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Bayesian Distance Clustering. 贝叶斯距离聚类
IF 4.3 3区 计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS Pub Date : 2021-01-01
Leo L Duan, David B Dunson

Model-based clustering is widely used in a variety of application areas. However, fundamental concerns remain about robustness. In particular, results can be sensitive to the choice of kernel representing the within-cluster data density. Leveraging on properties of pairwise differences between data points, we propose a class of Bayesian distance clustering methods, which rely on modeling the likelihood of the pairwise distances in place of the original data. Although some information in the data is discarded, we gain substantial robustness to modeling assumptions. The proposed approach represents an appealing middle ground between distance- and model-based clustering, drawing advantages from each of these canonical approaches. We illustrate dramatic gains in the ability to infer clusters that are not well represented by the usual choices of kernel. A simulation study is included to assess performance relative to competitors, and we apply the approach to clustering of brain genome expression data.

基于模型的聚类被广泛应用于各种应用领域。然而,人们对其稳健性仍然存在根本性的担忧。特别是,结果可能对代表聚类内部数据密度的核的选择很敏感。利用数据点之间成对差异的特性,我们提出了一类贝叶斯距离聚类方法,这种方法依赖于对成对距离的可能性建模来代替原始数据。虽然丢弃了数据中的一些信息,但我们获得了对建模假设的实质性稳健性。所提出的方法是距离聚类和基于模型的聚类之间的一个有吸引力的中间地带,汲取了这两种典型方法的优点。我们展示了在推断通常选择的内核不能很好代表的聚类的能力方面取得的巨大进步。我们将这种方法应用于大脑基因组表达数据的聚类。
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引用次数: 0
Adversarial Monte Carlo Meta-Learning of Optimal Prediction Procedures. 最佳预测程序的对抗性蒙特卡罗元学习。
IF 6 3区 计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS Pub Date : 2021-01-01
Alex Luedtke, Incheoul Chung, Oleg Sofrygin

We frame the meta-learning of prediction procedures as a search for an optimal strategy in a two-player game. In this game, Nature selects a prior over distributions that generate labeled data consisting of features and an associated outcome, and the Predictor observes data sampled from a distribution drawn from this prior. The Predictor's objective is to learn a function that maps from a new feature to an estimate of the associated outcome. We establish that, under reasonable conditions, the Predictor has an optimal strategy that is equivariant to shifts and rescalings of the outcome and is invariant to permutations of the observations and to shifts, rescalings, and permutations of the features. We introduce a neural network architecture that satisfies these properties. The proposed strategy performs favorably compared to standard practice in both parametric and nonparametric experiments.

我们将预测程序的元学习设计为在双人游戏中寻找最佳策略。在这场博弈中,"自然 "会对产生由特征和相关结果组成的标记数据的分布选择一个先验,而 "预测者 "则观察从该先验的分布中采样的数据。预测者的目标是学习一个从新特征映射到相关结果估计值的函数。我们发现,在合理的条件下,预测器有一个最优策略,该策略对结果的移动和重定向具有等变性,并且对观察结果的排列以及特征的移动、重定向和排列具有不变性。我们引入了一种满足这些特性的神经网络架构。在参数和非参数实验中,与标准实践相比,所提出的策略都表现出色。
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引用次数: 0
Empirical Bayes Matrix Factorization. 经验贝叶斯矩阵分解。
IF 6 3区 计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS Pub Date : 2021-01-01
Wei Wang, Matthew Stephens

Matrix factorization methods, which include Factor analysis (FA) and Principal Components Analysis (PCA), are widely used for inferring and summarizing structure in multivariate data. Many such methods use a penalty or prior distribution to achieve sparse representations ("Sparse FA/PCA"), and a key question is how much sparsity to induce. Here we introduce a general Empirical Bayes approach to matrix factorization (EBMF), whose key feature is that it estimates the appropriate amount of sparsity by estimating prior distributions from the observed data. The approach is very flexible: it allows for a wide range of different prior families and allows that each component of the matrix factorization may exhibit a different amount of sparsity. The key to this flexibility is the use of a variational approximation, which we show effectively reduces fitting the EBMF model to solving a simpler problem, the so-called "normal means" problem. We demonstrate the benefits of EBMF with sparse priors through both numerical comparisons with competing methods and through analysis of data from the GTEx (Genotype Tissue Expression) project on genetic associations across 44 human tissues. In numerical comparisons EBMF often provides more accurate inferences than other methods. In the GTEx data, EBMF identifies interpretable structure that agrees with known relationships among human tissues. Software implementing our approach is available at https://github.com/stephenslab/flashr.

矩阵分解方法,包括因子分析(FA)和主成分分析(PCA),被广泛用于推断和总结多元数据中的结构。许多这样的方法使用惩罚或先验分布来实现稀疏表示(“稀疏FA/PCA”),关键问题是诱导多少稀疏性。在这里,我们介绍了一种用于矩阵分解(EBMF)的通用经验贝叶斯方法,其关键特征是通过从观测数据中估计先验分布来估计适当的稀疏性。该方法非常灵活:它允许广泛的不同先验族,并允许矩阵分解的每个分量可能表现出不同的稀疏性。这种灵活性的关键是使用变分近似,我们证明了变分近似有效地减少了EBMF模型的拟合,从而解决了一个更简单的问题,即所谓的“正态均值”问题。我们通过与竞争方法的数值比较以及对GTEx(基因型组织表达)项目中44个人类组织的遗传关联数据的分析,证明了稀疏先验的EBMF的优势。在数值比较中,EBMF通常比其他方法提供更准确的推断。在GTEx数据中,EBMF确定了与人类组织之间的已知关系一致的可解释结构。实现我们方法的软件可在https://github.com/stephenslab/flashr.
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引用次数: 0
Flexible Signal Denoising via Flexible Empirical Bayes Shrinkage. 通过灵活的经验贝叶斯收缩技术实现灵活的信号去噪。
IF 6 3区 计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS Pub Date : 2021-01-01
Zhengrong Xing, Peter Carbonetto, Matthew Stephens

Signal denoising-also known as non-parametric regression-is often performed through shrinkage estimation in a transformed (e.g., wavelet) domain; shrinkage in the transformed domain corresponds to smoothing in the original domain. A key question in such applications is how much to shrink, or, equivalently, how much to smooth. Empirical Bayes shrinkage methods provide an attractive solution to this problem; they use the data to estimate a distribution of underlying "effects," hence automatically select an appropriate amount of shrinkage. However, most existing implementations of empirical Bayes shrinkage are less flexible than they could be-both in their assumptions on the underlying distribution of effects, and in their ability to handle heteroskedasticity-which limits their signal denoising applications. Here we address this by adopting a particularly flexible, stable and computationally convenient empirical Bayes shrinkage method and applying it to several signal denoising problems. These applications include smoothing of Poisson data and heteroskedastic Gaussian data. We show through empirical comparisons that the results are competitive with other methods, including both simple thresholding rules and purpose-built empirical Bayes procedures. Our methods are implemented in the R package smashr, "SMoothing by Adaptive SHrinkage in R," available at https://www.github.com/stephenslab/smashr.

信号去噪--也称为非参数回归--通常是通过在变换(如小波)域中进行收缩估计来实现的;变换域中的收缩相当于原始域中的平滑。此类应用中的一个关键问题是缩小多少,或者说,平滑多少。经验贝叶斯收缩方法为这一问题提供了一个极具吸引力的解决方案;它们利用数据来估计潜在 "效应 "的分布,从而自动选择适当的收缩量。然而,大多数现有的经验贝叶斯收缩法的实现都不够灵活,无论是在对基本效应分布的假设上,还是在处理异方差的能力上,都限制了它们在信号去噪方面的应用。为了解决这个问题,我们采用了一种特别灵活、稳定且计算方便的经验贝叶斯收缩方法,并将其应用于几个信号去噪问题。这些应用包括平滑泊松数据和异方差高斯数据。通过经验比较,我们发现该方法的结果与其他方法(包括简单的阈值规则和专门设计的经验贝叶斯程序)相比具有竞争力。我们的方法在 R 软件包 smashr("SMoothing by Adaptive SHrinkage in R")中实现,请访问 https://www.github.com/stephenslab/smashr。
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引用次数: 0
Nonparametric graphical model for counts. 计数的非参数图形模型。
IF 6 3区 计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS Pub Date : 2020-12-01
Arkaprava Roy, David B Dunson

Although multivariate count data are routinely collected in many application areas, there is surprisingly little work developing flexible models for characterizing their dependence structure. This is particularly true when interest focuses on inferring the conditional independence graph. In this article, we propose a new class of pairwise Markov random field-type models for the joint distribution of a multivariate count vector. By employing a novel type of transformation, we avoid restricting to non-negative dependence structures or inducing other restrictions through truncations. Taking a Bayesian approach to inference, we choose a Dirichlet process prior for the distribution of a random effect to induce great flexibility in the specification. An efficient Markov chain Monte Carlo (MCMC) algorithm is developed for posterior computation. We prove various theoretical properties, including posterior consistency, and show that our COunt Nonparametric Graphical Analysis (CONGA) approach has good performance relative to competitors in simulation studies. The methods are motivated by an application to neuron spike count data in mice.

尽管在许多应用领域中经常收集多变量计数数据,但令人惊讶的是,很少有工作开发灵活的模型来表征它们的依赖结构。当兴趣集中在推断条件独立图时,这一点尤其正确。本文提出了一类新的多元计数向量联合分布的成对马尔可夫随机场模型。通过采用一种新颖的变换,我们避免了对非负依赖结构的限制或通过截断引起的其他限制。采用贝叶斯方法进行推理,我们为随机效应的分布选择了一个Dirichlet过程,以在规范中诱导很大的灵活性。提出了一种有效的后验计算马尔可夫链蒙特卡罗算法。我们证明了各种理论性质,包括后验一致性,并表明我们的计数非参数图形分析(CONGA)方法在模拟研究中相对于竞争对手具有良好的性能。这些方法的动机来自于对小鼠神经元尖峰计数数据的应用。
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引用次数: 0
Learning from Binary Multiway Data: Probabilistic Tensor Decomposition and its Statistical Optimality. 二元多路数据学习:概率张量分解及其统计最优性。
IF 6 3区 计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS Pub Date : 2020-07-01
Miaoyan Wang, Lexin Li

We consider the problem of decomposing a higher-order tensor with binary entries. Such data problems arise frequently in applications such as neuroimaging, recommendation system, topic modeling, and sensor network localization. We propose a multilinear Bernoulli model, develop a rank-constrained likelihood-based estimation method, and obtain the theoretical accuracy guarantees. In contrast to continuous-valued problems, the binary tensor problem exhibits an interesting phase transition phenomenon according to the signal-to-noise ratio. The error bound for the parameter tensor estimation is established, and we show that the obtained rate is minimax optimal under the considered model. Furthermore, we develop an alternating optimization algorithm with convergence guarantees. The efficacy of our approach is demonstrated through both simulations and analyses of multiple data sets on the tasks of tensor completion and clustering.

我们考虑具有二元项的高阶张量的分解问题。这类数据问题在神经成像、推荐系统、主题建模、传感器网络定位等应用中经常出现。提出了多线性伯努利模型,提出了基于秩约束的似然估计方法,并获得了理论精度保证。与连续值问题相比,根据信噪比,二元张量问题表现出有趣的相变现象。建立了参数张量估计的误差界,并证明了在考虑的模型下得到的速率是极小极大最优的。在此基础上,提出了一种具有收敛性保证的交替优化算法。通过对多个数据集的张量补全和聚类任务的模拟和分析,证明了我们方法的有效性。
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引用次数: 0
Quantile Graphical Models: Bayesian Approaches. 分位数图形模型:贝叶斯方法。
IF 6 3区 计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS Pub Date : 2020-01-01
Nilabja Guha, Veera Baladandayuthapani, Bani K Mallick

Graphical models are ubiquitous tools to describe the interdependence between variables measured simultaneously such as large-scale gene or protein expression data. Gaussian graphical models (GGMs) are well-established tools for probabilistic exploration of dependence structures using precision matrices and they are generated under a multivariate normal joint distribution. However, they suffer from several shortcomings since they are based on Gaussian distribution assumptions. In this article, we propose a Bayesian quantile based approach for sparse estimation of graphs. We demonstrate that the resulting graph estimation is robust to outliers and applicable under general distributional assumptions. Furthermore, we develop efficient variational Bayes approximations to scale the methods for large data sets. Our methods are applied to a novel cancer proteomics data dataset where-in multiple proteomic antibodies are simultaneously assessed on tumor samples using reverse-phase protein arrays (RPPA) technology.

图形模型是描述同时测量的变量之间的相互依赖关系的普遍工具,例如大规模的基因或蛋白质表达数据。高斯图形模型(GGMs)是利用精度矩阵对相关结构进行概率探索的成熟工具,它是在多元正态联合分布下生成的。然而,由于它们是基于高斯分布假设,因此存在一些缺点。在本文中,我们提出了一种基于贝叶斯分位数的图稀疏估计方法。我们证明了所得到的图估计对异常值具有鲁棒性,并且适用于一般分布假设。此外,我们开发了有效的变分贝叶斯近似来扩展大型数据集的方法。我们的方法应用于一个新的癌症蛋白质组学数据集,其中使用反相蛋白质阵列(RPPA)技术同时评估肿瘤样品中的多个蛋白质组学抗体。
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引用次数: 0
Near-optimal Individualized Treatment Recommendations. 近乎最佳的个体化治疗建议。
IF 6 3区 计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS Pub Date : 2020-01-01
Haomiao Meng, Ying-Qi Zhao, Haoda Fu, Xingye Qiao

The individualized treatment recommendation (ITR) is an important analytic framework for precision medicine. The goal of ITR is to assign the best treatments to patients based on their individual characteristics. From the machine learning perspective, the solution to the ITR problem can be formulated as a weighted classification problem to maximize the mean benefit from the recommended treatments given patients' characteristics. Several ITR methods have been proposed in both the binary setting and the multicategory setting. In practice, one may prefer a more flexible recommendation that includes multiple treatment options. This motivates us to develop methods to obtain a set of near-optimal individualized treatment recommendations alternative to each other, called alternative individualized treatment recommendations (A-ITR). We propose two methods to estimate the optimal A-ITR within the outcome weighted learning (OWL) framework. Simulation studies and a real data analysis for Type 2 diabetic patients with injectable antidiabetic treatments are conducted to show the usefulness of the proposed A-ITR framework. We also show the consistency of these methods and obtain an upper bound for the risk between the theoretically optimal recommendation and the estimated one. An R package aitr has been developed, found at https://github.com/menghaomiao/aitr.

个体化治疗推荐(ITR)是精准医疗的重要分析框架。ITR的目标是根据患者的个体特征分配最佳治疗方案。从机器学习的角度来看,ITR问题的解决方案可以被表述为一个加权分类问题,以最大化根据患者特征推荐治疗的平均收益。在二元设置和多类别设置下,提出了几种ITR方法。实际上,人们可能更喜欢更灵活的建议,包括多种治疗方案。这促使我们开发方法来获得一组相互替代的接近最佳的个体化治疗建议,称为替代个体化治疗建议(a - itr)。我们提出了两种方法来估计结果加权学习(OWL)框架下的最优A-ITR。通过对2型糖尿病患者注射降糖治疗的模拟研究和真实数据分析,证明了所提出的a - itr框架的有效性。我们还证明了这些方法的一致性,并得到了理论最优推荐和估计风险之间的上界。已经开发了一个R包,可以在https://github.com/menghaomiao/aitr上找到。
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引用次数: 0
Robust Asynchronous Stochastic Gradient-Push: Asymptotically Optimal and Network-Independent Performance for Strongly Convex Functions. 鲁棒异步随机梯度推:强凸函数的渐近最优和网络无关性能。
IF 6 3区 计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS Pub Date : 2020-01-01
Artin Spiridonoff, Alex Olshevsky, Ioannis Ch Paschalidis

We consider the standard model of distributed optimization of a sum of functions F ( z ) = i = 1 n f i ( z ) , where node i in a network holds the function fi (z). We allow for a harsh network model characterized by asynchronous updates, message delays, unpredictable message losses, and directed communication among nodes. In this setting, we analyze a modification of the Gradient-Push method for distributed optimization, assuming that (i) node i is capable of generating gradients of its function fi (z) corrupted by zero-mean bounded-support additive noise at each step, (ii) F(z) is strongly convex, and (iii) each fi (z) has Lipschitz gradients. We show that our proposed method asymptotically performs as well as the best bounds on centralized gradient descent that takes steps in the direction of the sum of the noisy gradients of all the functions f 1(z), …, fn (z) at each step.

我们考虑函数和的分布式优化的标准模型F (z) =∑i = 1 n F i (z),其中网络中的节点i保存函数fi (z)。我们允许一个苛刻的网络模型,其特征是异步更新,消息延迟,不可预测的消息丢失和节点之间的定向通信。在此设置中,我们分析了用于分布式优化的Gradient-Push方法的修改,假设(i)节点i能够生成其函数fi (z)的梯度,该函数在每一步都被零均值有界支持加性噪声破坏,(ii) F(z)是强凸的,以及(iii)每个fi (z)具有Lipschitz梯度。我们表明,我们提出的方法在集中梯度下降上的渐近性能与最佳边界一样好,该方法在每一步都朝着所有函数f1 (z),…,fn (z)的噪声梯度之和的方向采取步骤。
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引用次数: 0
A Regularization-Based Adaptive Test for High-Dimensional Generalized Linear Models. 高维广义线性模型的基于正则化的自适应检验。
IF 6 3区 计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS Pub Date : 2020-01-01 Epub Date: 2020-07-26
Chong Wu, Gongjun Xu, Xiaotong Shen, Wei Pan

In spite of its urgent importance in the era of big data, testing high-dimensional parameters in generalized linear models (GLMs) in the presence of high-dimensional nuisance parameters has been largely under-studied, especially with regard to constructing powerful tests for general (and unknown) alternatives. Most existing tests are powerful only against certain alternatives and may yield incorrect Type I error rates under high-dimensional nuisance parameter situations. In this paper, we propose the adaptive interaction sum of powered score (aiSPU) test in the framework of penalized regression with a non-convex penalty, called truncated Lasso penalty (TLP), which can maintain correct Type I error rates while yielding high statistical power across a wide range of alternatives. To calculate its p-values analytically, we derive its asymptotic null distribution. Via simulations, its superior finite-sample performance is demonstrated over several representative existing methods. In addition, we apply it and other representative tests to an Alzheimer's Disease Neuroimaging Initiative (ADNI) data set, detecting possible gene-gender interactions for Alzheimer's disease. We also put R package "aispu" implementing the proposed test on GitHub.

尽管在大数据时代具有紧迫的重要性,但在存在高维干扰参数的情况下测试广义线性模型(GLM)中的高维参数在很大程度上被研究不足,尤其是在为一般(和未知)替代方案构建强大的测试方面。大多数现有的测试仅针对某些替代方案是强大的,并且在高维干扰参数情况下可能产生不正确的I型错误率。在本文中,我们提出了在具有非凸惩罚的惩罚回归框架下的自适应交互和幂分数(aiSPU)检验,称为截断Lasso惩罚(TLP),它可以保持正确的I型错误率,同时在广泛的备选方案中产生高统计幂。为了解析地计算它的p值,我们导出了它的渐近零分布。通过仿真,与几种具有代表性的现有方法相比,证明了其优越的有限样本性能。此外,我们将其和其他具有代表性的测试应用于阿尔茨海默病神经成像倡议(ADNI)数据集,检测阿尔茨海默病可能的基因-性别相互作用。我们还在GitHub上放了R包“aispu”来实现所提出的测试。
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引用次数: 0
期刊
Journal of Machine Learning Research
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