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The FASTCLIME Package for Linear Programming and Large-Scale Precision Matrix Estimation in R

JOURNAL OF MACHINE LEARNING RESEARCH 2014年第1期15卷 489-493页

作者： Pang, Haotian Liu, Han Vanderbei, Robets Princeton Univ Dept Elect Engn Princeton NJ 08540 USA Princeton Univ Dept Operat Res & Financial Engn Princeton NJ 08540 USA

We develop an R package FASTCLIME for solving a family of regularized linear programming (LP) problems. Our package efficiently implements the parametric simplex algorithm, which provides a scalable and sophisticated tool for solving large-scale linear programs. As an illustrative example, one use of our LP solver is to implement an important sparse precision matrix estimation method called CLIME (Constrained L-1 Minimization Estimator). Compared with existing packages for this problem such as CLIME and FLARE, our package has three advantages: (1) it efficiently calculates the full piecewise-linear regularization path;(2) it provides an accurate dual certificate as stopping criterion;(3) it is completely coded in C and is highly portable. This package is designed to be useful to statisticians and machine learning researchers for solving a wide range of problems.

关键词： high dimensional data sparse precision matrix linear programming parametric simplex method undirected graphical model

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Path weights in concentration graphs

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BIOMETRIKA 2020年第3期107卷 705-722页

作者： Roverato, Alberto Castelo, Robert Univ Padua Dept Stat Sci Via C Battisti 241 I-35121 Padua Italy Univ Pompeu Fabra Dept Expt & Hlth Sci Dr Aiguader 88 E-08003 Barcelona Spain

A graphical model provides a compact and efficient representation of the association structure in a multivariate distribution by means of a graph. Relevant features of the distribution are represented by vertices, edges and higher-order graphical structures such as cliques or paths. Typically, paths play a central role in these models because they determine the dependence relationships between variables. However, while a theory of path coefficients is available for directed graph models, little research exists on the strength of the association represented by a path in an undirected graph. Essentially, it has been shown that the covariance between two variables can be decomposed into a sum of weights associated with each of the paths connecting the two variables in the corresponding concentration graph. In this context, we consider concentration graph models and provide an extensive analysis of the properties of path weights and their interpretation. Specifically, we give an interpretation of covariance weights through their factorization into a partial covariance and an inflation factor. We then extend the covariance decomposition over the paths of an undirected graph to other measures of association, such as the marginal correlation coefficient and a quantity that we call the inflated correlation. Application of these results is illustrated with an analysis of dietary intake networks.

关键词： Concentration graph Covariance decomposition Inflation factor Partial correlation undirected graphical model undirected path

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Hyperspectral Image Clustering based on Variational Expectation Maximization 11

Hyperspectral Image Clustering based on Variational Expectat...

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IEEE 11th Sensor Array and Multichannel Signal Processing Workshop (SAM)

作者： Jiao, Yuchen Ma, Yirong Gu, Yuantao Tsinghua Univ Dept Elect Engn Beijing Peoples R China 69010 Unit PLA Urumqi Peoples R China

ISBN: (纸本)9781728119465

Hyperspectral image clustering is an important and challenging problem, which aims to group image pixels according to the land cover information extracted from the spectrum. The spectrum observed at adjacent pixels are often highly-correlated, and leveraging such spatial correlation can greatly improve the clustering accuracy. Markov Random Field (MRF) is a powerful model to characterize such correlation. However, in this model the spatial parameter beta often needs to be manually tuned, which brings difficulty in finding an optimal value. In this paper, we propose a novel hyperspectral clustering algorithm, which is able to learn parameter beta from the data and thus achieves better performance. Specifically, we model the spectral information with Gaussian mixture model, and use variational expectation maximization method to complete the parameter estimation and clustering task. Experiments on both synthetic and real-world data sets verify the effectiveness of the proposed algorithm.

关键词： Hyperspectral Image clustering undirected graphical model variational expectation maximization spatial parameter

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QUANTIFYING INPUT UNCERTAINTY IN AN ASSEMBLE-TO-ORDER SYSTEM SIMULATION WITH CORRELATED INPUT VARIABLES OF MIXED TYPES 14

QUANTIFYING INPUT UNCERTAINTY IN AN ASSEMBLE-TO-ORDER SYSTEM...

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Winter Simulation Conference

作者： Akcay, Alp Biller, Bahar Bilkent Univ Dept Ind Engn TR-06800 Ankara Turkey Carnegie Mellon Univ Tepper Sch Business Pittsburgh PA 15213 USA

ISBN: (纸本)9781479974863

We consider an assemble-to-order production system where the product demands and the time since the last customer arrival are not independent. The simulation of this system requires a multivariate input model that generates random input vectors with correlated discrete and continuous components. In this paper, we capture the dependence between input variables in an undirected graphical model and decouple the statistical estimation of the univariate input distributions and the underlying dependence measure into separate problems. The estimation errors due to finiteness of the real-world data introduce the so-called input uncertainty in the simulation output. We propose a method that accounts for input uncertainty by sampling the univariate empirical distribution functions via bootstrapping and by maintaining a posterior distribution of the precision matrix that corresponds to the dependence structure of the graphical model. The method improves the coverages of the confidence intervals for the expected profit the per period.

关键词： assembling graph theory manufacturing systems matrix algebra production management profitability statistical analysis statistical distributions assemble-to-order production system assemble-to-order system simulation bootstrapping estimation errors input uncertainty quantification mixed type correlated input variables precision matrix posterior distribution product demands profit statistical estimation undirected graphical model univariate empirical distribution functions univariate input distributions Analytical models Correlation Data models Distribution functions graphical models Input variables Uncertainty Input variables Statistical Estimation graphical models Error analysis bootstrapping Distribution function data models statistical distribution production control Manufacturing Management matrix algebra Manufacturing systems ANALYSIS modelS Graph theory Uncertainty

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Exploiting non-redundant local patterns and probabilistic models for analyzing structured and semi-structured data

Exploiting non-redundant local patterns and probabilistic mo...

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作者： Wang, Chao The Ohio State University

学位级别：Ph.D.

This work seeks to develop a probabilistic framework for modeling, querying and analyzing large-scale structured and semi-structured data. The framework has three components: (1) Mining non-redundant local patterns from data; (2) Gluing these local patterns together by employing probabilistic models (e.g., Markov random field (MRF), Bayesian network); and (3) Reasoning (making inference) over the data for solving various data analysis tasks. In more detail, our contributions are as follows:@pqdt@break@Mining non-redundant frequent itemset patterns on large transactional data. Often times in many real-world problems frequent pattern mining algorithms yield so many frequent patterns that the end-user is swamped when it comes to interpreting the results. We present an approach of employing probabilistic models to identify non-redundant itemset patterns from a large collection of frequent itemsets on transactional data. We show that our approach can effectively eliminate a large amount of redundancy from a large collection of itemset patterns.@pqdt@break@Employing local probabilistic models to glue non-redundant itemset patterns on large transactional or network data. We propose a technique of employing local probabilistic models to glue non-redundant itemset patterns together in tackling the link prediction task in co-authorship network analysis. The new technique effectively combines topology analysis on network structure data and frequency analysis on network event log data. The main idea is to consider the co-occurrence probability of two end nodes associated with a candidate link. We propose a method of building MRFs over local data regions to compute this co-occurrence probability. Experimental results demonstrate that the co-occurrence probability inferred from the local probabilistic models is very useful for link prediction.@pqdt@break@Employing global probabilistic models to glue non-redundant itemset patterns on large transactional data. We explore employing

关键词： Computer Science Probabilistic graphical model undirected graphical model Markov Random Field Maximum Entropy Feature Selection Frequent Pattern Mining Non-Redundant Frequent Pattern Structured and Semi-Structure Data Social Network Analysis Link Prediction

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Bayesian model selection for high-dimensional Ising models, with applications to educational data

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2022年 165卷 107325-107325页

作者： Park, Jaewoo Jin, Ick Hoon Schweinberger, Michael Yonsei Univ Dept Stat & Data Sci Seoul South Korea Yonsei Univ Dept Appl Stat Seoul South Korea Univ Missouri Dept Stat Columbia MO 65211 USA

Doubly-intractable posterior distributions arise in many applications of statistics concerned with discrete and dependent data, including physics, spatial statistics, machine learning, the social sciences, and other fields. A specific example is psychometrics, which has adapted high-dimensional Ising models from machine learning, with a view to studying the interactions among binary item responses in educational assessments. To estimate high-dimensional Ising models from educational assessment data, l(1)-penalized nodewise logistic regressions have been used. Theoretical results in high-dimensional statistics show that l(1)-penalized nodewise logistic regressions can recover the true interaction structure with high probability, provided that certain assumptions are satisfied. Those assumptions are hard to verify in practice and may be violated, and quantifying the uncertainty about the estimated interaction structure and parameter estimators is challenging. We propose a Bayesian approach that helps quantify the uncertainty about the interaction structure and parameters without requiring strong assumptions, and can be applied to Ising models with thousands of parameters. We demonstrate the advantages of the proposed Bayesian approach compared with l(1)-penalized nodewise logistic regressions by simulation studies and applications to small and large educational data sets with up to 2,485 parameters. Among other things, the simulation studies suggest that the Bayesian approach is more robust against model misspecification due to omitted covariates than l(1)-penalized nodewise logistic regressions. (C) 2021 Elsevier B.V. All rights reserved.

关键词： Bayesian model selection Doubly intractable posterior distribution Ising model undirected graphical model Psychometrics

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Toward sampling from undirected probabilistic graphical models using a D-Wave quantum annealer

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QUANTUM INFORMATION PROCESSING 2020年第10期19卷 353-353页

作者： Koshka, Yaroslav Novotny, M. A. Mississippi State Univ HPC2 Ctr Computat Sci Dept Elect & Comp Engn Mississippi State MS 39762 USA Mississippi State Univ HPC2 Ctr Computat Sci Dept Phys & Astron Mississippi State MS 39762 USA

A D-Wave quantum annealer (QA) having a 2048 qubit lattice, with no missing qubits and couplings, allowed embedding of a complete graph of a restricted Boltzmann machine (RBM). A handwritten digit OptDigits dataset having 8x7 pixels of visible units was used to train the RBM using classical contrastive divergence. Embedding of the classically trained RBM into the D-Wave lattice was used to demonstrate that the QA offers a high-efficiency alternative to the classical Markov chain Monte Carlo (MCMC) for reconstructing missing labels of the test images as well as a generative model on a classically trained RBM. At any training iteration, the D-Wave-based classification had classification error less than half of that in MCMC. The main goal of this study was to investigate the quality of the QA sample from the RBM model probability distribution and compare it to a classical MCMC during the Gibbs sampling traditionally used in RBM training. For the OptDigits dataset, the states in the D-Wave sample belonged to about twice as many local valleys (LVs) as in the MCMC sample. All the lowest energy (the highest joint probability), local minima in the MCMC sample were also found by the D-Wave. The D-Wave missed many of the higher-energy LVs, while also finding many "new" LVs consistently missed by the MCMC. It was established that the "new" LVs that the D-Wave finds are important for the model distribution in terms of the energy of the corresponding local minima, the width of the LVs and the height of the escape barrier.

关键词： Adiabatic quantum annealer Boltzmann machine Local extrema Monte Carlo undirected graphical model Sampling Simulated annealing Simulated warming

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A superpixel-based CRF saliency detection approach

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Neurocomputing 2017年 244卷 19-32页

作者： Wenliang Qiu Xinbo Gao Bing Han Video and Image Processing System Laboratory School of Electronic Engineering Xidian University Xi’an 710071 China

Salient object detection, experienced several decades, has been an active and popular topic in computer vision. Although a large amount of detection algorithms have been proposed, the obtained saliency maps are still not satisfying enough. To this end, we proposed a simple and novel supervised algorithm to detect a pure background saliency map using conditional random fields (CRF) and saliency cues. Most existing CRF approaches set up the probabilistic graphical models with pixel-wise eight neighborhood grid-shaped graph, while our superpixel level graph handling can not only simplify the model but also promote the performance due to the superpixel level two-ring with pseudo-background neighborhood system. It is intuitive and easy to interpret. As a result, the saliency maps generated by the proposed model have relatively pure background regions. Extensive experimental evaluations on six benchmark datasets with pixel-wise ground truths validated the robustness and effectiveness of the proposed saliency model.

关键词： Saliency detection Conditional random fields Superpixel undirected graphical model Saliency model

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Instability, Sensitivity, and Degeneracy of Discrete Exponential Families

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JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 2011年第496期106卷 1361-1370页

作者： Schweinberger, Michael Penn State Univ Dept Stat University Pk PA 16802 USA

A number of discrete exponential family models for dependent data, first and foremost relational data, have turned out to be near-degenerate and problematic in terms of Markov chain Monte Carlo (MCMC) simulation and statistical inference. I introduce the notion of instability with an eye to characterize, detect, and penalize discrete exponential family models that are near-degenerate and problematic in terms of MCMC simulation and statistical inference. I show that unstable discrete exponential family models are characterized by excessive sensitivity and near-degeneracy. In special cases, the subset of the natural parameter space corresponding to nondegenerate distributions and mean-value parameters far from the boundary of the mean-value parameter space turns out to be a lower-dimensional subspace of the natural parameter space. These characteristics of unstable discrete exponential family models tend to obstruct MCMC simulation and statistical inference. In applications to relational data, I show that discrete exponential family models with Markov dependence tend to be unstable, and that the parameter space of some curved exponential families contains unstable subsets.

关键词： Curved exponential family Markov chain Monte Carlo Social network Statistical exponential family undirected graphical model

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The fastclime package for linear programming and large-scale precision matrix estimation in R

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2014年第1期15卷

作者： Kevin Murphy Bernhard Schölkopf Haotian Pang Han Liu Robert Vanderbei Google Department of Electrical Engineering Princeton University Princeton NJ Department of Operations Research and Financial Engineering Princeton University Princeton NJ

We develop an R package FASTCLIME for solving a family of regularized linear programming (LP) problems. Our package efficiently implements the parametric simplex algorithm, which provides a scalable and sophisticated tool for solving large-scale linear programs. As an illustrative example, one use of our LP solver is to implement an important sparse precision matrix estimation method called CLIME (Constrained L1 Minimization Estimator). Compared with existing packages for this problem such as CLIME and FLARE, our package has three advantages: (1) it efficiently calculates the full piecewise-linear regularization path; (2) it provides an accurate dual certificate as stopping criterion; (3) it is completely coded in C and is highly portable. This package is designed to be useful to statisticians and machine learning researchers for solving a wide range of problems.

关键词： high dimensional data linear programming parametric simplex method sparse precision matrix undirected graphical model

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