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Optimization algorithms on subspaces: Revisiting missing data problem in low-rank matrix

INTERNATIONAL JOURNAL OF COMPUTER VISION 2008年第1期80卷 125-142页

作者： Chen, Pei Chinese Univ Hong Kong Chinese Acad Sci Shenzhen Inst Adv Int Technol Shenzhen Peoples R China

Low-rank matrix approximation has applications in many fields, such as 3D reconstruction from an image sequence and 2D filter design. In this paper, one issue with low-rank matrix approximation is re-investigated: the missing data problem. Much effort was devoted to this problem, and the Wiberg algorithm or the damped Newton algorithm were recommended in previous studies. However, the Wiberg or damped Newton algorithms do not suit for large (especially "long") matrices, because one needs to solve a large linear system in every iteration. In this paper, we revitalize the usage of the Levenberg-Marquardt algorithm for solving the missing data problem, by utilizing the property that low-rank approximation is a minimization problem on subspaces. In two proposed implementations of the Levenberg-Marquardt algorithm, one only needs to solve a much smaller linear system in every iteration, especially for "long" matrices. Simulations and experiments on real data show the superiority of the proposed algorithms. Though the proposed algorithms achieve a high success rate in estimating the optimal solution by random initialization, as illustrated by real examples;it still remains an open issue how to properly do the initialization in a severe situation (that is, a large amount of data is missing and with high-level noise).

关键词： low-rank matrix approximation missing data problem subspace singular value decomposition Levenberg-Marquardt algorithm

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The S-U algorithm for missing data problems

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COMPUTATIONAL STATISTICS 2000年第2期15卷 243-277页

作者： Satten, GA Datta, S Ctr Dis Control & Prevent Natl Ctr HIV STD & TB Prevent Atlanta GA 30333 USA Univ Georgia Dept Stat Athens GA 30602 USA

We present a new Monte-Carlo method for finding the solution of an estimating equation that can be expressed as the expected value of a 'full data' estimating equation in which the expected value is with respect to the 'distribution of the missing data given the observed data. Equations such as these arise whenever the E-M algorithm can be used. The algorithm alternates between two steps: an S-step, in which the missing data are simulated, either from the conditional distribution described above or from a more convenient importance sampling distribution, and a U-step, in which parameters are updated using a closed-form expression that does not require a numerical maximization. We present two numerical examples to illustrate the method. Theoretical results are obtained establishing consistency and asymptotic normality of the approximate solution obtained by our method.

关键词： estimating equation missing data problem simulate and update maximum likelihood EM algorithm Monte-Carlo method

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Multi-Domain Image Completion for Random missing Input data

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IEEE TRANSACTIONS ON MEDICAL IMAGING 2021年第4期40卷 1113-1122页

作者： Shen, Liyue Zhu, Wentao Wang, Xiaosong Xing, Lei Pauly, John M. Turkbey, Baris Harmon, Stephanie Anne Sanford, Thomas Hogue Mehralivand, Sherif Choyke, Peter L. Wood, Bradford J. Xu, Daguang Stanford Univ Dept Elect Engn Palo Alto CA 94306 USA NVIDIA Corp Santa Clara CA 95051 USA Stanford Univ Dept Radiat Oncol Palo Alto CA 94306 USA NCI Mol Imaging Branch Bethesda MD 20892 USA NCI Clin Res Directorate Frederick Natl Lab Canc Res Bethesda MD 20892 USA NIH Clin Ctr Bethesda MD 20892 USA NIH Ctr Intervent Oncol Bethesda MD 20892 USA

Multi-domain data are widely leveraged in vision applications taking advantage of complementary information from different modalities, e.g., brain tumor segmentation from multi-parametric magnetic resonance imaging (MRI). However, due to possible data corruption and different imaging protocols, the availability of images for each domain could vary amongst multiple data sources in practice, which makes it challenging to build a universal model with a varied set of input data. To tackle this problem, we propose a general approach to complete the random missing domain(s) data in real applications. Specifically, we develop a novel multi-domain image completion method that utilizes a generative adversarial network (GAN) with a representational disentanglement scheme to extract shared content encoding and separate style encoding across multiple domains. We further illustrate that the learned representation in multi-domain image completion could be leveraged for high-level tasks, e.g., segmentation, by introducing a unified framework consisting of image completion and segmentation with a shared content encoder. The experiments demonstrate consistent performance improvement on three datasets for brain tumor segmentation, prostate segmentation, and facial expression image completion respectively.

关键词： Image segmentation Tumors Task analysis Image synthesis Magnetic resonance imaging Image reconstruction Biomedical imaging Multi-domain image-to-image translation multi-contrast MRI missing data problem missing-domain segmentation medical image synthesis

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Process regulation via genealogical decision trees

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OPTIMAL CONTROL APPLICATIONS & METHODS 2009年第2期30卷 121-133页

作者： Ikonen, E. Gomez-Rarnirez, E. Najim, K. Univ Oulu Syst Engn Lab Dept Proc & Environm Engn FIN-90014 Oulu Finland La Salle Univ Mexico City DF Mexico ENSIACET Toulouse France

This paper deals with regulation control on the basis of genealogical decision trees (GDTs). GDTs are a population-based random search technique for solving sequential multimodal and multivariable trajectory tracking problems, when gradient information is not available or does not exist. A direct application of GDT results in an open-loop control. In this paper, feedback regulation based on GDT is considered. In the proposed scheme, GDTs are used for solving off-line a number of predictive control problems;a finite set of initial states is then constructed from these simulations, for each of which an optimal control sequence has been computed. Natural handling of missing state vector measurements is provided. Numerical examples dealing with the van der Vusse CSTR illustrate the feasibility and the efficiency of this feedback control algorithm. A discussion on alternative approaches and a numerical comparison with the Markov-decision-process-based optimal policy are provided. Copyright (c) 2008 John Wiley & Sons, Ltd.

关键词： feedback control missing data problem Monte Carlo method optimal control optimization problems particle filtering population-based search

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missing-data Nonparametric Coherency Estimation

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IEEE SIGNAL PROCESSING LETTERS 2021年 28卷 1704-1708页

作者： Haley, C. Argonne Natl Lab Math & Comp Sci Div Lemont IL 60439 USA

Chave recently proposed an estimator for multitaper spectral density where the time series contains missing values. In this article we generalize this technique to a multitaper estimator of coherence and phase and show that one can also obtain bootstrapped confidence intervals. We give two examples. The first is a toy example in which the true coherence is known. In the second example we show that the multitaper missing-data coherence estimator computed on real data with a single gap comprising 11% of the data outperforms the Daniell-smoothed coherence estimator where there are no gaps. The case where the two time series have different missing indices is also discussed.

关键词： Coherence Time series analysis Frequency estimation Smoothing methods Recruitment Oscillators Indexes Coherence Lomb-Scargle periodogram missing data problem multivariate time series multitaper power spectrum

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GENERALIZED THEME DICTIONARY MODELS FOR ASSOCIATION PATTERN DISCOVERY

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ANNALS OF APPLIED STATISTICS 2023年第1期17卷 269-293页

作者： Yang, By yang Deng, K. E. Nankai Univ Sch Stat & Data Sci LPMC & KLMDASR Tianjin Peoples R China Tsinghua Univ Ctr Stat Sci Beijing Peoples R China Tsinghua Univ Dept Ind Engn Beijing Peoples R China

Discovering association patterns of items from a collection of baskets composed of different items is an important problem in various fields. Assum-ing that each basket is composed of themes of items randomly sampled from a theme dictionary, the theme dictionary model provides a general framework to achieve efficient association pattern discovery with statistical inference. This paper extends the original theme dictionary model by allowing more than one category of items in a basket and only presence/absence of items is observed for each basket with all quantitative information missing. The ex-tended models can solve a larger range of practical problems that cannot be handled by the original theme dictionary model. Both simulation studies and real data applications confirm the superiority of the proposed methods over the existing ones.

关键词： Association rule mining theme dictionary model cross-category association patterns missing data problem Monte Carlo expectation-maximization algorithm

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Combining Forecasts with missing data: Making Use of Portfolio Theory

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COMPUTATIONAL ECONOMICS 2014年第2期44卷 127-152页

作者： Fastrich, Bjoern Winker, Peter Univ Giessen Inst Stat & Econometr D-35394 Giessen Germany

In this work we propose the construction of optimized forecast-portfolios where analysts are thought of as "assets" with specific characteristics that may be combined in portfolios. The analysts' forecasts were made about the German stock market index DAX on a 6-month horizon as provided by the ZEW Financial Market Survey. A Differential Evolution algorithm is applied that is flexible enough to work with the holey structure of the survey dataset, as it allows for the introduction of a weights-shifting scheme that prevents the exclusion of analysts with missing data and the resulting loss of information. The method is implemented for each of three objective functions that translate ideas from financial management into the forecast-portfolio framework: the mean-variance, the Value-at-Risk, and an asymmetric target strategy. With a backtest we show that weighting several individual forecasts with a forecast-portfolio can indeed improve the forecast quality.

关键词： Analysts' forecasts Stochastic search heuristic missing data problem Portfolio selection

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Do campaign web sites really matter in electoral civic engagement? Empirical evidence from the 2004 post-election Internet tracking survey

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SOCIAL SCIENCE COMPUTER REVIEW 2008年第2期26卷 190-212页

作者： Park, Hun Myoung Perry, James L. Indiana Univ UITS Ctr Stat & Math Comp Indianapolis IN 46204 USA Indiana Univ Sch Publ & Environm Affairs Bloomington IN 47405 USA

This study explores the impact of campaign web sites on electoral civic engagement by examining 2004 Internet Tracking Survey data. Propensity score matching and the recursive bivariate probit model are employed to deal with endogeneity and the missing data problem, which are often ignored in existing literature. Findings show that effects of campaign web sites vary across individual engagements and generally support reinforcement theory rather than mobilization theory.

关键词： electoral civic engagement campaign web sites deliberative engagement endogeneity missing data problem propensity score matching

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Improvements and extensions of the item count technique

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ELECTRONIC JOURNAL OF STATISTICS 2014年第2期8卷 2321-2351页

作者： Groenitz, Heiko Univ Marburg Dept Stat Fac 02 D-35032 Marburg Germany

The item count technique (ICT) is a helpful tool to conduct surveys on sensitive characteristics such as tax evasion, corruption, insurance fraud, social fraud or drug consumption. The ICT yields cooperation of the respondents by protecting their privacy. There have been several interesting developments on the ICT in recent years. However, some approaches are incomplete while some research questions can not be tackled by the ICT so far. For these reasons, we broaden the existing literature in two main directions. First, we generalize the single sample count (SSC) technique, which is a simplified version of the original ICT, and derive an admissible estimate for the proportion of persons bearing a stigmatizing attribute, bootstrap variance estimates and bootstrap confidence intervals. Moreover, we present both a Bayesian and a covariate extension of the generalized SSC technique. The Bayesian set up allows the incorporation of prior information (e.g., available front a previous study) into the estimation and thus can lead to more efficient estimates. Our covariate extension is useful to conduct regression analysis, i.e., to estimate the effects of explanatory variables on the sensitive characteristic. Second, we establish a new ICT that is applicable to multicategorical sensitive variables such as the number of times a respondent has evaded taxes or the amount of money earned by undeclared work (recorded in classes). The estimation of the distribution of such attributes was not at all treated in the literature on the ICT so far. Therefore, we derive estimates for the marginal distribution of the sensitive characteristic, Bayesian estimates and regression estimates corresponding to our multicategorical ICT.

关键词： Sensitive question socially desired answer randomized response missing data problem Bayesian inference logistic regression

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Artificial seed aging reveals the invisible fraction: Implications for evolution experiments using the resurrection approach

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EVOLUTIONARY ECOLOGY 2019年第6期33卷 811-824页

作者： Franks, Steven J. Sekor, Michael R. Davey, Samuel Weis, Arthur E. Fordham Univ Dept Biol Sci Bronx NY 10458 USA Univ Toronto Dept Ecol & Evolutionary Biol Toronto ON M5S 3B2 Canada Univ Toronto Koffler Sci Reserve Jokers Hill Toronto ON M5S 3B2 Canada

Non-random mortality is a key driver of evolution, but mortality that occurs early in life leaves adult traits of individuals that died unknown. This can lead to the invisible fraction problem, which causes difficulty in measuring selection and evolution in natural and experimental populations. Furthermore, seeds or other propagules that are stored intentionally or that persist in dormant states in nature can experience storage conditions that alter adult traits. Invisible fraction and storage condition effects can cause bias in evolutionary studies such as those using the resurrection approach of comparing ancestors and descendants in common environments. To investigate invisible fraction and storage condition effects, we subjected seeds of Brassica rapa Fast Plants to artificial aging under hot, humid conditions. We grew plants from artificially aged seeds alongside unaged control seeds for two generations and measured morphological and phenological traits on adult plants. We found that the plants from artificially aged seeds flowered later than those from unaged seeds in both the first and second generation, indicating storage condition and invisible fraction biases. However, the difference in flowering time was smaller in the second generation, indicating that the refresher generation decreased the storage condition effect. We also found that seeds that survived artificial aging were smaller than seeds that did not survive, indicating a potential physical basis for non-random mortality in storage. These results suggest that invisible fraction and storage condition effects can bias the results of resurrection experiments, and that the proper storage of seeds for use in resurrection experiments, as well as a refresher generation, are critical for valid results. The results also demonstrate that artificial aging can be used as a tool for studying mortality of propagules in nature, such as in soil seed banks, thus providing insight into evolutionary processes that w

关键词： Adaptation Brassica rapa Climate change Contemporary evolution missing data problem Phenology Seed storage

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