The Linearized Hellinger--Kantorovich Distance
نویسندگان
چکیده
Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 19 February 2021Accepted: 27 August 2021Published online: 04 January 2022Keywordsoptimal transport, linear embeddings, Hellinger--Kantorovich Distance, exponential and logarithmic mapsAMS Subject Headings49M30, 49K20, 49N90Publication DataISSN (online): 1936-4954Publisher: Society for Industrial Applied MathematicsCODEN: sjisbi
منابع مشابه
Hellinger distance
In this lecture, we will introduce a new notion of distance between probability distributions called Hellinger distance. Using some of the nice properties of this distance, we will generalize the fooling set argument for deterministic protocols to the randomized setting. We will then use this to prove a Ω(n) lower bound for the communication complexity of Disjointness. We will also see how this...
متن کاملOptimal Transport in Competition with Reaction: The Hellinger-Kantorovich Distance and Geodesic Curves
We discuss a new notion of distance on the space of finite and nonnegative measures on Ω ⊂ Rd, which we call Hellinger–Kantorovich distance. It can be seen as an infconvolution of the well-known Kantorovich–Wasserstein distance and the HellingerKakutani distance. The new distance is based on a dynamical formulation given by an Onsager operator that is the sum of a Wasserstein diffusion part and...
متن کاملOptimal Entropy-Transport problems and a new Hellinger-Kantorovich distance between positive measures
We develop a full theory for the new class of Optimal Entropy-Transport problems between nonnegative and finite Radon measures in general topological spaces. They arise quite naturally by relaxing the marginal constraints typical of Optimal Transport problems: given a couple of finite measures (with possibly different total mass), one looks for minimizers of the sum of a linear transport functi...
متن کاملHellinger distance for fuzzy measures
Hellinger distance is a distance between two additive measures defined in terms of the RadonNikodym derivative of these two measures. This measure proposed in 1909 has been used in a large variety of contexts. In this paper we define an analogous measure for fuzzy measures. We discuss them for distorted probabilities and give two examples.
متن کاملOptimal robust estimates using the Hellinger distance
Optimal robust M-estimates of a multidimensional parameter are described using Hampel’s infinitesimal approach. The optimal estimates are derived by minimizing a measure of efficiency under the model, subject to a bounded measure of infinitesimal robustness. To this purpose we define measures of efficiency and infinitesimal sensitivity based on the Hellinger distance. We show that these two mea...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Siam Journal on Imaging Sciences
سال: 2022
ISSN: ['1936-4954']
DOI: https://doi.org/10.1137/21m1400080