Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userStructure-Adaptive Sequential Testing for Online False Discovery Rate Control
116
0
0.0
(
0
)
Added by
Bowen Gang
Publication date
2020
fields
Mathematical Statistics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
Consider the online testing of a stream of hypotheses where a real--time decision must be made before the next data point arrives. The error rate is required to be controlled at {all} decision points. Conventional emph{simultaneous testing rules} are no longer applicable due to the more stringent error constraints and absence of future data. Moreover, the online decision--making process may come to a halt when the total error budget, or alpha--wealth, is exhausted. This work develops a new class of structure--adaptive sequential testing (SAST) rules for online false discover rate (FDR) control. A key element in our proposal is a new alpha--investment algorithm that precisely characterizes the gains and losses in sequential decision making. SAST captures time varying structures of the data stream, learns the optimal threshold adaptively in an ongoing manner and optimizes the alpha-wealth allocation across different time periods. We present theory and numerical results to show that the proposed method is valid for online FDR control and achieves substantial power gain over existing online testing rules.
rate research
Read More
Multiple hypothesis testing, a situation when we wish to consider many hypotheses, is a core problem in statistical inference that arises in almost every scientific field. In this setting, controlling the false discovery rate (FDR), which is the expected proportion of type I error, is an important challenge for making meaningful inferences. In this paper, we consider the problem of controlling FDR in an online manner. Concretely, we consider an ordered, possibly infinite, sequence of hypotheses, arriving one at each timestep, and for each hypothesis we observe a p-value along with a set of features specific to that hypothesis. The decision whether or not to reject the current hypothesis must be made immediately at each timestep, before the next hypothesis is observed. The model of multi-dimensional feature set provides a very general way of leveraging the auxiliary information in the data which helps in maximizing the number of discoveries. We propose a new class of powerful online testing procedures, where the rejections thresholds (significance levels) are learnt sequentially by incorporating contextual information and previous results. We prove that any rule in this class controls online FDR under some standard assumptions. We then focus on a subclass of these procedures, based on weighting significance levels, to derive a practical algorithm that learns a parametric weight function in an online fashion to gain more discoveries. We also theoretically prove, in a stylized setting, that our proposed procedures would lead to an increase in the achieved statistical power over a popular online testing procedure proposed by Javanmard & Montanari (2018). Finally, we demonstrate the favorable performance of our procedure, by comparing it to state-of-the-art online multiple testing procedures, on both synthetic data and real data generated from different applications.
Large-scale multiple testing is a fundamental problem in high dimensional statistical inference. It is increasingly common that various types of auxiliary information, reflecting the structural relationship among the hypotheses, are available. Exploiting such auxiliary information can boost statistical power. To this end, we propose a framework based on a two-group mixture model with varying probabilities of being null for different hypotheses a priori, where a shape-constrained relationship is imposed between the auxiliary information and the prior probabilities of being null. An optimal rejection rule is designed to maximize the expected number of true positives when average false discovery rate is controlled. Focusing on the ordered structure, we develop a robust EM algorithm to estimate the prior probabilities of being null and the distribution of $p$-values under the alternative hypothesis simultaneously. We show that the proposed method has better power than state-of-the-art competitors while controlling the false discovery rate, both empirically and theoretically. Extensive simulations demonstrate the advantage of the proposed method. Datasets from genome-wide association studies are used to illustrate the new methodology.
Adaptive multiple testing with covariates is an important research direction that has gained major attention in recent years. It has been widely recognized that leveraging side information provided by auxiliary covariates can improve the power of false discovery rate (FDR) procedures. Currently, most such procedures are devised with $p$-values as their main statistics. However, for two-sided hypotheses, the usual data processing step that transforms the primary statistics, known as $z$-values, into $p$-values not only leads to a loss of information carried by the main statistics, but can also undermine the ability of the covariates to assist with the FDR inference. We develop a $z$-value based covariate-adaptive (ZAP) methodology that operates on the intact structural information encoded jointly by the $z$-values and covariates. It seeks to emulate the oracle $z$-value procedure via a working model, and its rejection regions significantly depart from those of the $p$-value adaptive testing approaches. The key strength of ZAP is that the FDR control is guaranteed with minimal assumptions, even when the working model is misspecified. We demonstrate the state-of-the-art performance of ZAP using both simulated and real data, which shows that the efficiency gain can be substantial in comparison with $p$-value based methods. Our methodology is implemented in the $texttt{R}$ package $texttt{zap}$.
Selecting relevant features associated with a given response variable is an important issue in many scientific fields. Quantifying quality and uncertainty of a selection result via false discovery rate (FDR) control has been of recent interest. This paper introduces a way of using data-splitting strategies to asymptotically control the FDR while maintaining a high power. For each feature, the method constructs a test statistic by estimating two independent regression coefficients via data splitting. FDR control is achieved by taking advantage of the statistics property that, for any null feature, its sampling distribution is symmetric about zero. Furthermore, we propose Multiple Data Splitting (MDS) to stabilize the selection result and boost the power. Interestingly and surprisingly, with the FDR still under control, MDS not only helps overcome the power loss caused by sample splitting, but also results in a lower variance of the false discovery proportion (FDP) compared with all other methods in consideration. We prove that the proposed data-splitting methods can asymptotically control the FDR at any designated level for linear and Gaussian graphical models in both low and high dimensions. Through intensive simulation studies and a real-data application, we show that the proposed methods are robust to the unknown distribution of features, easy to implement and computationally efficient, and are often the most powerful ones amongst competitors especially when the signals are weak and the correlations or partial correlations are high among features.
Transfer learning for high-dimensional Gaussian graphical models (GGMs) is studied with the goal of estimating the target GGM by utilizing the data from similar and related auxiliary studies. The similarity between the target graph and each auxiliary graph is characterized by the sparsity of a divergence matrix. An estimation algorithm, Trans-CLIME, is proposed and shown to attain a faster convergence rate than the minimax rate in the single study setting. Furthermore, a debiased Trans-CLIME estimator is introduced and shown to be element-wise asymptotically normal. It is used to construct a multiple testing procedure for edge detection with false discovery rate control. The proposed estimation and multiple testing procedures demonstrate superior numerical performance in simulations and are applied to infer the gene networks in a target brain tissue by leveraging the gene expressions from multiple other brain tissues. A significant decrease in prediction errors and a significant increase in power for link detection are observed.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
