In probability theory, integral probability metrics are types of distance functions between probability distributions, defined by how well a class of functions...

The only f-divergence that is also an integral probability metric is the total variation. A pair of probability distributions can be viewed as a game...

The total variation distance is an f-divergence and an integral probability metric. The total variation distance is related to the Kullback–Leibler divergence...

metric Wasserstein metric: also known as the Kantorovich metric, or earth mover's distance Mahalanobis distance Amari distance Integral probability metrics...

distance or Kantorovich–Rubinstein metric is a distance function defined between probability distributions on a given metric space M {\displaystyle M} . It...

metric is a particular Riemannian metric which can be defined on a smooth statistical manifold, i.e., a smooth manifold whose points are probability measures...

entropy integral is a mathematical concept in the field of probability theory that describes a relationship involving the entropy of certain metric spaces...

mathematical theory of probability, we confine our study to a probability measure μ, which satisfies μ(E) = 1. Lebesgue's theory defines integrals for a class of...

The partition function or configuration integral, as used in probability theory, information theory and dynamical systems, is a generalization of the definition...

A prior probability distribution of an uncertain quantity, often simply called the prior, is its assumed probability distribution before some evidence...

In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption...

between two probability distributions. It is a type of f-divergence. The Hellinger distance is defined in terms of the Hellinger integral, which was introduced...

Corrective Commit Probability Code Quality Metric". arXiv:2007.10912 [cs.SE]. Binstock, Andrew (March 2010). "Integration Watch: Using metrics effectively"...

application in probability and stochastic processes, and in certain branches of analysis including potential theory. The Lebesgue–Stieltjes integral ∫ a b f...

statistical distance, it is not a metric on the space of probability distributions, but instead it is a divergence. While metrics are symmetric and generalize...

with metric spaces as their state spaces. Two stochastic processes X {\displaystyle X} and Y {\displaystyle Y} defined on the same probability space...

distinct measures that give the same moments. Given a Borel measure μ on a metric space X such that μ(X) > 0 and μ(B(x, r)) ≤ rs holds for some constant s...

the geodesic distance between the probability distributions p , q {\displaystyle p,q} under the chi-squared metric d s 2 = 1 2 ∑ i d p i 2 p i {\displaystyle...

1]\subset \mathbb {R} \right\}.} This metric has some limitations. For example, the space of Radon probability measures on X, P ( X ) = { m ∈ M + ( X...

{\displaystyle f} is a probability density function, then the value of the integral above is called the n-th moment of the probability distribution. More...

problem Prior probability distribution Total variation distance Hellinger distance Wasserstein metric Lévy–Prokhorov metric Lévy metric Continuity correction...

measures or integrals. For example, it is used to equate a probability for a random variable X {\displaystyle X} with the Lebesgue-Stieltjes integral typically...

is a Polish space, the total variation metric coincides with the Radon metric. If μ and ν are both probability measures, then the total variation distance...

infinitesimals", it has two major branches, differential calculus and integral calculus. The former concerns instantaneous rates of change, and the slopes...

equal to the probability that an arbitrary demand unit is delivered without delay. This approach usually involves calculating a loss integral, whose values...

Measure space Metric space Minkowski space Müntz space Normed space Paracompact space Perfectoid space Planar space Polish space Probability space Projective...

Probability mass function Probability matching Probability metric Probability of error Probability of precipitation Probability plot Probability plot correlation...

1}\left(\mathbb {E} [f(X)]-\mathbb {E} [f(Y)]\right),} a form of integral probability metric. Given n training examples from P ( X ) {\displaystyle P(X)}...

In integral geometry (otherwise called geometric probability theory), Hadwiger's theorem characterises the valuations on convex bodies in R n . {\displaystyle...

in 1967. Integrals of correspondences have applications in general equilibrium theory in mathematical economics, random sets in probability theory, partial...