Methods to integrate multinormals and compute classification measures
Methods to integrate multinormals and compute classification measures
复制标题
整合多重正态和计算分类度量的方法
DOI：
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
W. Geisler
中科院分区：
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作者：
Abhranil Das;W. Geisler
单变量和多变量正态概率分布在不确定性决策建模中被广泛使用。计算这些模型的性能需要将这些分布集成到特定的域中，这些域在不同的模型中可能会有很大的差异。除某些特殊情况外，这些积分还没有一般的解析表达式、标准的数值方法和软件。在这里，我们提出了数学结果和开源软件，提供了（i）任何参数的任何维度的任何域中的正态分布的概率，（ii）正态向量的任何函数的概率密度，累积分布和逆累积分布，（iii）任何数量的正态分布之间的分类误差，贝叶斯最佳区分指数和与操作特性的关系，（iv）这些问题的降维和可视化，以及（v）测试这些方法在给定数据上的可靠性。我们展示了这些工具与视觉研究的应用程序，在自然场景中检测遮挡物体，并检测伪装。
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) dimension reduction and visualizations for such problems, and (v) 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.