In the task of comparing two classification algorithms, the widely-used McNemar's test aims to infer the presence of a significant difference between the error rates of the two classification algorithms. However, the power of the conventional McNemar's test is usually unpromising because the hold-out (HO) method in the test merely uses a single train-validation split that usually produces a highly varied estimation of the error rates. In contrast, a cross-validation (CV) method repeats the HO method in multiple times and produces a stable estimation. Therefore, a CV method has a great advantage to improve the power of McNemar's test. Among all types of CV methods, a block-regularized 5$\times$2 CV (BCV) has been shown in many previous studies to be superior to the other CV methods in the comparison task of algorithms because the 5$\times$2 BCV can produce a high-quality estimator of the error rate by regularizing the numbers of overlapping records between all training sets. In this study, we compress the 10 correlated contingency tables in the 5$\times$2 BCV to form an effective contingency table. Then, we define a 5$\times$2 BCV McNemar's test on the basis of the effective contingency table. We demonstrate the reasonable type I error and the promising power of the proposed 5$\times$2 BCV McNemar's test on multiple simulated and real-world data sets.

Time series analysis is needed almost in any quantitative field and real-life systems that collect data over time, i.e., temporal datasets. Building predictive models on temporal datasets for the future evolution of systems in consideration are usually called forecasting. The validation of such models deviates from the standard holdout method of having random disjoint splits of train, test, and validation sets used in supervised learning. This stems from the fact that time series are ordered, and order induces all sorts of statistical properties that should be retained. For this reason, applying direct cross-validation to time-series model building is not possible and only restricted to out-of-sample (OOS) validation, using the end-tail of a temporal set as a single test set.

In machine learning, statistics, econometrics and statistical physics, $k$-fold cross-validation (CV) is used as a standard approach in quantifying the generalization performance of a statistical model. Applying this approach directly to time series models is avoided by practitioners due to intrinsic nature of serial correlations in the ordered data due to implications like absurdity of using future data to predict past and non-stationarity issues. In this work, we propose a technique called {\it reconstructive cross validation} ($rCV$) that avoids all these issues enabling generalized learning in time-series as a meta-algorithm. In $rCV$, data points in the test fold, randomly selected points from the time series, are first removed. Then, a secondary time series model or a technique is used in reconstructing the removed points from the test fold, i.e., imputation or smoothing. Thereafter, the primary model is build using new dataset coming from the secondary model or a technique. The performance of the primary model on the test set by computing the deviations from the originally removed and out-of-sample (OSS) data are evaluated simultaneously. This amounts to reconstruction and prediction errors. By this procedure serial correlations and data order is retained and $k$-fold cross-validation is reached generically. If reconstruction model uses a technique whereby the existing data points retained exactly, such as Gaussian process regression, the reconstruction itself will not result in information loss from non-reconstructed portion of the original data points. We have applied $rCV$ to estimate the general performance of the model build on simulated Ornstein-Uhlenbeck process. We have shown an approach to build a time-series learning curves utilizing $rCV$.

Explanations for deep neural network predictions in terms of domain-related concepts can be valuable in medical applications, where justifications are important for confidence in the decision-making. In this work, we propose a methodology to exploit continuous concept measures as Regression Concept Vectors (RCVs) in the activation space of a layer. The directional derivative of the decision function along the RCVs represents the network sensitivity to increasing values of a given concept measure. When applied to breast cancer grading, nuclei texture emerges as a relevant concept in the detection of tumor tissue in breast lymph node samples. We evaluate score robustness and consistency by statistical analysis.