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Optimal Sparse Linear Prediction for Block-missing Multi-modality Data Without Imputation
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| Pengarang | : | Guan Yu |
| Nama Majalah/Jurnal | : | Journal of the American Statistical Association |
| Volume / Edisi | : | 115 (No. 531) |
| Halaman | : | 1406-1419 |
| Abstrak | : | In modern scientific research, data are often collected from multiple modalities. Since different modalities could provide complementary information, statistical prediction methods using multimodality data could deliver better prediction performance than using single modality data. However, one special challenge for using multimodality data is related to block-missing data. In practice, due to dropouts or the high cost of measures, the observations of a certain modality can be missing completely for some subjects. In this paper, we propose a new direct sparse regression procedure using covariance from multimodality data (DISCOM). Our proposed DISCOM method includes two steps to find the optimal linear prediction of a continuous response variable using block-missing multimodality predictors. In the first step, rather than deleting or imputing missing data, we make use of all available information to estimate the covariance matrix of the predictors and the cross-covariance vector between the predictors and the response variable. The proposed new estimate of the covariance matrix is a linear combination of the identity matrix, the estimates of the intra-modality covariance matrix and the cross-modality covariance matrix. Flexible estimates for both the sub-Gaussian and heavy-tailed cases are considered. In the second step, based on the estimated covariance matrix and the estimated cross-covariance vector, an extended Lasso-type estimator is used to deliver a sparse estimate of the coefficients in the optimal linear prediction. The number of samples that are effectively used by DISCOM is the minimum number of samples with available observations from two modalities, which can be much larger than the number of samples with complete observations from all modalities. The effectiveness of the proposed method is demonstrated by theoretical studies, simulated examples, and a real application from the Alzheimer’s Disease Neuroimaging Initiative. The comparison between DISCOM and some existing methods also indicates the advantages of our proposed method. |
Model-Free Forward Screening Via Cumulative Divergence
| Pengarang | : | Tingyou Zhou |
| Nama Majalah/Jurnal | : | Journal of the American Statistical Association |
| Volume / Edisi | : | 115 (No. 531) |
| Halaman | : | 393-1405 |
| Abstrak | : | Feature screening plays an important role in the analysis of ultrahigh dimensional data. Due to complicated model structure and high noise level, existing screening methods often suffer from model misspecification and the presence of outliers. To address these issues, we introduce a new metric named cumulative divergence (CD), and develop a CD-based forward screening procedure. This forward screening method is model-free and resistant to the presence of outliers in the response. It also incorporates the joint effects among covariates into the screening process. With a data-driven threshold, the new method can automatically determine the number of features that should be retained after screening. These merits make the CD-based screening very appealing in practice. Under certain regularity conditions, we show that the proposed method possesses sure screening property. The performance of our proposal is illustrated through simulations and a real data example. Supplementary materials for this article are available online. |
Distribution on Warp Maps for Alignment of Open and Closed Curves
| Pengarang | : | Karthik Bharath |
| Nama Majalah/Jurnal | : | Journal of the American Statistical Association |
| Volume / Edisi | : | 115 (No. 531) |
| Halaman | : | 1378-1392 |
| Abstrak | : | Alignment of curve data is an integral part of their statistical analysis, and can be achieved using model- or optimization-based approaches. The parameter space is usually the set of monotone, continuous warp maps of a domain. Infinite-dimensional nature of the parameter space encourages sampling based approaches, which require a distribution on the set of warp maps. Moreover, the distribution should also enable sampling in the presence of important landmark information on the curves which constrain the warp maps. For alignment of closed and open curves in ?????,????=1,2,3, possibly with landmark information, we provide a constructive, point-process based definition of a distribution on the set of warp maps of [0, 1] and the unit circle ????, that is, (1) simple to sample from, and (2) possesses the desiderata for decomposition of the alignment problem with landmark constraints into multiple unconstrained ones. For warp maps on [0, 1], the distribution is related to the Dirichlet process. We demonstrate its utility by using it as a prior distribution on warp maps in a Bayesian model for alignment of two univariate curves, and as a proposal distribution in a stochastic algorithm that optimizes a suitable alignment functional for higher-dimensional curves. Several examples from simulated and real datasets are provided. |
A Likelihood Ratio Approach to Sequential Change Point Detection for a General Class of Parameters
| Pengarang | : | Holger Dette |
| Nama Majalah/Jurnal | : | Journal of the American Statistical Association |
| Volume / Edisi | : | 115 (No. 531) |
| Halaman | : | 1361-1377 |
| Abstrak | : | In this article, we propose a new approach for sequential monitoring of a general class of parameters of a d-dimensional time series, which can be estimated by approximately linear functionals of the empirical distribution function. We consider a closed-end method, which is motivated by the likelihood ratio test principle and compare the new method with two alternative procedures. We also incorporate self-normalization such that estimation of the long-run variance is not necessary. We prove that for a large class of testing problems the new detection scheme has asymptotic level α and is consistent. The asymptotic theory is illustrated for the important cases of monitoring a change in the mean, variance, and correlation. By means of a simulation study it is demonstrated that the new test performs better than the currently available procedures for these problems. Finally, the methodology is illustrated by a small data example investigating index prices from the dot-com bubble. Supplementary materials for this article are available online. |
Comparing and Weighting Imperfect Models Using D-Probabilities
| Pengarang | : | Meng Li |
| Nama Majalah/Jurnal | : | Journal of the American Statistical Association |
| Volume / Edisi | : | 115 (No. 531) |
| Halaman | : | 1349-1360 |
| Abstrak | : | We propose a new approach for assigning weights to models using a divergence-based method (D-probabilities), relying on evaluating parametric models relative to a nonparametric Bayesian reference using Kullback–Leibler divergence. D-probabilities are useful in goodness-of-fit assessments, in comparing imperfect models, and in providing model weights to be used in model aggregation. D-probabilities avoid some of the disadvantages of Bayesian model probabilities, such as large sensitivity to prior choice, and tend to place higher weight on a greater diversity of models. In an application to linear model selection against a Gaussian process reference, we provide simple analytic forms for routine implementation and show that D-probabilities automatically penalize model complexity. Some asymptotic properties are described, and we provide interesting probabilistic interpretations of the proposed model weights. The framework is illustrated through simulation examples and an ozone data application. Supplementary materials for this aricle are available online. |
Tests for Scale Changes Based on Pairwise Differences
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Journal of the American Statistical Association |
| Volume / Edisi | : | 115 (No. 531) |
| Halaman | : | 1336-1348 |
| Abstrak | : | In many applications it is important to know whether the amount of fluctuation in a series of observations changes over time. In this article, we investigate different tests for detecting changes in the scale of mean-stationary time series. The classical approach, based on the CUSUM test applied to the squared centered observations, is very vulnerable to outliers and impractical for heavy-tailed data, which leads us to contemplate test statistics based on alternative, less outlier-sensitive scale estimators. It turns out that the tests based on Gini’s mean difference (the average of all pairwise distances) and generalized Qn estimators (sample quantiles of all pairwise distances) are very suitable candidates. They improve upon the classical test not only under heavy tails or in the presence of outliers, but also under normality. We use recent results on the process convergence of U-statistics and U-quantiles for dependent sequences to derive the limiting distribution of the test statistics and propose estimators for the long-run variance. We show the consistency of the tests and demonstrate the applicability of the new change-point detection methods at two real-life data examples from hydrology and finance. Supplementary materials for this article are available online. |
Bayesian Model Search for Nonstationary Periodic Time Series
| Pengarang | : | Beniamino Hadj-Amar |
| Nama Majalah/Jurnal | : | Journal of the American Statistical Association |
| Volume / Edisi | : | 115 (No. 531) |
| Halaman | : | 1320-1335 |
| Abstrak | : | We propose a novel Bayesian methodology for analyzing nonstationary time series that exhibit oscillatory behavior. We approximate the time series using a piecewise oscillatory model with unknown periodicities, where our goal is to estimate the change-points while simultaneously identifying the potentially changing periodicities in the data. Our proposed methodology is based on a trans-dimensional Markov chain Monte Carlo algorithm that simultaneously updates the change-points and the periodicities relevant to any segment between them. We show that the proposed methodology successfully identifies time changing oscillatory behavior in two applications which are relevant to e-Health and sleep research, namely the occurrence of ultradian oscillations in human skin temperature during the time of night rest, and the detection of instances of sleep apnea in plethysmographic respiratory traces. Supplementary materials for this article are available online. |
Likelihood Ratio Tests for a Large Directed Acyclic Graph
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Journal of the American Statistical Association |
| Volume / Edisi | : | 115 (No. 531) |
| Halaman | : | 1304-1319 |
| Abstrak | : | Inference of directional pairwise relations between interacting units in a directed acyclic graph (DAG), such as a regulatory gene network, is common in practice, imposing challenges because of lack of inferential tools. For example, inferring a specific gene pathway of a regulatory gene network is biologically important. Yet, frequentist inference of directionality of connections remains largely unexplored for regulatory models. In this article, we propose constrained likelihood ratio tests for inference of the connectivity as well as directionality subject to nonconvex acyclicity constraints in a Gaussian directed graphical model. Particularly, we derive the asymptotic distributions of the constrained likelihood ratios in a high-dimensional situation. For testing of connectivity, the asymptotic distribution is either chi-squared or normal depending on if the number of testable links in a DAG model is small. For testing of directionality, the asymptotic distribution is the minimum of d independent chi-squared variables with one-degree of freedom or a generalized Gamma distribution depending on if d is small, where d is number of breakpoints in a hypothesized pathway. Moreover, we develop a computational method to perform the proposed tests, which integrates an alternating direction method of multipliers and difference convex programming. Finally, the power analysis and simulations suggest that the tests achieve the desired objectives of inference. An analysis of an Alzheimer’s disease gene expression dataset illustrates the utility of the proposed method to infer a directed pathway in a gene network. |
Main Effects and Interactions in Mixed and Incomplete Data Frames
| Pengarang | : | Geneviève Robin |
| Nama Majalah/Jurnal | : | Journal of the American Statistical Association |
| Volume / Edisi | : | 115 (No. 531) |
| Halaman | : | 1292-1303 |
| Abstrak | : | A mixed data frame (MDF) is a table collecting categorical, numerical, and count observations. The use of MDF is widespread in statistics and the applications are numerous from abundance data in ecology to recommender systems. In many cases, an MDF exhibits simultaneously main effects, such as row, column, or group effects and interactions, for which a low-rank model has often been suggested. Although the literature on low-rank approximations is very substantial, with few exceptions, existing methods do not allow to incorporate main effects and interactions while providing statistical guarantees. The present work fills this gap. We propose an estimation method which allows to recover simultaneously the main effects and the interactions. We show that our method is near optimal under conditions which are met in our targeted applications. We also propose an optimization algorithm which provably converges to an optimal solution. Numerical experiments reveal that our method, mimi, performs well when the main effects are sparse and the interaction matrix has low-rank. We also show that mimi compares favorably to existing methods, in particular when the main effects are significantly large compared to the interactions, and when the proportion of missing entries is large. The method is available as an R package on the Comprehensive R Archive Network. Supplementary materials for this article are available online. |
Simultaneous Covariance Inference for Multimodal Integrative Analysis
| Pengarang | : | Andiola, Lindsay M. ,Hux, Candice T.,Noga, Tracy J. |
| Nama Majalah/Jurnal | : | Journal of the American Statistical Association |
| Volume / Edisi | : | 115 (No. 531) |
| Halaman | : | 1279-1291 |
| Abstrak | : | Multimodal integrative analysis fuses different types of data collected on the same set of experimental subjects. It is becoming a norm in many branches of scientific research, such as multi-omics and multimodal neuroimaging analysis. In this article, we address the problem of simultaneous covariance inference of associations between multiple modalities, which is of a vital interest in multimodal integrative analysis. Recognizing that there are few readily available solutions in the literature for this type of problem, we develop a new simultaneous testing procedure. It provides an explicit quantification of statistical significance, a much improved detection power, as well as a rigid false discovery control. Our proposal makes novel and useful contributions from both the scientific perspective and the statistical methodological perspective. We demonstrate the efficacy of the new method through both simulations and a multimodal positron emission tomography study of associations between two hallmark pathological proteins of Alzheimer’s disease. |