Cross-Validation (CV), and out-of-sample performance-estimation protocols in general, are often employed both for (a) selecting the optimal combination of algorithms and values of hyper-parameters (called a configuration) for producing the final predictive model, and (b) estimating the predictive performance of the final model. However, the cross-validated performance of the best configuration is optimistically biased. We present an efficient bootstrap method that corrects for the bias, called Bootstrap Bias Corrected CV (BBC-CV). BBC-CV's main idea is to bootstrap the whole process of selecting the best-performing configuration on the out-of-sample predictions of each configuration, without additional training of models. In comparison to the alternatives, namely the nested cross-validation and a method by Tibshirani and Tibshirani, BBC-CV is computationally more efficient, has smaller variance and bias, and is applicable to any metric of performance (accuracy, AUC, concordance index, mean squared error). Subsequently, we employ again the idea of bootstrapping the out-of-sample predictions to speed up the CV process. Specifically, using a bootstrap-based hypothesis test we stop training of models on new folds of statistically-significantly inferior configurations. We name the method Bootstrap Corrected with Early Dropping CV (BCED-CV) that is both efficient and provides accurate performance estimates.
Krueger @cite_14 in 2015 introduced the so-called (CVST) which uses nonparametric testing together with sequential analysis in order to choose the best performing configuration on the basis of linearly increasing subsets of data. At each step, the Friedman @cite_22 or the Cochran's Q test @cite_18 (for regression and classification tasks respectively) are employed in order to detect statistically significant differences between configurations' performances. Then, the seemingly under-performing configurations are further tested through sequential analysis to determine which of them will be discharged. Finally, an early stopping criterion is employed to further speed up the CV process. The winner configuration is the one that has the best average ranking, based on performance, in the last few iterations specified in advance. The disadvantage of CVST is that it initially operates on smaller subsets, thus risking the early elimination of good models when the original dataset is already small.
@cite_18 @cite_14 @cite_22
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Context: This paper presents an approach for selecting regression test cases in the context of large-scale database applications. We focus on a black-box (specification-based) approach, relying on classification tree models to model the input domain of the system under test (SUT), in order to obtain a more practical and scalable solution. We perform an experiment in an industrial setting where the SUT is a large database application in Norway's tax department. Objective: We investigate the use of similarity-based test case selection for supporting black box regression testing of database applications. We have developed a practical approach and tool (DART) for functional black-box regression testing of database applications. In order to make the regression test approach scalable for large database applications, we needed a test case selection strategy that reduces the test execution costs and analysis effort. We used classification tree models to partition the input domain of the SUT in order to then select test cases. Rather than selecting test cases at random from each partition, we incorporated a similarity-based test case selection, hypothesizing that it would yield a higher fault detection rate. Method: An experiment was conducted to determine which similarity-based selection algorithm was the most suitable in selecting test cases in large regression test suites, and whether similarity-based selection was a worthwhile and practical alternative to simpler solutions. Results: The results show that combining similarity measurement with partition-based test case selection, by using similarity-based test case selection within each partition, can provide improved fault detection rates over simpler solutions when specific conditions are met regarding the partitions. Conclusions: Under the conditions present in the experiment the improvements were marginal. However, a detailed analysis concludes that the similarity-based selection strategy should be applied when a large number of test cases are contained in each partition and there is significant variability within partitions. If these conditions are not present, incorporating similarity measures is not worthwhile, since the gain is negligible over a random selection within each partition. We consider the linear regression problem under semi-supervised settings wherein the available data typically consists of: (i) a small or moderate sized 'labeled' data, and (ii) a much larger sized 'unlabeled' data. Such data arises naturally from settings where the outcome, unlike the covariates, is expensive to obtain, a frequent scenario in modern studies involving large databases like electronic medical records (EMR). Supervised estimators like the ordinary least squares (OLS) estimator utilize only the labeled data. It is often of interest to investigate if and when the unlabeled data can be exploited to improve estimation of the regression parameter in the adopted linear model. In this paper, we propose a class of 'Efficient and Adaptive Semi-Supervised Estimators' (EASE) to improve estimation efficiency. The EASE are two-step estimators adaptive to model mis-specification, leading to improved (optimal in some cases) efficiency under model mis-specification, and equal (optimal) efficiency under a linear model. This adaptive property, often unaddressed in the existing literature, is crucial for advocating 'safe' use of the unlabeled data. The construction of EASE primarily involves a flexible 'semi-non-parametric' imputation, including a smoothing step that works well even when the number of covariates is not small; and a follow up 'refitting' step along with a cross-validation (CV) strategy both of which have useful practical as well as theoretical implications towards addressing two important issues: under-smoothing and over-fitting. We establish asymptotic results including consistency, asymptotic normality and the adaptive properties of EASE. We also provide influence function expansions and a 'double' CV strategy for inference. The results are further validated through extensive simulations, followed by application to an EMR study on auto-immunity. With the increasing size of today's data sets, nding the right parameter configuration in model selection via cross-validation can be an extremely time-consuming task. In this paper we propose an improved cross-validation procedure which uses nonparametric testing coupled with sequential analysis to determine the best parameter set on linearly increasing subsets of the data. By eliminating underperforming candidates quickly and keeping promising candidates as long as possible, the method speeds up the computation while preserving the power of the full cross-validation. Theoretical considerations underline the statistical power of our procedure. The experimental evaluation shows that our method reduces the computation time by a factor of up to 120 compared to a full cross-validation with a negligible impact on the accuracy. We propose in this paper a new approach to train the Generative Adversarial Nets (GANs) with a mixture of generators to overcome the mode collapsing problem. The main intuition is to employ multiple generators, instead of using a single one as in the original GAN. The idea is simple, yet proven to be extremely effective at covering diverse data modes, easily overcoming the mode collapsing problem and delivering state-of-the-art results. A minimax formulation was able to establish among a classifier, a discriminator, and a set of generators in a similar spirit with GAN. Generators create samples that are intended to come from the same distribution as the training data, whilst the discriminator determines whether samples are true data or generated by generators, and the classifier specifies which generator a sample comes from. The distinguishing feature is that internal samples are created from multiple generators, and then one of them will be randomly selected as final output similar to the mechanism of a probabilistic mixture model. We term our method Mixture Generative Adversarial Nets (MGAN). We develop theoretical analysis to prove that, at the equilibrium, the Jensen-Shannon divergence (JSD) between the mixture of generators’ distributions and the empirical data distribution is minimal, whilst the JSD among generators’ distributions is maximal, hence effectively avoiding the mode collapsing problem. By utilizing parameter sharing, our proposed model adds minimal computational cost to the standard GAN, and thus can also efficiently scale to large-scale datasets. We conduct extensive experiments on synthetic 2D data and natural image databases (CIFAR-10, STL-10 and ImageNet) to demonstrate the superior performance of our MGAN in achieving state-of-the-art Inception scores over latest baselines, generating diverse and appealing recognizable objects at different resolutions, and specializing in capturing different types of objects by the generators.