Developing state-of-the-art approaches for specific tasks is a major driving force in our research community. Depending on the prestige of the task, publishing it can come along with a lot of visibility. The question arises how reliable are our evaluation methodologies to compare approaches? One common methodology to identify the state-of-the-art is to partition data into a train, a development and a test set. Researchers can train and tune their approach on some part of the dataset and then select the model that worked best on the development set for a final evaluation on unseen test data. Test scores from different approaches are compared, and performance differences are tested for statistical significance. In this publication, we show that there is a high risk that a statistical significance in this type of evaluation is not due to a superior learning approach. Instead, there is a high risk that the difference is due to chance. For example for the CoNLL 2003 NER dataset we observed in up to 26 of the cases type I errors (false positives) with a threshold of p < 0.05, i.e., falsely concluding a statistically significant difference between two identical approaches. We prove that this evaluation setup is unsuitable to compare learning approaches. We formalize alternative evaluation setups based on score distributions.
As the test set is finite in size, there is a chance that a model achieves a better score on the test set, but would not yield a better score on the data population as a whole. To guard against this case, a significance test like the approximate randomized test @cite_4 or the bootstrap test @cite_9 can be applied. Those methods test the null hypothesis that both models would perform equally on the population as a whole. Significance tests typically estimate the confidence @math , which should be an upper-bound for the probability of a type I error (a false positive error).
@cite_9 @cite_4
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We investigate some pitfalls regarding the discriminatory power of MT evaluation metrics and the accuracy of statistical significance tests. In a discriminative reranking experiment for phrase-based SMT we show that the NIST metric is more sensitive than BLEU or F-score despite their incorporation of aspects of fluency or meaning adequacy into MT evaluation. In an experimental comparison of two statistical significance tests we show that p-values are estimated more conservatively by approximate randomization than by bootstrap tests, thus increasing the likelihood of type-I error for the latter. We point out a pitfall of randomly assessing significance in multiple pairwise comparisons, and conclude with a recommendation to combine NIST with approximate randomization, at more stringent rejection levels than is currently standard. A new non parametric approach to the problem of testing the independence of two random process is developed. The test statistic is the Hilbert Schmidt Independence Criterion (HSIC), which was used previously in testing independence for i.i.d pairs of variables. The asymptotic behaviour of HSIC is established when computed from samples drawn from random processes. It is shown that earlier bootstrap procedures which worked in the i.i.d. case will fail for random processes, and an alternative consistent estimate of the p-values is proposed. Tests on artificial data and real-world Forex data indicate that the new test procedure discovers dependence which is missed by linear approaches, while the earlier bootstrap procedure returns an elevated number of false positives. The code is available online: this https URL . This paper presents a review and critique of statistical null hypothesis testing in ecological studies in general, and wildlife studies in particular, and describes an alternative. Our review of Ecology and the Journal of Wildlife Management found the use of null hypothesis testing to be pervasive. The estimated number of P-values appearing within articles of Ecology exceeded 8,000 in 1991 and has exceeded 3,000 in each year since 1984, whereas the estimated number of P-values in the Journal of Wildlife Management exceeded 8,000 in 1997 and has exceeded 3,000 in each year since 1994. We estimated that 47 (SE = 3.9 ) of the P-values in the Journal of Wildlife Management lacked estimates of means or effect sizes or even the sign of the difference in means or other parameters. We find that null hypothesis testing is uninformative when no estimates of means or effect size and their precision are given. Contrary to common dogma, tests of statistical null hypotheses have relatively little utility in science and are not a fundamental aspect of the scientific method. We recommend their use be reduced in favor of more informative approaches. Towards this objective, we describe a relatively new paradigm of data analysis based on Kullback-Leibler information. This paradigm is an extension of likelihood theory and, when used correctly, avoids many of the fundamental limitations and common misuses of null hypothesis testing. Information-theoretic methods focus on providing a strength of evidence for an a priori set of alternative hypotheses, rather than a statistical test of a null hypothesis. This paradigm allows the following types of evidence for the alternative hypotheses: the rank of each hypothesis, expressed as a model; an estimate of the formal likelihood of each model, given the data; a measure of precision that incorporates model selection uncertainty; and simple methods to allow the use of the set of alternative models in making, formal inference. We provide an example of the information-theoretic approach using data on the effect of lead on survival in spectacled eider ducks (Somateria fischeri). Regardless of the analysis paradigm used, we strongly recommend inferences based on a priori considerations be clearly separated from those resulting from some form of data dredging. Consistently checking the statistical significance of experimental results is one of the mandatory methodological steps to address the so-called "reproducibility crisis" in deep reinforcement learning. In this tutorial paper, we explain how the number of random seeds relates to the probabilities of statistical errors. For both the t-test and the bootstrap confidence interval test, we recall theoretical guidelines to determine the number of random seeds one should use to provide a statistically significant comparison of the performance of two algorithms. Finally, we discuss the influence of deviations from the assumptions usually made by statistical tests. We show that they can lead to inaccurate evaluations of statistical errors and provide guidelines to counter these negative effects. We make our code available to perform the tests 1 .