Methods to integrate multinormals and compute classification measures

Autor:	Das, Abhranil, Geisler, Wilson S
Rok vydání:	2020
Předmět:	Statistics - Machine Learning Computer Science - Computer Vision and Pattern Recognition Computer Science - Machine Learning 28-08 (Primary) 28-04 62-08 (Secondary) 62-04 68Txx I.2.10 I.2.5 I.5.1 G.3 G.4 J.4
Druh dokumentu:	Working Paper
Popis:	Univariate and multivariate normal probability distributions are widely used when modeling decisions under uncertainty. Computing the performance of such models requires integrating these distributions over specific domains, which can vary widely across models. Besides some special cases, there exist no general analytical expressions, standard numerical methods or software for these integrals. Here we present mathematical results and open-source software that provide (i) the probability in any domain of a normal in any dimensions with any parameters, (ii) the probability density, cumulative distribution, and inverse cumulative distribution of any function of a normal vector, (iii) the classification errors among any number of normal distributions, the Bayes-optimal discriminability index and relation to the operating characteristic, (iv) ways to scale the discriminability of two distributions, (v) dimension reduction and visualizations for such problems, and (vi) tests for how reliably these methods may be used on given data. We demonstrate these tools with vision research applications of detecting occluding objects in natural scenes, and detecting camouflage. Comment: 16 pages, 9 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2012.14331 Zobrazit plný text záznamu View this record from Arxiv