A GLRT for estimating the number of correlated components in sample-poor mCCA

Tanuj Hasija, Tim Marrinan
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Abstract

In many applications, components correlated across multiple data sets represent meaningful patterns and commonalities. Estimates of these patterns can be improved when the number of correlated components is known, but since data exploration often occurs in an unsupervised setting, the number of correlated components is generally not known. In this paper, we derive a generalized likelihood ratio test (GLRT) for estimating the number of components correlated across multiple data sets. In particular, we are concerned with the scenario where the number of available samples is small. As a result of the small sample support, correlation coefficients and other summary statistics are significantly overestimated by traditional methods. The proposed test combines linear dimensionality reduction with a GLRT based on a measure of multiset correlation referred as the generalized variance cost function (mCCA-GENVAR). By jointly estimating the rank of the dimensionality reduction and the number of correlated components, we are able to provide high-accuracy estimates in the challenging sample-poor setting. These advantages are illustrated in numerical experiments that compare and contrast the proposed method with existing techniques.
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用于估计样本贫乏的mCCA中相关成分数量的GLRT
在许多应用程序中,跨多个数据集关联的组件表示有意义的模式和共性。当相关组件的数量已知时,可以改进这些模式的估计,但是由于数据探索经常发生在无监督的设置中,因此相关组件的数量通常是未知的。在本文中,我们推导了一个广义似然比检验(GLRT)来估计多个数据集之间相关成分的数量。特别是,我们关心的是可用样本数量很少的情况。由于样本支持度小,传统方法明显高估了相关系数和其他汇总统计量。提出的测试结合了线性降维和基于多集相关度量的GLRT,即广义方差成本函数(mCCA-GENVAR)。通过联合估计降维的等级和相关成分的数量,我们能够在具有挑战性的样本贫乏设置中提供高精度的估计。这些优点在数值实验中得到了说明,并与现有技术进行了比较。
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