weighti

Weighti is a term used in a variety of mathematical and computational contexts to denote a family of weights indexed by i. The concept is not standardized and its exact meaning depends on the field and problem at hand.

Formally, weighti refers to a family of functions {w_i} with domain X and codomain nonnegative real numbers, often written as w_i: X -> R_{\ge 0}. Each w_i assigns a nonnegative weight to elements of X, representing importance, frequency, or probability mass. In graph theory, weighti(e) denotes the weight of edge e under scenario i.

Applications include computing weighted sums or averages across i, or using weights in optimization and inference. In graphs, weighti can influence shortest-path computations or tree constructions under a given scenario i. In statistics and machine learning, weighti can serve as importance weights for observations or as weights for ensemble components or time-dependent kernels.

Variants may include normalizing weights so that sum_i w_i(x) = 1 for each x, or making weights depend on confidence or data quality. Weights can be static or dynamic, and they may follow rules such as exponential decay with i or polynomial schemes.

See also: weight function, weighting, kernel, weighted sum. Weighti is a flexible, context-dependent concept rather than a single standard definition.