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There are various applications, where companies need to decide to which individuals they should best allocate treatment. To support such decisions, uplift models are applied to predict treatment effects on an individual level. Based on the predicted treatment effects, individuals can be ranked and treatment allocation can be prioritized according to this ranking. An implicit assumption, which has not been doubted in the previous uplift modeling literature, is that this treatment prioritization approach tends to bring individuals with high treatment effects to the top and individuals with low treatment effects to the bottom of the ranking. In our research, we show that heteroskedastictity in the training data can cause a bias of the uplift model ranking: individuals with the highest treatment effects can get accumulated in large numbers at the bottom of the ranking. We explain theoretically how heteroskedasticity can bias the ranking of uplift models and show this process in a simulation and on real-world data. We argue that this problem of ranking bias due to heteroskedasticity might occur in many real-world applications and requires modification of the treatment prioritization to achieve an efficient treatment allocation.

Public policy also represent a special subdiscipline within political science, within political science. They are given increasing importance and importance in the context of scientific research and scientific approaches. Public policy as a discipline of political science have their own special subject and method of research. A particularly important aspect of the scientific approach to public policy is the aspect of applying research methods as one of the stages and phases of designing scientific research. In this sense, the goal of this research is to present the application of scientific research methods in the field of public policy. Those methods are based on scientific achievements developed within the framework of modern methodology of social sciences. Scientific research methods represent an important functional part of the research project as a model of the scientific research system, predominantly of an empirical character, which is applicable to all types of research. This is precisely what imposes the need to develop a project as a prerequisite for applying scientific methods and conducting scientific research, and therefore for a more complete understanding of public policy. The conclusions that will be reached point to the fact that scientific research of public policy can not be carried out without the creation of a scientific research project as a complex scientific and operational document and the application of appropriate methods and techniques developed within the framework of scientific achievements of modern social science methodology.

We describe a novel algorithm for solving general parametric (nonlinear) eigenvalue problems. Our method has two steps: first, high-accuracy solutions of non-parametric versions of the problem are gathered at some values of the parameters; these are then combined to obtain global approximations of the parametric eigenvalues. To gather the non-parametric data, we use non-intrusive contour-integration-based methods, which, however, cannot track eigenvalues that migrate into/out of the contour as the parameter changes. Special strategies are described for performing the combination-over-parameter step despite having only partial information on such migrating eigenvalues. Moreover, we dedicate a special focus to the approximation of eigenvalues that undergo bifurcations. Finally, we propose an adaptive strategy that allows one to effectively apply our method even without any a priori information on the behavior of the sought-after eigenvalues. Numerical tests are performed, showing that our algorithm can achieve remarkably high approximation accuracy.

In estimating the average treatment effect in observational studies, the influence of confounders should be appropriately addressed. To this end, the propensity score is widely used. If the propensity scores are known for all the subjects, bias due to confounders can be adjusted by using the inverse probability weighting (IPW) by the propensity score. Since the propensity score is unknown in general, it is usually estimated by the parametric logistic regression model with unknown parameters estimated by solving the score equation under the strongly ignorable treatment assignment (SITA) assumption. Violation of the SITA assumption and/or misspecification of the propensity score model can cause serious bias in estimating the average treatment effect. To relax the SITA assumption, the IPW estimator based on the outcome-dependent propensity score has been successfully introduced. However, it still depends on the correctly specified parametric model and its identification. In this paper, we propose a simple sensitivity analysis method for unmeasured confounders. In the standard practice, the estimating equation is used to estimate the unknown parameters in the parametric propensity score model. Our idea is to make inference on the average causal effect by removing restrictive parametric model assumptions while still utilizing the estimating equation. Using estimating equations as constraints, which the true propensity scores asymptotically satisfy, we construct the worst-case bounds for the average treatment effect with linear programming. Different from the existing sensitivity analysis methods, we construct the worst-case bounds with minimal assumptions. We illustrate our proposal by simulation studies and a real-world example.

We define and study a fully-convolutional neural network stochastic model, NN-Turb, which generates a 1-dimensional field with some turbulent velocity statistics. In particular, the generated process satisfies the Kolmogorov 2/3 law for second order structure function. It also presents negative skewness across scales (i.e. Kolmogorov 4/5 law) and exhibits intermittency as characterized by skewness and flatness. Furthermore, our model is never in contact with turbulent data and only needs the desired statistical behavior of the structure functions across scales for training.

Test-negative designs are widely used for post-market evaluation of vaccine effectiveness. Different from classical test-negative designs where only healthcare-seekers with symptoms are included, recent test-negative designs have involved individuals with various reasons for testing, especially in an outbreak setting. While including these data can increase sample size and hence improve precision, concerns have been raised about whether they will introduce bias into the current framework of test-negative designs, thereby demanding a formal statistical examination of this modified design. In this article, using statistical derivations, causal graphs, and numerical simulations, we show that the standard odds ratio estimator may be biased if various reasons for testing are not accounted for. To eliminate this bias, we identify three categories of reasons for testing, including symptoms, disease-unrelated reasons, and case contact tracing, and characterize associated statistical properties and estimands. Based on our characterization, we propose stratified estimators that can incorporate multiple reasons for testing to achieve consistent estimation and improve precision by maximizing the use of data. The performance of our proposed method is demonstrated through simulation studies.

This paper presents a general methodology for deriving information-theoretic generalization bounds for learning algorithms. The main technical tool is a probabilistic decorrelation lemma based on a change of measure and a relaxation of Young's inequality in $L_{\psi_p}$ Orlicz spaces. Using the decorrelation lemma in combination with other techniques, such as symmetrization, couplings, and chaining in the space of probability measures, we obtain new upper bounds on the generalization error, both in expectation and in high probability, and recover as special cases many of the existing generalization bounds, including the ones based on mutual information, conditional mutual information, stochastic chaining, and PAC-Bayes inequalities. In addition, the Fernique-Talagrand upper bound on the expected supremum of a subgaussian process emerges as a special case.

To understand high precision observations of exoplanets and brown dwarfs, we need detailed and complex general circulation models (GCMs) that incorporate hydrodynamics, chemistry, and radiation. For this study, we specifically examined the coupling between chemistry and radiation in GCMs and compared different methods for the mixing of opacities of different chemical species in the correlated-k assumption, when equilibrium chemistry cannot be assumed. We propose a fast machine learning method based on DeepSets (DS), which effectively combines individual correlated-k opacities (k-tables). We evaluated the DS method alongside other published methods such as adaptive equivalent extinction (AEE) and random overlap with rebinning and resorting (RORR). We integrated these mixing methods into our GCM (expeRT/MITgcm) and assessed their accuracy and performance for the example of the hot Jupiter HD~209458 b. Our findings indicate that the DS method is both accurate and efficient for GCM usage, whereas RORR is too slow. Additionally, we observed that the accuracy of AEE depends on its specific implementation and may introduce numerical issues in achieving radiative transfer solution convergence. We then applied the DS mixing method in a simplified chemical disequilibrium situation, where we modeled the rainout of TiO and VO, and confirmed that the rainout of TiO and VO would hinder the formation of a stratosphere. To further expedite the development of consistent disequilibrium chemistry calculations in GCMs, we provide documentation and code for coupling the DS mixing method with correlated-k radiative transfer solvers. The DS method has been extensively tested to be accurate enough for GCMs; however, other methods might be needed for accelerating atmospheric retrievals.

A growing number of scholars and data scientists are conducting randomized experiments to analyze causal relationships in network settings where units influence one another. A dominant methodology for analyzing these network experiments has been design-based, leveraging randomization of treatment assignment as the basis for inference. In this paper, we generalize this design-based approach so that it can be applied to more complex experiments with a variety of causal estimands with different target populations. An important special case of such generalized network experiments is a bipartite network experiment, in which the treatment assignment is randomized among one set of units and the outcome is measured for a separate set of units. We propose a broad class of causal estimands based on stochastic intervention for generalized network experiments. Using a design-based approach, we show how to estimate the proposed causal quantities without bias, and develop conservative variance estimators. We apply our methodology to a randomized experiment in education where a group of selected students in middle schools are eligible for the anti-conflict promotion program, and the program participation is randomized within this group. In particular, our analysis estimates the causal effects of treating each student or his/her close friends, for different target populations in the network. We find that while the treatment improves the overall awareness against conflict among students, it does not significantly reduce the total number of conflicts.

The prediction accuracy of machine learning methods is steadily increasing, but the calibration of their uncertainty predictions poses a significant challenge. Numerous works focus on obtaining well-calibrated predictive models, but less is known about reliably assessing model calibration. This limits our ability to know when algorithms for improving calibration have a real effect, and when their improvements are merely artifacts due to random noise in finite datasets. In this work, we consider detecting mis-calibration of predictive models using a finite validation dataset as a hypothesis testing problem. The null hypothesis is that the predictive model is calibrated, while the alternative hypothesis is that the deviation from calibration is sufficiently large. We find that detecting mis-calibration is only possible when the conditional probabilities of the classes are sufficiently smooth functions of the predictions. When the conditional class probabilities are H\"older continuous, we propose T-Cal, a minimax optimal test for calibration based on a debiased plug-in estimator of the $\ell_2$-Expected Calibration Error (ECE). We further propose Adaptive T-Cal, a version that is adaptive to unknown smoothness. We verify our theoretical findings with a broad range of experiments, including with several popular deep neural net architectures and several standard post-hoc calibration methods. T-Cal is a practical general-purpose tool, which -- combined with classical tests for discrete-valued predictors -- can be used to test the calibration of virtually any probabilistic classification method.