called the likelihood) is the joint probability mass (or probability density) of observed data viewed as a function of the...
linear-error loss respectively—which are more representative of typical lossfunctions—and for a continuous posterior distribution there is no lossfunction which...
certain time. The survival function is also known as the survivor function or reliability function. The term reliability function is common in engineering...
or the median. Scoring rules and scoring functions can be thought of as "cost functions" or "lossfunctions". They are evaluated as empirical mean of...