The EM algorithm for graphical association models with missing data

Lauritzen, Steffen

doi:10.1016/0167-9473(93)e0056-a

Cited by 526 publications

(263 citation statements)

References 24 publications

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“…Our analysis revealed that under standard independence assumptions the off-diagonal of the classifiers covariance matrix corresponds to a rank-one matrix, whose eigenvector entries are proportional to the classifiers balanced accuracies. Our work gives a computationally efficient and asymptotically consistent solution to the classical problem posed by Dawid and Skene (15) in 1979, for which to the best of our knowledge only nonconvex iterative likelihood maximization solutions have been proposed (18,(26)(27)(28)(29). Our work not only provides a principled spectral approach for unsupervised ensemble learning (such as our SML), but also raises several interesting questions for future research.…”

Section: Summary and Discussionmentioning

confidence: 99%

Ranking and combining multiple predictors without labeled data

Parisi

Strino

Nadler

et al. 2014

Proc. Natl. Acad. Sci. U.S.A.

106

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In a broad range of classification and decision-making problems, one is given the advice or predictions of several classifiers, of unknown reliability, over multiple questions or queries. This scenario is different from the standard supervised setting, where each classifier's accuracy can be assessed using available labeled data, and raises two questions: Given only the predictions of several classifiers over a large set of unlabeled test data, is it possible to (i) reliably rank them and (ii) construct a metaclassifier more accurate than most classifiers in the ensemble? Here we present a spectral approach to address these questions. First, assuming conditional independence between classifiers, we show that the offdiagonal entries of their covariance matrix correspond to a rank-one matrix. Moreover, the classifiers can be ranked using the leading eigenvector of this covariance matrix, because its entries are proportional to their balanced accuracies. Second, via a linear approximation to the maximum likelihood estimator, we derive the Spectral Meta-Learner (SML), an unsupervised ensemble classifier whose weights are equal to these eigenvector entries. On both simulated and real data, SML typically achieves a higher accuracy than most classifiers in the ensemble and can provide a better starting point than majority voting for estimating the maximum likelihood solution. Furthermore, SML is robust to the presence of small malicious groups of classifiers designed to veer the ensemble prediction away from the (unknown) ground truth.spectral analysis | classifier balanced accuracy | unsupervised learning | cartels | crowdsourcing E very day, multiple decisions are made based on input and suggestions from several sources, either algorithms or advisers, of unknown reliability. Investment companies handle their portfolios by combining reports from several analysts, each providing recommendations on buying, selling, or holding multiple stocks (1, 2). Central banks combine surveys of several professional forecasters to monitor rates of inflation, real gross domestic product growth, and unemployment (3-6). Biologists study the genomic binding locations of proteins by combining or ranking the predictions of several peak detection algorithms applied to large-scale genomics data (7). Physician tumor boards convene a number of experts from different disciplines to discuss patients whose diseases pose diagnostic and therapeutic challenges (8). Peer-review panels discuss multiple grant applications and make recommendations to fund or reject them (9). The examples above describe scenarios in which several human advisers or algorithms provide their predictions or answers to a list of queries or questions. A key challenge is to improve decision making by combining these multiple predictions of unknown reliability. Automating this process of combining multiple predictors is an active field of research in decision science (cci.mit.edu/research), medicine (10), business (refs. 11 and 12 and www.kaggle.com/competitions), and government...

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Section: Summary and Discussionmentioning

confidence: 99%

Ranking and combining multiple predictors without labeled data

Parisi

Strino

Nadler

et al. 2014

Proc. Natl. Acad. Sci. U.S.A.

106

View full text Add to dashboard Cite

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“…The EM algorithm has been adapted to the particular case of Bayesian networks [16]. In BN some nodes X i may represent variables that are missing.…”

Section: Em Algorithm For Bayesian Networkmentioning

confidence: 99%

“…To solve this problem we use the Expectation Maximization (EM) algorithm [15] and more particularly its adaptation to the case of Bayesian networks [16]. Our previously mentioned expert model of the GPON-FTTH network [8] is used as an initialization point for the EM algorithm.…”

Section: Introductionmentioning

confidence: 99%

A tutorial on the EM algorithm for Bayesian networks: Application to self-diagnosis of GPON-FTTH networks

Tembo¹,

Vaton²,

Courant³

et al. 2016

2016 International Wireless Communications and Mobile Computing Conference (IWCMC)

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Abstract-Network behavior modelling is a central issue for model-based approaches of self-diagnosis of telecommunication networks. There are two methods to build such models. The model can be built from expert knowledge acquired from network standards and/or the model can be learnt from data generated by network components by data mining algorithms. In a recent work, we proposed a model of architecture and fault propagation for the GPON-FTTH (Gigabit Passive Optical Network-Fiber To The Home) access network. This model is based on a Bayesian network which encodes expert knowledge. This includes dependencies that encode fault propagation and conditional probability distributions that encode the strength of those dependencies. In this paper we consider the problem of automatically tuning the above mentioned probability distributions. This is a parameter estimation problem under missing data conditions that we solve with the Expectation Maximization (EM) algorithm. Conditional probability distributions are learnt from the tremendous amount of alarms generated by an operating GPON-FTTH network during two months in 2015. Self-diagnosis is carried out to analyze the root cause of alarms. The performance of the diagnosis is evaluated with respect to an expert system based on deterministic decision rules currently used by the Internet Access Provider to diagnose network problems.

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“…For example, the MS-EM (Model Selection -Expectation Maximization) [22], which plays relatively few iterations to find the best network with incomplete data, implements a version of the EM and uses a metric to choose the best Bayesian model. Other methods applying the EM algorithm can be seen in [15,23].…”

Section: Related Workmentioning

confidence: 99%

Evaluating a Nearest-Neighbor Method to Substitute Continuous Missing Values

Hruschka

Ebecken

2003

Lecture Notes in Computer Science

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Abstract. This work proposes and evaluates a Nearest-Neighbor Method to substitute missing values in datasets formed by continuous attributes. In the substitution process, each instance containing missing values is compared with complete instances, and the closest instance is used to assign the attribute missing value. We evaluate this method in simulations performed in four datasets that are usually employed as benchmarks for data mining methods -Iris Plants, Wisconsin Breast Cancer, Pima Indians Diabetes and Wine Recognition. First, we consider the substitution process as a prediction task. In this sense, we employ two metrics (Euclidean and Manhattan) to simulate substitutions both in original and normalized datasets. The obtained results were compared to those provided by a usually employed method to perform this task, i.e. substitution by the mean value. Based on these simulations, we propose a substitution procedure for the well-known K-Means Clustering Algorithm. Then, we perform clustering simulations, comparing the results obtained in the original datasets with the substituted ones. These results indicate that the proposed method is a suitable estimator for substituting missing values, i.e. it preserves the relationships between variables in the clustering process. Therefore, the proposed Nearest-Neighbor Method is an appropriate data preparation tool for the K-Means Clustering Algorithm.

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The EM algorithm for graphical association models with missing data

Cited by 526 publications

References 24 publications

Ranking and combining multiple predictors without labeled data

Ranking and combining multiple predictors without labeled data

A tutorial on the EM algorithm for Bayesian networks: Application to self-diagnosis of GPON-FTTH networks

Evaluating a Nearest-Neighbor Method to Substitute Continuous Missing Values

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