Statistical tests that compare classification algorithms are univariate and use a single performance measure, e.g., misclassification error, F measure, AUC, and so on. In multivariate tests, comparison is done using multiple measures simultaneously. For example, error is the sum of false positives and false negatives and a univariate test on error cannot make a distinction between these two sou...

A. Appendix A A.1. Proof of Theorem 1 The proof is by contradiction. Fix a distribution P satisfying conditional independence, and let x denote a fixed set of instances. Denote P(Y = 1|xi) = ηi and the optimal classifier by s∗ ∈ {0, 1}n. Suppose there exist indices j, k such that sj = 1, sk = 0 and ηj < ηk. Let s′ ∈ {0, 1}n be such that sj = 0 and sk = 1, but identical to s∗ otherwise i.e. si =...

A linear classification rule (used with equal covariance matrices) was contrasted with a quadratic rule (used with unequal covariance matrices) for accuracy of internal and external classification. The comparisons were made for seven situations which resulted from combining conditions (equal and unequal covariance matrices, and two and three criterion groups) for different sets of real data. Fo...

Multivariate loss functions are extensively employed in several prediction tasks arising in Information Retrieval. Often, the goal in the tasks is to minimize expected loss when retrieving relevant items from a presented set of items, where the expectation is with respect to the joint distribution over item sets. Our key result is that for most multivariate losses, the expected loss is provably...

t he relationship between the price of oil and the level of economic activity is a fundamental empirical issue in macroeconomics. in this research, by using a multivariate garch-in-mean var, we try to investigate direct effects of uncertainty of oil price on macroeconomics of iran by using annually data from 1965 to 2013.results show that uncertainty about oil prices had a negative and signific...

Traditional image texture measure usually allows a texture description of a single band of the spectrum, characterizing the spatial variability of gray-level values within the singleband image. A problem with the approach while applied to multispectral images is that it only uses the texture information from selected bands. In this paper, we propose a new multivariate texture measure based on t...