Ruben Zamar

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Papers by Ruben Zamar

RSKC : An R Package for a Robust and Sparse K-Means Clustering Algorithm

Journal of Statistical Software, 2016

Globally robust inference for the location and simple linear regression models

Journal of Statistical Planning and Inference, Feb 1, 2004

We define globally robust confidence intervals and p-values for the location and simple linear re... more We define globally robust confidence intervals and p-values for the location and simple linear regression models. The need for robust inference has been noticed and partially addressed in the statistical literature (see for example the book by Barnett and Lewis, Outliers in Statistical Data, Wiley, New York, 1994 and references therein). We construct intervals that are stable in the sense

An Iterative Non-parametric Clustering Algorithm Based on Local Shrinking

In this paper, we propose a new non-parametric clustering method based on local shrinking. Each d... more In this paper, we propose a new non-parametric clustering method based on local shrinking. Each data point is transformed in such a way that it moves a specific distance toward a cluster center. The direction and the associated size of each movement are determined by the median of its K-nearest neighbors. This process is repeated until a pre-defined convergence criterion is satisfied. The optimal value of the K is decided by optimizing index functions that measure the strengths of clusters. The number of clusters and the final partition are determined automatically without any input parameter except the stopping rule for convergence. Our performance studies have shown that this algorithm converges fast and achieves high accuracy.

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Bias Robust Estimation of Scale

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High Breakdown-Point Estimates of Regression by Means of the Minimization of an Efficient Scale

A new class of robust estimates, τ estimates, is introduced. The estimates have simultaneously th... more

Robust nonparametic inference for the median

Annals of Statistics, 2004

Ensembling Classification Models Based on Phalanxes of Variables with Applications in Drug Discovery

Statistical detection of a rare class of objects in a two-class classification problem can pose s... more Statistical detection of a rare class of objects in a two-class classification problem can pose several challenges. Because the class of interest is rare in the training data, there is relatively little information in the known class response labels for model building. At the same time the available explanatory variables are often moderately high dimensional. In the four assays of our drug-discovery application, compounds are active or not against a specific biological target, such as lung cancer tumor cells, and active compounds are rare. Several sets of chemical descriptor variables from computational chemistry are available to classify the active versus inactive class; each can have up to thousands of variables characterizing molecular structure of the compounds. The statistical challenge is to make use of the richness of the explanatory variables in the presence of scant response information. Our algorithm divides the explanatory variables into subsets adaptively and passes each subset to a base classifier. The various base classifiers are then ensembled to produce one model to rank new objects by their estimated probabilities of belonging to the rare class of interest. The essence of the algorithm is to choose the subsets such that variables in the same group work well together; we call such groups phalanxes.

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Uniform asymptotics for robust location estimates when the scale is unknown

The Annals of Statistics, Aug 1, 2004

Most asymptotic results for robust estimates rely on regularity conditions that are difficult to ... more Most asymptotic results for robust estimates rely on regularity conditions that are difficult to verify in practice. Moreover, these results apply to fixed distribution functions. In the robustness context the distribution of the data remains largely unspecified and hence results that hold uniformly over a set of possible distribution functions are of theoretical and practical interest. Also, it is desirable to be able to determine the size of the set of distribution functions where the uniform properties hold. In this paper we study the problem of obtaining verifiable regularity conditions that suffice to yield uniform consistency and uniform asymptotic normality for location robust estimates when the scale of the errors is unknown. We study M-location estimates calculated with an S-scale and we obtain uniform asymptotic results over contamination neighborhoods. Moreover, we show how to calculate the maximum size of the contamination neighborhoods where these uniform results hold. There is a trade-off between the size of these neighborhoods and the breakdown point of the scale estimate.

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A robust and sparse K-means clustering algorithm

In many situations where the interest lies in identifying clusters one might expect that not all ... more In many situations where the interest lies in identifying clusters one might expect that not all available variables carry information about these groups. Furthermore, data quality (e.g. outliers or missing entries) might present a serious and sometimes hard-to-assess problem for large and complex datasets. In this paper we show that a small proportion of atypical observations might have serious adverse effects on the solutions found by the sparse clustering algorithm of Witten and Tibshirani (2010). We propose a robustification of their sparse K-means algorithm based on the trimmed K-means algorithm of Cuesta-Albertos et al. (1997) Our proposal is also able to handle datasets with missing values. We illustrate the use of our method on microarray data for cancer patients where we are able to identify strong biological clusters with a much reduced number of genes. Our simulation studies show that, when there are outliers in the data, our robust sparse K-means algorithm performs better than other competing methods both in terms of the selection of features and also the identified clusters. This robust sparse K-means algorithm is implemented in the R package RSKC which is publicly available from the CRAN repository.

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The Fast-t Estimator for Regression

J Comput Graph Stat, 2008

A natural framework for sparse hierarchical clustering

ABSTRACT There has been a surge in the number of large and flat data sets - data sets containing ... more ABSTRACT There has been a surge in the number of large and flat data sets - data sets containing a large number of features and a relatively small number of observations - due to the growing ability to collect and store information in medical research and other fi?elds. Hierarchical clustering is a widely used clustering tool. In hierarchical clustering, large and flat data sets may allow for a better coverage of clustering features (features that help explain the true underlying clusters) but, such data sets usually include a large fraction of noise features (non-clustering features) that may hide the underlying clusters. Witten and Tibshirani (2010) proposed a sparse hierarchical clustering framework to cluster the observations using an adaptively chosen subset of the features, however, we show that this framework has some limitations when the data sets contain clustering features with complex structure. In this paper, another sparse hierarchical clustering (SHC) framework is proposed. We show that, using simulation studies and real data examples, the proposed framework produces superior feature selection and clustering performance comparing to the classical (of-the-shelf) hierarchical clustering and the existing sparse hierarchical clustering framework.

CLUES: A non-parametric clustering method based on local shrinking

Computational Statistics Data Analysis, Sep 1, 2007

In this paper, we propose a novel non-parametric clustering method based on non-parametric local ... more In this paper, we propose a novel non-parametric clustering method based on non-parametric local shrinking. Each data point is transformed in such a way that it moves a specific distance toward a cluster center. The direction and the associated size of each movement are determined by the median of its K-nearest neighbors. This process is repeated until a pre-defined convergence criterion is satisfied. The optimal value of the number of neighbors is determined by optimizing some commonly used index functions that measure the strengths of clusters generated by the algorithm. The number of clusters and the final partition are determined automatically without any input parameter except the stopping rule for convergence. Our experiments on simulated and real data sets suggest that that the proposed algorithm achieves relatively high accuracies when compared with classical clustering algorithms.

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A Class of Locally and Globally Robust Regression Estimates

Journal of the American Statistical Association, Mar 1, 1999

... He and Simpson (1993) also showed that E* &amp;amp;amp;amp;lt; 2 for all affine-equivaria... more

clues: An R Package for Nonparametric Clustering Based on Local Shrinking

This introduction to the R package clues is a (slightly) modified version of , published in the J... more

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Robust Estimates of Location and Dispersion for High-Dimensional Datasets

Http Dx Doi Org 10 1198 004017002188618509, 2012

... Let W be a weight function, and defi ne tw and Vw as the weighted mean and covariance matrix,... more

MDQC: a new quality assessment method for microarrays based on quality control reports

Bioinformatics, Oct 12, 2007

The process of producing microarray data involves multiple steps, some of which may suffer from t... more The process of producing microarray data involves multiple steps, some of which may suffer from technical problems and seriously damage the quality of the data. Thus, it is essential to identify those arrays with low quality. This article addresses two questions: (1) how to assess the quality of a microarray dataset using the measures provided in quality control (QC) reports; (2) how to identify possible sources of the quality problems. Results: We propose a novel multivariate approach to evaluate the quality of an array that examines the 'Mahalanobis distance' of its quality attributes from those of other arrays. Thus, we call it Mahalanobis Distance Quality Control (MDQC) and examine different approaches of this method. MDQC flags problematic arrays based on the idea of outlier detection, i.e. it flags those arrays whose quality attributes jointly depart from those of the bulk of the data. Using two case studies, we show that a multivariate analysis gives substantially richer information than analyzing each parameter of the QC report in isolation. Moreover, once the QC report is produced, our quality assessment method is computationally inexpensive and the results can be easily visualized and interpreted. Finally, we show that computing these distances on subsets of the quality measures in the report may increase the method's ability to detect unusual arrays and helps to identify possible reasons of the quality problems.

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www.elsevier.com/locate/csda Linear grouping using orthogonal regression

Bias robustness of three median-based regression estimates

Journal of Statistical Planning and Inference, May 1, 2004

The need for regression estimates with small biases has been highlighted in view of the renewed i... more The need for regression estimates with small biases has been highlighted in view of the renewed interest in robust inference beyond point estimation. Estimates with small biases are essential for stable and informative robust inference (see Outliers in Statistical Data by V. T. Lewis, 1994, p. 74 and Fraiman et al., 2001, Ann. Statist, to appear). In this paper we study the bias performance of three median-based estimates: Brown and Mood (1951) estimate, and Sen (1968) estimate and Siegel's repeated median (1982), which exhibits an outstanding bias performance. We also consider a one-step version of Brown and Mood's estimate. We pay special attention to the maximum asymptotic bias of the intercept parameter which has been mostly ignored in the robustness literature (with exceptions pointed out in the introduction).

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Robust nonparametric inference for the median

Eprint Arxiv Math 0503665, Mar 29, 2005

We consider the problem of constructing robust nonparametric confidence intervals and tests of hy... more We consider the problem of constructing robust nonparametric confidence intervals and tests of hypothesis for the median when the data distribution is unknown and the data may contain a small fraction of contamination. We propose a modification of the sign test (and its associated confidence interval) which attains the nominal significance level (probability coverage) for any distribution in the contamination neighborhood of a continuous distribution. We also define some measures of robustness and efficiency under contamination for confidence intervals and tests. These measures are computed for the proposed procedures.

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Optimally Bounding a Generalized Gross Error Sensitivity of Unbounded Influence M-Estimates of Regression

_ First we show that many robust estimates of regression which depend only on the regression resi... more _ First we show that many robust estimates of regression which depend only on the regression residuals (including M-, S-, Tau-, least median of squares-least trimmed of squares-and some R-estimates) have infinite gross-error-sensitivity. More precisely, we show that the maximumbias function of these estimates, called residual admissible in , is of order f€ near zero. Based on this finding we define a new robustness measure, the generalized contamination sensitivity, which generalizes Hampel's gross-error-sensitivity, and compute this measure for regression M-estimates with a general scale. Then we solve Hampel's problem of minimizing the asymptotic variance subject to a bound on the generalized contamination sensitivity, for estimates in this class. Finally, we find a sharp lower bound for the generalized contamination sensitivity of residual admissible estimates and show that it is achieved by a member of the family of the least a-quantile estimates. In the Gaussian case a = .683.

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