The estimated accuracy of a classifier is a random quantity with variability. A common practice in supervised machine learning, is thus to test if the estimated accuracy is significantly better... Show moreThe estimated accuracy of a classifier is a random quantity with variability. A common practice in supervised machine learning, is thus to test if the estimated accuracy is significantly better than chance level. This method of signal detection is particularly popular in neuroimaging and genetics. We provide evidence that using a classifier's accuracy as a test statistic can be an underpowered strategy for finding differences between populations, compared to a bona fide statistical test. It is also computationally more demanding than a statistical test. Via simulation, we compare test statistics that are based on classification accuracy, to others based on multivariate test statistics. We find that the probability of detecting differences between two distributions is lower for accuracy-based statistics. We examine several candidate causes for the low power of accuracy-tests. These causes include: the discrete nature of the accuracy-test statistic, the type of signal accuracy-tests are designed to detect, their inefficient use of the data, and their suboptimal regularization. When the purpose of the analysis is the evaluation of a particular classifier, not signal detection, we suggest several improvements to increase power. In particular, to replace V-fold cross-validation with the Leave-One-Out Bootstrap. Show less
We describe certain birational modifications of nodal relative curves over a regular base of arbitrary dimension. Using these modifications, we provide criteria for the existence of Néron models of... Show moreWe describe certain birational modifications of nodal relative curves over a regular base of arbitrary dimension. Using these modifications, we provide criteria for the existence of Néron models of nodal curves and their Jacobians over a regular base of arbitrary dimension, and describe the Néron models explicitly when they exist. Then, we study the descent behavior of Néron models of abelian varieties under tamely ramified and surjective maps between regular schemes. Show less
