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In probability theory, the chain rule [1] (also called the general product rule [2] [3]) describes how to calculate the probability of the intersection of, not necessarily independent, events or the joint distribution of random variables respectively, using conditional probabilities.
The Probability Jaccard Index has a geometric interpretation as the area of an intersection of simplices. Every point on a unit -simplex corresponds to a probability distribution on + elements, because the unit -simplex is the set of points in + dimensions that sum to 1. To derive the Probability Jaccard Index geometrically, represent a ...
For example, the union of three sets A, B, and C contains all elements of A, all elements of B, and all elements of C, and nothing else. Thus, x is an element of A ∪ B ∪ C if and only if x is in at least one of A, B, and C. A finite union is the union of a finite number of sets; the phrase does not imply that the union set is a finite set ...
Given a subset Z in the intersection = of varieties, understand the complement of Z in the intersection; i.e., the residual set to Z. The intersection determines a class ( X 1 ⋯ X r ) {\displaystyle (X_{1}\cdots X_{r})} , the intersection product , in the Chow group of an ambient space and, in this situation, the problem is to understand the ...
The goal of MinHash is to estimate J(A,B) quickly, without explicitly computing the intersection and union. Let h be a hash function that maps the members of U to distinct integers, let perm be a random permutation of the elements of the set U , and for any subset S of U define h min ( S ) to be the minimal member of S with respect to h ∘ ...
In probability theory, Boole's inequality, also known as the union bound, says that for any finite or countable set of events, the probability that at least one of the events happens is no greater than the sum of the probabilities of the individual events. This inequality provides an upper bound on the probability of occurrence of at least one ...
In mathematics, the limit of a sequence of sets,, … (subsets of a common set ) is a set whose elements are determined by the sequence in either of two equivalent ways: (1) by upper and lower bounds on the sequence that converge monotonically to the same set (analogous to convergence of real-valued sequences) and (2) by convergence of a sequence of indicator functions which are themselves ...
Let A and B be fuzzy sets that A,B ⊆ U, u is any element (e.g. value) in the U universe: u ∈ U. Standard complement = ()The complement is sometimes denoted by ∁A or A ∁ instead of ¬A.