In industry, online randomized controlled experiment (a.k.a A/B experiment) is a standard approach to measure the impact of a causal change. These experiments have small treatment effect to reduce the potential blast radius. As a result, these experiments often lack statistical significance due to low signal-to-noise ratio. To improve the precision (or reduce standard error), we introduce the idea of trigger observations where the output of the treatment and the control model are different. We show that the evaluation with full information about trigger observations (full knowledge) improves the precision in comparison to a baseline method. However, detecting all such trigger observations is a costly affair, hence we propose a sampling based evaluation method (partial knowledge) to reduce the cost. The randomness of sampling introduces bias in the estimated outcome. We theoretically analyze this bias and show that the bias is inversely proportional to the number of observations used for sampling. We also compare the proposed evaluation methods using simulation and empirical data. In simulation, evaluation with full knowledge reduces the standard error as much as 85%. In empirical setup, evaluation with partial knowledge reduces the standard error by 36.48%.
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Cross-sectional incidence estimation based on recency testing has become a widely used tool in HIV research. Recently, this method has gained prominence in HIV prevention trials to estimate the "placebo" incidence that participants might experience without preventive treatment. The application of this approach faces challenges due to non-representative sampling, as individuals aware of their HIV-positive status may be less likely to participate in screening for an HIV prevention trial. To address this, a recent phase 3 trial excluded individuals based on whether they have had a recent HIV test. To the best of our knowledge, the validity of this approach has yet to be studied. In our work, we investigate the performance of cross-sectional HIV incidence estimation when excluding individuals based on prior HIV tests in realistic trial settings. We develop a statistical framework that incorporates a testing-based criterion and possible non-representative sampling. We introduce a metric we call the effective mean duration of recent infection (MDRI) that mathematically quantifies bias in incidence estimation. We conduct an extensive simulation study to evaluate incidence estimator performance under various scenarios. Our findings reveal that when screening attendance is affected by knowledge of HIV status, incidence estimators become unreliable unless all individuals with recent HIV tests are excluded. Additionally, we identified a trade-off between bias and variability: excluding more individuals reduces bias from non-representative sampling but in many cases increases the variability of incidence estimates. These findings highlight the need for caution when applying testing-based criteria and emphasize the importance of refining incidence estimation methods to improve the design and evaluation of future HIV prevention trials.
We propose a new density estimation algorithm. Given $n$ i.i.d. observations from a distribution belonging to a class of densities on $\mathbb{R}^d$, our estimator outputs any density in the class whose ``perceptron discrepancy'' with the empirical distribution is at most $O(\sqrt{d/n})$. The perceptron discrepancy is defined as the largest difference in mass two distribution place on any halfspace. It is shown that this estimator achieves the expected total variation distance to the truth that is almost minimax optimal over the class of densities with bounded Sobolev norm and Gaussian mixtures. This suggests that the regularity of the prior distribution could be an explanation for the efficiency of the ubiquitous step in machine learning that replaces optimization over large function spaces with simpler parametric classes (such as discriminators of GANs). We also show that replacing the perceptron discrepancy with the generalized energy distance of Szekely and Rizzo (2013) further improves total variation loss. The generalized energy distance between empirical distributions is easily computable and differentiable, which makes it especially useful for fitting generative models. To the best of our knowledge, it is the first ``simple'' distance with such properties with minimax statistical guarantees.
Most of the scientific literature on causal modeling considers the structural framework of Pearl and the potential-outcome framework of Rubin to be formally equivalent, and therefore interchangeably uses do-interventions and the potential-outcome subscript notation to write counterfactual outcomes. In this paper, we agnostically superimpose the two causal models to specify under which mathematical conditions structural counterfactual outcomes and potential outcomes need to, do not need to, can, or cannot be equal (almost surely or law). Our comparison reminds that a structural causal model and a Rubin causal model compatible with the same observations do not have to coincide, and highlights real-world problems where they even cannot correspond. Then, we examine common claims and practices from the causal-inference literature in the light of these results. In doing so, we aim at clarifying the relationship between the two causal frameworks, and the interpretation of their respective counterfactuals.
The approximate discrete Radon transform (ADRT) is a hierarchical multiscale approximation of the Radon transform. In this paper, we factor the ADRT into a product of linear transforms that resemble convolutions, and derive an explicit spectral decomposition of each factor. We further show that this implies - for data lying in the range of the ADRT - that the transform of an $N \times N$ image can be formally inverted with complexity $\mathcal{O}(N^2 \log^2 N)$. We numerically test the accuracy of the inverse on images of moderate sizes and find that it is competitive with existing iterative algorithms in this special regime.
For several types of information relations, the induced rough sets system RS does not form a lattice but only a partially ordered set. However, by studying its Dedekind-MacNeille completion DM(RS), one may reveal new important properties of rough set structures. Building upon D. Umadevi's work on describing joins and meets in DM(RS), we previously investigated pseudo-Kleene algebras defined on DM(RS) for reflexive relations. This paper delves deeper into the order-theoretic properties of DM(RS) in the context of reflexive relations. We describe the completely join-irreducible elements of DM(RS) and characterize when DM(RS) is a spatial completely distributive lattice. We show that even in the case of a non-transitive reflexive relation, DM(RS) can form a Nelson algebra, a property generally associated with quasiorders. We introduce a novel concept, the core of a relational neighborhood, and use it to provide a necessary and sufficient condition for DM(RS) to determine a Nelson algebra.
In industrial contexts, effective workforce allocation is crucial for operational efficiency. This paper presents an ongoing project focused on developing a decision-making tool designed for workforce allocation, emphasising the explainability to enhance its trustworthiness. Our objective is to create a system that not only optimises the allocation of teams to scheduled tasks but also provides clear, understandable explanations for its decisions, particularly in cases where the problem is infeasible. By incorporating human-in-the-loop mechanisms, the tool aims to enhance user trust and facilitate interactive conflict resolution. We implemented our approach on a prototype tool/digital demonstrator intended to be evaluated on a real industrial scenario both in terms of performance and user acceptability.
Batch effects are inevitable in large-scale metabolomics. Prior to formal data analysis, batch effect correction (BEC) is applied to prevent from obscuring biological variations, and batch effect evaluation (BEE) is used for correction assessment. However, existing BEE algorithms neglect covariances between the variables, and existing BEC algorithms might fail to adequately correct the covariances. Therefore, we resort to recent advancements in high-dimensional statistics, and respectively propose "quality control-based simultaneous tests (QC-ST)" and "covariance correction (CoCo)". Validated by the simulation data, QC-ST can simultaneously detect the statistical significance of QC samples' mean vectors and covariance matrices across different batches, and has a satisfactory statistical performance in empirical sizes, empirical powers, and computational speed. Then, we apply four QC-based BEC algorithms to two large cohort datasets, and find that extreme gradient boost (XGBoost) performs best in relative standard deviation (RSD) and dispersion-ratio (D-ratio). After prepositive BEC, if QC-ST still suggests that batch effects between some two batches are significant, CoCo should be implemented. And after CoCo (if necessary), the four metrics (i.e., RSD, D-ratio, classification performance, and QC-ST) might be further improved. In summary, under the guidance of QC-ST, we can develop a matching strategy to integrate multiple BEC algorithms more rationally and flexibly, and minimize batch effects for reliable biological conclusions.
Uplift modeling and Heterogeneous Treatment Effect (HTE) estimation aim at predicting the causal effect of an action, such as a medical treatment or a marketing campaign on a specific individual. In this paper, we focus on data from Randomized Controlled Experiments which guarantee causal interpretation of the outcomes. Class and treatment imbalance are important problems in uplift modeling/HTE, but classical undersampling or oversampling based approaches are hard to apply in this case since they distort the predicted effect. Calibration methods have been proposed in the past, however, they do not guarantee correct predictions. In this work, we propose an approach alternative to undersampling, based on flipping the class value of selected records. We show that the proposed approach does not distort the predicted effect and does not require calibration. The method is especially useful for models based on class variable transformation (modified outcome models). We address those models separately, designing a transformation scheme which guarantees correct predictions and addresses also the problem of treatment imbalance which is especially important for those models. Experiments fully confirm our theoretical results. Additionally, we demonstrate that our method is a viable alternative also for standard classification problems.
Finite element discretization of Stokes problems can result in singular, inconsistent saddle point linear algebraic systems. This inconsistency can cause many iterative methods to fail to converge. In this work, we consider the lowest-order weak Galerkin finite element method to discretize Stokes flow problems and study a consistency enforcement by modifying the right-hand side of the resulting linear system. It is shown that the modification of the scheme does not affect the optimal-order convergence of the numerical solution. Moreover, inexact block diagonal and triangular Schur complement preconditioners and the minimal residual method (MINRES) and the generalized minimal residual method (GMRES) are studied for the iterative solution of the modified scheme. Bounds for the eigenvalues and the residual of MINRES/GMRES are established. Those bounds show that the convergence of MINRES and GMRES is independent of the viscosity parameter and mesh size. The convergence of the modified scheme and effectiveness of the preconditioners are verified using numerical examples in two and three dimensions.
Crystal plasticity (CP) modeling is a vital tool for predicting the mechanical behavior of materials, but its calibration involves numerous (>8) constitutive parameters, often requiring time-consuming trial-and-error methods. This paper proposes a robust calibration approach using Bayesian optimization (BO) to identify optimal CP model parameters under fatigue loading conditions. Utilizing cyclic data from additively manufactured Hastelloy X specimens at 500 degree-F, the BO framework, integrated with a Gaussian process surrogate model, significantly reduces the number of required simulations. A novel objective function is developed to match experimental stress-strain data across different strain amplitudes. Results demonstrate that effective CP model calibration is achieved within 75 iterations, with as few as 50 initial simulations. Sensitivity analysis reveals the influence of CP parameters at various loading points on the stress-strain curve. The results show that the stress-strain response is predominantly controlled by parameters related to yield, with increased influence from backstress parameters during compressive loading. In addition, the effect of introducing twins into the synthetic microstructure on fatigue behavior is studied, and a relationship between microstructural features and the fatigue indicator parameter is established. Results show that larger diameter grains, which exhibit a higher Schmid factor and an average misorientation of approximately 42 degrees +/- 1.67 degree, are identified as probable sites for failure. The proposed optimization framework can be applied to any material system or CP model, streamlining the calibration process and improving the predictive accuracy of such models.
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