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Bayesian Variable Selection and Sparse Estimation for High-Dimensional Graphical Models

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arXiv 2024年

作者： Chakravarti, Anwesha Narisetty, Naveen N. Liang, Feng University of Illinois at Urbana Champaign Department of Statistics United States

We introduce a novel Bayesian approach for both covariate selection and sparse precision matrix estimation in the context of high-dimensional Gaussian graphical models involving multiple responses. Our approach provides a sparse estimation of the three distinct sparsity structures: the regression coefficient matrix, the conditional dependency structure among responses, and between responses and covariates. This contrasts with existing methods, which typically focus on any two of these structures but seldom achieve simultaneous sparse estimation for all three. A key aspect of our method is that it leverages the structural sparsity information gained from the presence of irrelevant covariates in the dataset to introduce covariate-level sparsity in the precision and regression coefficient matrices. This is achieved through a Bayesian conditional random field model using a hierarchical spike and slab prior setup. Despite the non-convex nature of the problem, we establish statistical accuracy for points in the high posterior density region, including the maximum-a-posteriori (MAP) estimator. We also present an efficient expectation-maximization (EM) algorithm for computing the estimators. Through simulation experiments, we demonstrate the competitive performance of our method, particularly in scenarios with weak signal strength in the precision matrices. Finally, we apply our method to a bike-share dataset, showcasing its predictive performance. © 2024, CC BY-NC-SA.

关键词： expectation maximization algorithm

Mini-batch Submodular maximization

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arXiv 2024年

作者： Schwartzman, Gregory JAIST Japan

We present the first mini-batch algorithm for maximizing a non-negative monotone decomposable submodular function, (Equation presented), under a set of constraints. We consider two sampling approaches: uniform and weighted. We first show that mini-batch with weighted sampling improves over the state of the art sparsifier based approach both in theory and in practice. Surprisingly, our experimental results show that uniform sampling is superior to weighted sampling. However, it is impossible to explain this using worst-case analysis. Our main contribution is using smoothed analysis to provide a theoretical foundation for our experimental results. We show that, under very mild assumptions, uniform sampling is superior for both the mini-batch and the sparsifier approaches. We empirically verify that these assumptions hold for our datasets. Uniform sampling is simple to implement and has complexity independent of N, making it the perfect candidate to tackle massive real-world datasets. Copyright © 2024, The Authors. All rights reserved.

关键词： expectation maximization algorithm

BAYESIAN EXPERIMENTAL DESIGN VIA CONTRASTIVE DIFFUSIONS

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arXiv 2024年

作者： Iollo, Jacopo Heinkelé, Christophe Alliez, Pierre Forbes, Florence Université Grenoble Alpes Inria CNRS G-INP France Cerema Endsum Strasbourg France Université Côte d’Azur Inria France

Bayesian Optimal Experimental Design (BOED) is a powerful tool to reduce the cost of running a sequence of experiments. When based on the Expected Information Gain (EIG), design optimization corresponds to the maximization of some intractable expected contrast between prior and posterior distributions. Scaling this maximization to high dimensional and complex settings has been an issue due to BOED inherent computational complexity. In this work, we introduce a pooled posterior distribution with cost-effective sampling properties and provide a tractable access to the EIG contrast maximization via a new EIG gradient expression. Diffusion-based samplers are used to compute the dynamics of the pooled posterior and ideas from bi-level optimization are leveraged to derive an efficient joint sampling-optimization loop. The resulting efficiency gain allows to extend BOED to the well-tested generative capabilities of diffusion models. By incorporating generative models into the BOED framework, we expand its scope and its use in scenarios that were previously impractical. Numerical experiments and comparison with state-of-the-art methods show the potential of the approach. © 2024, CC BY-SA.

关键词： expectation maximization algorithm

Optimizing Adaptive Experiments: A Unified Approach to Regret Minimization and Best-Arm Identification

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arXiv 2024年

作者： Qin, Chao Russo, Daniel Columbia University United States

Practitioners conducting adaptive experiments often encounter two competing priorities: maximizing total welfare (or 'reward') through effective treatment assignment and swiftly concluding experiments to implement population-wide treatments. Current literature addresses these priorities separately, with regret minimization studies focusing on the former and bestarm identification research on the latter. This paper bridges this divide by proposing a unified model that simultaneously accounts for within-experiment performance and post-experiment outcomes. We provide a sharp theory of optimal performance in large populations that not only unifies canonical results in the literature but also uncovers novel insights. Our theory reveals that familiar algorithms, such as the recently proposed top-two Thompson sampling algorithm, can optimize a broad class of objectives if a single scalar parameter is appropriately adjusted. In addition, we demonstrate that substantial reductions in experiment duration can often be achieved with minimal impact on both within-experiment and post-experiment regret. Copyright © 2024, The Authors. All rights reserved.

关键词： expectation maximization algorithm

Research on Network Self-protection System Model and Its Security Event Correlation Engine

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Research on Network Self-protection System Model and Its Sec...

2010 International Conference on Services Science, Management and Engineering (SSME 2010)

作者： Hongyu Yang School of Computer Science and Technology Civil Aviation University of China Tianjin 300300,China Dongming Wang School of Computer Science and Technology Civil Aviation University of China Tianjin 300300,China Chuangxi Chen Dep.of ground maintenance China Southern Airlines Co.Ltd. Guangzhou 510406,China

Manual analysis of security events inevitably results in a large number of attacks can not being detected timely This paper presents a new network self-protection system model,gives its architecture and designs its information security event correlative analysis *** the correlation engine,the expectation maximization(EM) algorithm was designed to solve the problem by lack of security *** the bucket elimination algorithm was used to enhance the computational efficiency of Bayesian *** experimental results demonstrate that the reasoning speed of the correlation engine fulfills the need of network protection against unknown attacks.

关键词： self-protection correlation engine Bayesian network bucket elimination algorithm expectation maximization algorithm

Policy Choice in Time Series by Empirical Welfare maximization

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arXiv 2022年

作者： Kitagawa, Toru Wang, Weining Xu, Mengshan Department of Economics Brown University United States Department of Economics University College London United Kingdom Faculty of economics and business University of Groningen Netherlands Department of Economics University of Mannheim Germany

This paper develops a novel method for policy choice in a dynamic setting where the available data is a multi-variate time series. Building on the statistical treatment choice framework, we propose Time-series Empirical Welfare maximization (T-EWM) methods to estimate an optimal policy rule by maximizing an empirical welfare criterion constructed using nonparametric potential outcome time series. We characterize conditions under which T-EWM consistently learns a policy choice that is optimal in terms of conditional welfare given the time-series history. We derive a nonasymptotic upper bound for conditional welfare regret. To illustrate the implementation and uses of T-EWM, we perform simulation studies and apply the method to estimate optimal restriction rules against Covid-19. © 2022, CC BY.

关键词： expectation maximization algorithm

Scalable likelihood-based estimation and variable selection for the Cox model with incomplete covariates

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arXiv 2024年

作者： Kwok, Ngok Sang Wong, Kin Yau Department of Applied Mathematics The Hong Kong Polytechnic University Hong Kong

Regression analysis with missing data is a long-standing and challenging problem, particularly when there are many missing variables with arbitrary missing patterns. Likelihood-based methods, although theoretically appealing, are often computationally inefficient or even infeasible when dealing with a large number of missing variables. In this paper, we consider the Cox regression model with incomplete covariates that are missing at random. We develop an expectation-maximization (EM) algorithm for nonparametric maximum likelihood estimation, employing a transformation technique in the E-step so that it involves only a one-dimensional integration. This innovation makes our methods scalable with respect to the dimension of the missing variables. In addition, for variable selection, we extend the proposed EM algorithm to accommodate a LASSO penalty in the likelihood. We demonstrate the feasibility and advantages of the proposed methods over existing methods by large-scale simulation studies and apply the proposed methods to a cancer genomic study. © 2024, CC BY-NC-ND.

关键词： expectation maximization algorithm

Empirical Welfare maximization with Constraints

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arXiv 2021年

作者： Sun, Liyang UCL United Kingdom CEMFI Spain

Empirical Welfare maximization (EWM) is a framework that can be used to select welfare program eligibility policies based on data. This paper extends EWM by allowing for uncertainty in estimating the budget needed to implement the selected policy, in addition to its welfare. Due to the additional estimation error, I show there exist no rules that achieve the highest welfare possible while satisfying a budget constraint uniformly over a wide range of DGPs. This differs from the setting without a budget constraint where uniformity is achievable. I propose an alternative trade-off rule and illustrate it with Medicaid expansion, a setting with imperfect take-up and varying program costs. © 2021, CC BY.

关键词： expectation maximization algorithm

UNIVERSAL WYNER-ZIV CODING FOR GAUSSIAN SOURCES

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UNIVERSAL WYNER-ZIV CODING FOR GAUSSIAN SOURCES

IEEE International Conference on Acoustics, Speech and Signal Processing

作者： Elsa DUPRAZ Aline ROUMY Michel KIEFFER L2S - CNRS - SUPELEC - Univ Paris-Sud 91192 Gif-sur-Yvette France INRIA Campus de Beaulieu 35042 Rennes France

ISBN: (纸本)9781479903573

This paper considers the problem of lossy source coding with side information at the decoder only, for Gaussian sources, when the joint statistics of the sources are partly unknown. We propose a practical universal coding scheme based on scalar quantization and non-binary LDPC codes, which avoids the binarization of the quantized coefficients. We first explain how to choose the rate and to construct the LDPC coding matrix. Then, a decoding algorithm that jointly estimates the source sequence and the joint statistics of the sources is proposed. The proposed coding scheme suffers no loss compared to the practical coding scheme with same rate but known variance.

关键词： Source coding with side information Rate-distortion Low Density Parity Check codes expectation maximization algorithm low density parity check codes expectation-maximisation algorithm Rate distortion labeling scheme Gauss scalar quantization lossy source coding binarization