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Register a new userOptimal Stopping and Worker Selection in Crowdsourcing: an Adaptive Sequential Probability Ratio Test Framework
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Xiaoou Li
Publication date
2017
fields
Mathematical Statistics
and research's language is
English
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In this paper, we aim at solving a class of multiple testing problems under the Bayesian sequential decision framework. Our motivating application comes from binary labeling tasks in crowdsourcing, where the requestor needs to simultaneously decide which worker to choose to provide the label and when to stop collecting labels under a certain budget constraint. We start with the binary hypothesis testing problem to determine the true label of a single object, and provide an optimal solution by casting it under the adaptive sequential probability ratio test (Ada-SPRT) framework. We characterize the structure of the optimal solution, i.e., optimal adaptive sequential design, which minimizes the Bayes risk through log-likelihood ratio statistic. We also develop a dynamic programming algorithm that can efficiently approximate the optimal solution. For the multiple testing problem, we further propose to adopt an empirical Bayes approach for estimating class priors and show that our method has an averaged loss that converges to the minimal Bayes risk under the true model. The experiments on both simulated and real data show the robustness of our method and its superiority in labeling accuracy as compared to several other recently proposed approaches.
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Modeling correlated or highly stratified multiple-response data becomes a common data analysis task due to modern data monitoring facilities and methods. Generalized estimating equations (GEE) is one of the popular statistical methods for analyzing this kind of data. In this paper, we present a sequential estimation procedure for obtaining GEE-based estimates. In addition to the conventional random sampling, the proposed method features adaptive subject recruiting and variable selection. Moreover, we equip our method with an adaptive shrinkage property so that it can decide the effective variables during the estimation procedure and build a confidence set with a pre-specified precision for the corresponding parameters. In addition to the statistical properties of the proposed procedure, we assess our method using both simulated data and real data sets.
We discuss Bayesian model uncertainty analysis and forecasting in sequential dynamic modeling of multivariate time series. The perspective is that of a decision-maker with a specific forecasting objective that guides thinking about relevant models. Based on formal Bayesian decision-theoretic reasoning, we develop a time-adaptive approach to exploring, weighting, combining and selecting models that differ in terms of predictive variables included. The adaptivity allows for changes in the sets of favored models over time, and is guided by the specific forecasting goals. A synthetic example illustrates how decision-guided variable selection differs from traditional Bayesian model uncertainty analysis and standard model averaging. An applied study in one motivating application of long-term macroeconomic forecasting highlights the utility of the new approach in terms of improving predictions as well as its ability to identify and interpret different sets of relevant models over time with respect to specific, defined forecasting goals.
Sequential Monte Carlo (SMC), also known as particle filters, has been widely accepted as a powerful computational tool for making inference with dynamical systems. A key step in SMC is resampling, which plays the role of steering the algorithm towards the future dynamics. Several strategies have been proposed and used in practice, including multinomial resampling, residual resampling (Liu and Chen 1998), optimal resampling (Fearnhead and Clifford 2003), stratified resampling (Kitagawa 1996), and optimal transport resampling (Reich 2013). We show that, in the one dimensional case, optimal transport resampling is equivalent to stratified resampling on the sorted particles, and they both minimize the resampling variance as well as the expected squared energy distance between the original and resampled empirical distributions; in the multidimensional case, the variance of stratified resampling after sorting particles using Hilbert curve (Gerber et al. 2019) in $mathbb{R}^d$ is $O(m^{-(1+2/d)})$, an improved rate compared to the original $O(m^{-(1+1/d)})$, where $m$ is the number of resampled particles. This improved rate is the lowest for ordered stratified resampling schemes, as conjectured in Gerber et al. (2019). We also present an almost sure bound on the Wasserstein distance between the original and Hilbert-curve-resampled empirical distributions. In light of these theoretical results, we propose the stratified multiple-descendant growth (SMG) algorithm, which allows us to explore the sample space more efficiently compared to the standard i.i.d. multiple-descendant sampling-resampling approach as measured by the Wasserstein metric. Numerical evidence is provided to demonstrate the effectiveness of our proposed method.
During the rapid development cycle for Internet products (websites and mobile apps), new features are developed and rolled out to users constantly. Features with code defects or design flaws can cause outages and significant degradation of user experience. The traditional method of code review and change management can be time-consuming and error-prone. In order to make the feature rollout process safe and fast, this paper proposes a methodology for rolling out features in an automated way using an adaptive experimental design. Under this framework, a feature is gradually ramped up from a small proportion of users to a larger population based on real-time evaluation of the performance of important metrics. If there are any regression detected during the ramp-up step, the ramp-up process stops and the feature developer is alerted. There are two main algorithm components powering this framework: 1) a continuous monitoring algorithm - using a variant of the sequential probability ratio test (SPRT) to monitor the feature performance metrics and alert feature developers when a metric degradation is detected, 2) an automated ramp-up algorithm - deciding when and how to ramp up to the next stage with larger sample size. This paper presents one monitoring algorithm and three ramping up algorithms including time-based, power-based, and risk-based (a Bayesian approach) schedules. These algorithms are evaluated and compared on both simulated data and real data. There are three benefits provided by this framework for feature rollout: 1) for defective features, it can detect the regression early and reduce negative effect, 2) for healthy features, it rolls out the feature quickly, 3) it reduces the need for manual intervention via the automation of the feature rollout process.
We view sequential design as a model selection problem to determine which new observation is expected to be the most informative, given the existing set of observations. For estimating a probability distribution on a bounded interval, we use bounds constructed from kernel density estimators along with the estimated density itself to estimate the information gain expected from each observation. We choose Bernstein polynomials for the kernel functions because they provide a complete set of basis functions for polynomials of finite degree and thus have useful convergence properties. We illustrate the method with applications to estimating network reliability polynomials, which give the probability of certain sets of configurations in finite, discrete stochastic systems.
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