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Main concerns for data differencing are usability and space efficiency (patch size).. If one simply wishes to reconstruct the target given the source and patch, one may simply include the entire target in the patch and "apply" the patch by discarding the source and outputting the target that has been included in the patch; similarly, if the source and target have the same size one may create a ...
The study of dynamic equations on time scales reveals such discrepancies, and helps avoid proving results twice—once for differential equations and once again for difference equations. The general idea is to prove a result for a dynamic equation where the domain of the unknown function is a so-called time scale (also known as a time-set ...
Fisher information is widely used in optimal experimental design. Because of the reciprocity of estimator-variance and Fisher information, minimizing the variance corresponds to maximizing the information. When the linear (or linearized) statistical model has several parameters, the mean of the parameter estimator is a vector and its variance ...
Discrete differential calculus is the study of the definition, properties, and applications of the difference quotient of a function. The process of finding the difference quotient is called differentiation .
A bump function is a smooth function with compact support.. In mathematical analysis, the smoothness of a function is a property measured by the number of continuous derivatives (differentiability class) it has over its domain.
The classical finite-difference approximations for numerical differentiation are ill-conditioned. However, if is a holomorphic function, real-valued on the real line, which can be evaluated at points in the complex plane near , then there are stable methods.
Let : be a continuously-differentiable, strictly convex function defined on a convex set. The Bregman distance associated with F for points p , q ∈ Ω {\displaystyle p,q\in \Omega } is the difference between the value of F at point p and the value of the first-order Taylor expansion of F around point q evaluated at point p :
Leonard J. Savage argued that using non-Bayesian methods such as minimax, the loss function should be based on the idea of regret, i.e., the loss associated with a decision should be the difference between the consequences of the best decision that could have been made under circumstances will be known and the decision that was in fact taken before they were known.