亚洲男人的天堂2018av,欧美草比,久久久久久免费视频精选,国色天香在线看免费,久久久久亚洲av成人片仓井空

Estimating heterogeneous treatment effects in domains such as healthcare or social science often involves sensitive data where protecting privacy is important. We introduce a general meta-algorithm for estimating conditional average treatment effects (CATE) with differential privacy (DP) guarantees. Our meta-algorithm can work with simple, single-stage CATE estimators such as S-learner and more complex multi-stage estimators such as DR and R-learner. We perform a tight privacy analysis by taking advantage of sample splitting in our meta-algorithm and the parallel composition property of differential privacy. In this paper, we implement our approach using DP-EBMs as the base learner. DP-EBMs are interpretable, high-accuracy models with privacy guarantees, which allow us to directly observe the impact of DP noise on the learned causal model. Our experiments show that multi-stage CATE estimators incur larger accuracy loss than single-stage CATE or ATE estimators and that most of the accuracy loss from differential privacy is due to an increase in variance, not biased estimates of treatment effects.

Causal inference from observational datasets often relies on measuring and adjusting for covariates. In practice, measurements of the covariates can often be noisy and/or biased, or only measurements of their proxies may be available. Directly adjusting for these imperfect measurements of the covariates can lead to biased causal estimates. Moreover, without additional assumptions, the causal effects are not point-identifiable due to the noise in these measurements. To this end, we study the partial identification of causal effects given noisy covariates, under a user-specified assumption on the noise level. The key observation is that we can formulate the identification of the average treatment effects (ATE) as a robust optimization problem. This formulation leads to an efficient robust optimization algorithm that bounds the ATE with noisy covariates. We show that this robust optimization approach can extend a wide range of causal adjustment methods to perform partial identification, including backdoor adjustment, inverse propensity score weighting, double machine learning, and front door adjustment. Across synthetic and real datasets, we find that this approach provides ATE bounds with a higher coverage probability than existing methods.

Discrete kernel smoothing is now gaining importance in nonparametric statistics. In this paper, we investigate some asymptotic properties of the normalized discrete associated-kernel estimator of a probability mass function. We show, under some regularity and non-restrictive assumptions on the associated-kernel, that the normalizing random variable converges in mean square to 1. We then derive the consistency and the asymptotic normality of the proposed estimator. Various families of discrete kernels already exhibited satisfy the conditions, including the refined CoM-Poisson which is underdispersed and of second-order. Finally, the first-order binomial kernel is discussed and, surprisingly, its normalized estimator has a suitable asymptotic behaviour through simulations.

Off-policy evaluation and learning (OPE/L) use offline observational data to make better decisions, which is crucial in applications where experimentation is necessarily limited. OPE/L is nonetheless sensitive to discrepancies between the data-generating environment and that where policies are deployed. Recent work proposed distributionally robust OPE/L (DROPE/L) to remedy this, but the proposal relies on inverse-propensity weighting, whose regret rates may deteriorate if propensities are estimated and whose variance is suboptimal even if not. For vanilla OPE/L, this is solved by doubly robust (DR) methods, but they do not naturally extend to the more complex DROPE/L, which involves a worst-case expectation. In this paper, we propose the first DR algorithms for DROPE/L with KL-divergence uncertainty sets. For evaluation, we propose Localized Doubly Robust DROPE (LDR$^2$OPE) and prove its semiparametric efficiency under weak product rates conditions. Notably, thanks to a localization technique, LDR$^2$OPE only requires fitting a small number of regressions, just like DR methods for vanilla OPE. For learning, we propose Continuum Doubly Robust DROPL (CDR$^2$OPL) and show that, under a product rate condition involving a continuum of regressions, it enjoys a fast regret rate of $\mathcal{O}(N^{-1/2})$ even when unknown propensities are nonparametrically estimated. We further extend our results to general $f$-divergence uncertainty sets. We illustrate the advantage of our algorithms in simulations.

Data-driven methods for personalizing treatment assignment have garnered much attention from clinicians and researchers. Dynamic treatment regimes formalize this through a sequence of decision rules that map individual patient characteristics to a recommended treatment. Observational studies are commonly used for estimating dynamic treatment regimes due to the potentially prohibitive costs of conducting sequential multiple assignment randomized trials. However, estimating a dynamic treatment regime from observational data can lead to bias in the estimated regime due to unmeasured confounding. Sensitivity analyses are useful for assessing how robust the conclusions of the study are to a potential unmeasured confounder. A Monte Carlo sensitivity analysis is a probabilistic approach that involves positing and sampling from distributions for the parameters governing the bias. We propose a method for performing a Monte Carlo sensitivity analysis of the bias due to unmeasured confounding in the estimation of dynamic treatment regimes. We demonstrate the performance of the proposed procedure with a simulation study and apply it to an observational study examining tailoring the use of antidepressants for reducing symptoms of depression using data from Kaiser Permanente Washington (KPWA).

Observational studies can play a useful role in assessing the comparative effectiveness of competing treatments. In a clinical trial the randomization of participants to treatment and control groups generally results in well-balanced groups with respect to possible confounders, which makes the analysis straightforward. However, when analysing observational data, the potential for unmeasured confounding makes comparing treatment effects much more challenging. Causal inference methods such as the Instrumental Variable and Prior Even Rate Ratio approaches make it possible to circumvent the need to adjust for confounding factors that have not been measured in the data or measured with error. Direct confounder adjustment via multivariable regression and Propensity score matching also have considerable utility. Each method relies on a different set of assumptions and leverages different data. In this paper, we describe the assumptions of each method and assess the impact of violating these assumptions in a simulation study. We propose the prior outcome augmented Instrumental Variable method that leverages data from before and after treatment initiation, and is robust to the violation of key assumptions. Finally, we propose the use of a heterogeneity statistic to decide two or more estimates are statistically similar, taking into account their correlation. We illustrate our causal framework to assess the risk of genital infection in patients prescribed Sodium-glucose Co-transporter-2 inhibitors versus Dipeptidyl Peptidase-4 inhibitors as second-line treatment for type 2 diabets using observational data from the Clinical Practice Research Datalink.

Ensemble methods based on subsampling, such as random forests, are popular in applications due to their high predictive accuracy. Existing literature views a random forest prediction as an infinite-order incomplete U-statistic to quantify its uncertainty. However, these methods focus on a small subsampling size of each tree, which is theoretically valid but practically limited. This paper develops an unbiased variance estimator based on incomplete U-statistics, which allows the tree size to be comparable with the overall sample size, making statistical inference possible in a broader range of real applications. Simulation results demonstrate that our estimators enjoy lower bias and more accurate confidence interval coverage without additional computational costs. We also propose a local smoothing procedure to reduce the variation of our estimator, which shows improved numerical performance when the number of trees is relatively small. Further, we investigate the ratio consistency of our proposed variance estimator under specific scenarios. In particular, we develop a new "double U-statistic" formulation to analyze the Hoeffding decomposition of the estimator's variance.

Dyadic data is often encountered when quantities of interest are associated with the edges of a network. As such it plays an important role in statistics, econometrics and many other data science disciplines. We consider the problem of uniformly estimating a dyadic Lebesgue density function, focusing on nonparametric kernel-based estimators taking the form of dyadic empirical processes. Our main contributions include the minimax-optimal uniform convergence rate of the dyadic kernel density estimator, along with strong approximation results for the associated standardized and Studentized $t$-processes. A consistent variance estimator enables the construction of valid and feasible uniform confidence bands for the unknown density function. A crucial feature of dyadic distributions is that they may be "degenerate" at certain points in the support of the data, a property making our analysis somewhat delicate. Nonetheless our methods for uniform inference remain robust to the potential presence of such points. For implementation purposes, we discuss procedures based on positive semi-definite covariance estimators, mean squared error optimal bandwidth selectors and robust bias-correction techniques. We illustrate the empirical finite-sample performance of our methods both in simulations and with real-world data. Our technical results concerning strong approximations and maximal inequalities are of potential independent interest.

Data augmentation has been widely used for training deep learning systems for medical image segmentation and plays an important role in obtaining robust and transformation-invariant predictions. However, it has seldom been used at test time for segmentation and not been formulated in a consistent mathematical framework. In this paper, we first propose a theoretical formulation of test-time augmentation for deep learning in image recognition, where the prediction is obtained through estimating its expectation by Monte Carlo simulation with prior distributions of parameters in an image acquisition model that involves image transformations and noise. We then propose a novel uncertainty estimation method based on the formulated test-time augmentation. Experiments with segmentation of fetal brains and brain tumors from 2D and 3D Magnetic Resonance Images (MRI) showed that 1) our test-time augmentation outperforms a single-prediction baseline and dropout-based multiple predictions, and 2) it provides a better uncertainty estimation than calculating the model-based uncertainty alone and helps to reduce overconfident incorrect predictions.

In this paper we introduce a covariance framework for the analysis of EEG and MEG data that takes into account observed temporal stationarity on small time scales and trial-to-trial variations. We formulate a model for the covariance matrix, which is a Kronecker product of three components that correspond to space, time and epochs/trials, and consider maximum likelihood estimation of the unknown parameter values. An iterative algorithm that finds approximations of the maximum likelihood estimates is proposed. We perform a simulation study to assess the performance of the estimator and investigate the influence of different assumptions about the covariance factors on the estimated covariance matrix and on its components. Apart from that, we illustrate our method on real EEG and MEG data sets. The proposed covariance model is applicable in a variety of cases where spontaneous EEG or MEG acts as source of noise and realistic noise covariance estimates are needed for accurate dipole localization, such as in evoked activity studies, or where the properties of spontaneous EEG or MEG are themselves the topic of interest, such as in combined EEG/fMRI experiments in which the correlation between EEG and fMRI signals is investigated.