Indicator function

An indicator function, also known as a characteristic function, is a mathematical function that is defined on a set X and is used to indicate whether an element x belongs to a subset A of X. The indicator function takes on the values of either 0 or 1, with 1 indicating that the element is a member of the subset and 0 indicating that it is not. The notation ¡iA is commonly used to represent the indicator function for subset A, with the value of 1 denoting the presence of an element in the subset and 0 denoting its absence.From: Soft Computing and Its Applications, Volume One [2014], Data Science and Machine Learning [2019]

Decision Trees and Ensemble Methods

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Published in Dirk P. Kroese, Zdravko I. Botev, Thomas Taimre, Radislav Vaisman, Data Science and Machine Learning, 2019

Dirk P. Kroese, Zdravko I. Botev, Thomas Taimre, Radislav Vaisman

where 1 denotes the indicator function. The representation (8.1) is very general and depends on (1) how the regions {ℛw} are constructed via the logical conditions in the decision tree, as well as (2) how the regional prediction functions of the leaf nodes are defined. Simple logical conditions of the form xj ⩽ ξ split a Euclidean feature space into rectangles aligned with the axes. For example, Figure 8.2 partitions the feature space into six rectangles: two blue and four red rectangles. regional prediction functions

Accelerated dual-averaging primal–dual method for composite convex minimization

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Published in Optimization Methods and Software, 2020

Conghui Tan, Yuqiu Qian, Shiqian Ma, Tong Zhang

In this paper, we consider minimizing the following composite convex function: where , and both and are convex closed functions. Here f can be either smooth or non-smooth, and we assume g has easy proximal mapping. Problem (1) covers a wide range of applications. For example, choosing f to be the indicator function of a convex set corresponds to minimizing a convex function over a polyhedron. It covers the Lasso problem [21] by setting and . Another application of the form (1) is the support vector machine (SVM): where is the feature vector of the ith data sample and is the corresponding label.

Indicator function

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Decision Trees and Ensemble Methods

Accelerated dual-averaging primal–dual method for composite convex minimization