A New Toolkit for Mortality Data Analytics

A precise bare simulation approach to the minimization of some distances. Foundations

“…[315] for automatic alarm-triggering detection of events (e.g. patient health degradations) from collected data by biomedical sensors, Fu et al [128] for the study of income distributions in China, Ha et al [151] for x−ray spectrum reconstruction in computer tomography (CT) systems (with γ = 1), Iqbal & Seghouane [161] for robust sequential dictionary learning, Luppino et al [233] for unsupervised change detection in heterogeneous multitemporal satellite images (with γ = 1 2 ), Sason [320] in connection with data-processing and majorization inequalities, Krömer & Stummer [198] for the smoothing and error-correcting of crude mortality rates (where they even employ non-probability-type vectors), Bekhet & Ahmed [37] for effectiveness evaluations in video retrieval (with γ = −1, γ = 1 2 ), Cai et al [71] for the stabilization of trainings of generative adversarial networks (GANs), Fu et al [129] for automatic molecule optimization, Görtler et al [139] for dimensionality reduction on uncertain data in visualization and computer graphics (with γ = 1 2 ), Kammerer & Stummer [179] for optimal decision making in the presence of pandemics (e.g. COVID-19), Kanapram et al [180] for the development of collective self-awareness in a network of connected and autonomous vehicles through agent-centered detection of abnormal situations (with γ = 1…”

“…From the generator ϕ α,β1,β2, c given in (198), we construct the corresponding divergence (cf. ( 4))…”

“…To proceed, from formula (163) (see also (165)) we can derive -analogously to (198) -for all t ∈ R ϕ α,β1,…”

Optimal transport with some directed distances

“…= min {X∼È, T (X)∼É} E Υ φ,c,W,W3 (X, T (X)) (17) where ( 16) is called Monge transportation problem (MTP). Here, Γ (È, É) denotes the family of all measurable maps T : R → R such that È[T…”

“…More generally, Stummer [37] and Stummer & Vajda [38] introduced the concept of scaled Bregman distances, which enlarges and flexibilizes both the abovementioned CASM and CB divergence/distance classes; their use for robustness of minimum-distance parameter estimation, testing as well as applications can be found e.g. in Kißlinger & Stummer [13,14,15,16], Roensch & Stummer [31,32,33], Krömer & Stummer [17]. An even much wider framework of directed distances/divergences (BS distances) was introduced in the recent comprehensive paper of Broniatowski & Stummer [6].…”