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In machine learning and mathematical optimization, loss functions for classification are computationally feasible loss functions representing the price paid for inaccuracy of predictions in classification problems (problems of identifying which category a particular observation belongs to). [1]
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).
Effect of triplet loss minimization in training: the positive is moved closer to the anchor than the negative. Triplet loss is a loss function for machine learning algorithms where a reference input (called anchor) is compared to a matching input (called positive) and a non-matching input (called negative). The distance from the anchor to the ...
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]
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] For an intended output t = ±1 and a classifier score y, the hinge loss of the prediction y is defined as
The negative vector will force learning in the network, while the positive vector will act like a regularizer. For learning by contrastive loss there must be a weight decay to regularize the weights, or some similar operation like a normalization. A distance metric for a loss function may have the following properties [5] Non-negativity: (,)
Similarity learning is closely related to distance metric learning. Metric learning is the task of learning a distance function over objects. A metric or distance function has to obey four axioms: non-negativity, identity of indiscernibles, symmetry and subadditivity (or the triangle inequality). In practice, metric learning algorithms ignore ...
Next, define a family of complicated functions (such as a deep neural network) parametrized by . Finally, define a way to convert any f θ ( z ) {\displaystyle f_{\theta }(z)} into a distribution (in general simple too, but unrelated to p ( z ) {\displaystyle p(z)} ) over the observable random variable X {\displaystyle X} .