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  Subjects -> STATISTICS (Total: 130 journals)
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Advances in Data Analysis and Classification
Journal Prestige (SJR): 1.09
Citation Impact (citeScore): 1
Number of Followers: 52  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1862-5355 - ISSN (Online) 1862-5347
Published by Springer-Verlag Homepage  [2467 journals]
  • Robust instance-dependent cost-sensitive classification

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      Abstract: Abstract Instance-dependent cost-sensitive (IDCS) learning methods have proven useful for binary classification tasks where individual instances are associated with variable misclassification costs. However, we demonstrate in this paper by means of a series of experiments that IDCS methods are sensitive to noise and outliers in relation to instance-dependent misclassification costs and their performance strongly depends on the cost distribution of the data sample. Therefore, we propose a generic three-step framework to make IDCS methods more robust: (i) detect outliers automatically, (ii) correct outlying cost information in a data-driven way, and (iii) construct an IDCS learning method using the adjusted cost information. We apply this framework to cslogit, a logistic regression-based IDCS method, to obtain its robust version, which we name r-cslogit. The robustness of this approach is introduced in steps (i) and (ii), where we make use of robust estimators to detect and impute outlying costs of individual instances. The newly proposed r-cslogit method is tested on synthetic and semi-synthetic data and proven to be superior in terms of savings compared to its non-robust counterpart for variable levels of noise and outliers. All our code is made available online at https://github.com/SimonDeVos/Robust-IDCS.
      PubDate: 2023-01-07
       
  • Flexible mixture regression with the generalized hyperbolic distribution

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      Abstract: Abstract When modeling the functional relationship between a response variable and covariates via linear regression, multiple relationships may be present depending on the underlying component structure. Deploying a flexible mixture distribution can help with capturing a wide variety of such structures, thereby successfully modeling the response–covariate relationship while addressing the components. In that spirit, a mixture regression model based on the finite mixture of generalized hyperbolic distributions is introduced, and its parameter estimation method is presented. The flexibility of the generalized hyperbolic distribution can identify better-fitting components, which can lead to a more meaningful functional relationship between the response variable and the covariates. In addition, we introduce an iterative component combining procedure to aid the interpretability of the model. The results from simulated and real data analyses indicate that our method offers a distinctive edge over some of the existing methods, and that it can generate useful insights on the data set at hand for further investigation.
      PubDate: 2023-01-04
       
  • Sparse correspondence analysis for large contingency tables

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      Abstract: Abstract We propose sparse variants of correspondence analysis (CA) for large contingency tables like documents-terms matrices used in text mining. By seeking to obtain many zero coefficients, sparse CA remedies to the difficulty of interpreting CA results when the size of the table is large. Since CA is a double weighted PCA (for rows and columns) or a weighted generalized SVD, we adapt known sparse versions of these methods with specific developments to obtain orthogonal solutions and to tune the sparseness parameters. We distinguish two cases depending on whether sparseness is asked for both rows and columns, or only for one set.
      PubDate: 2023-01-02
       
  • Proximal methods for sparse optimal scoring and discriminant analysis

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      Abstract: Abstract Linear discriminant analysis (LDA) is a classical method for dimensionality reduction, where discriminant vectors are sought to project data to a lower dimensional space for optimal separability of classes. Several recent papers have outlined strategies, based on exploiting sparsity of the discriminant vectors, for performing LDA in the high-dimensional setting where the number of features exceeds the number of observations in the data. However, many of these proposed methods lack scalable methods for solution of the underlying optimization problems. We consider an optimization scheme for solving the sparse optimal scoring formulation of LDA based on block coordinate descent. Each iteration of this algorithm requires an update of a scoring vector, which admits an analytic formula, and an update of the corresponding discriminant vector, which requires solution of a convex subproblem; we will propose several variants of this algorithm where the proximal gradient method or the alternating direction method of multipliers is used to solve this subproblem. We show that the per-iteration cost of these methods scales linearly in the dimension of the data provided restricted regularization terms are employed, and cubically in the dimension of the data in the worst case. Furthermore, we establish that when this block coordinate descent framework generates convergent subsequences of iterates, then these subsequences converge to the stationary points of the sparse optimal scoring problem. We demonstrate the effectiveness of our new methods with empirical results for classification of Gaussian data and data sets drawn from benchmarking repositories, including time-series and multispectral X-ray data, and provide Matlab and R implementations of our optimization schemes.
      PubDate: 2022-12-21
       
  • LASSO regularization within the LocalGLMnet architecture

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      Abstract: Abstract Deep learning models have been very successful in the application of machine learning methods, often out-performing classical statistical models such as linear regression models or generalized linear models. On the other hand, deep learning models are often criticized for not being explainable nor allowing for variable selection. There are two different ways of dealing with this problem, either we use post-hoc model interpretability methods or we design specific deep learning architectures that allow for an easier interpretation and explanation. This paper builds on our previous work on the LocalGLMnet architecture that gives an interpretable deep learning architecture. In the present paper, we show how group LASSO regularization (and other regularization schemes) can be implemented within the LocalGLMnet architecture so that we receive feature sparsity for variable selection. We benchmark our approach with the recently developed LassoNet of Lemhadri et al. ( LassoNet: a neural network with feature sparsity. J Mach Learn Res 22:1–29, 2021).
      PubDate: 2022-12-13
       
  • Correction to: Robust optimal classification trees under noisy labels

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      PubDate: 2022-12-01
      DOI: 10.1007/s11634-021-00477-0
       
  • Correction to: Principal component analysis constrained by layered simple
           structures

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      Abstract: A Correction to this paper has been published: 10.1007/s11634-022-00503-9
      PubDate: 2022-12-01
      DOI: 10.1007/s11634-022-00506-6
       
  • Correction to: Multivariate cluster weighted models using skewed
           distributions

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      Abstract: Abstract In the original publication of the article, the line after equation (5) has been published incorrectly
      PubDate: 2022-12-01
      DOI: 10.1007/s11634-021-00487-y
       
  • Polynomial approximate discretization of geometric centers in
           high-dimensional Euclidean space

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      Abstract: Abstract Many geometric optimization problems can be reduced to choosing points in space (centers) minimizing some objective function which continuously depends on the distances from the chosen centers to given input points. We prove that, for any fixed \(\varepsilon >0\) , every finite set of points in any-dimensional real space admits a polynomial-size set of candidate centers which can be computed in polynomial time and which contains a \((1+\varepsilon )\) -approximation of each point of space with respect to the Euclidean distances to all the given points. It provides a universal approximation-preserving reduction of any geometric center-based problems whose objective function satisfies a natural continuity-type condition to their discrete versions where the desired centers are selected from a polynomial-size set of candidates. The obtained polynomial upper bound for the size of a universal centers set is supplemented by a theoretical lower bound for this size in the worst case.
      PubDate: 2022-12-01
      DOI: 10.1007/s11634-021-00481-4
       
  • Independence versus indetermination: basis of two canonical clustering
           criteria

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      Abstract: Abstract This paper aims at comparing two coupling approaches as basic layers for building clustering criteria, suited for modularizing and clustering very large networks. We briefly use “optimal transport theory” as a starting point, and a way as well, to derive two canonical couplings: “statistical independence” and “logical indetermination”. A symmetric list of properties is provided and notably the so called “Monge’s properties”, applied to contingency matrices, and justifying the \(\otimes \) versus \(\oplus \) notation. A study is proposed, highlighting “logical indetermination”, because it is, by far, lesser known. Eventually we estimate the average difference between both couplings as the key explanation of their usually close results in network clustering.
      PubDate: 2022-12-01
      DOI: 10.1007/s11634-021-00484-1
       
  • Least-squares bilinear clustering of three-way data

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      Abstract: Abstract A least-squares bilinear clustering framework for modelling three-way data, where each observation consists of an ordinary two-way matrix, is introduced. The method combines bilinear decompositions of the two-way matrices with clustering over observations. Different clusterings are defined for each part of the bilinear decomposition, which decomposes the matrix-valued observations into overall means, row margins, column margins and row–column interactions. Therefore up to four different classifications are defined jointly, one for each type of effect. The computational burden is greatly reduced by the orthogonality of the bilinear model, such that the joint clustering problem reduces to separate problems which can be handled independently. Three of these sub-problems are specific cases of k-means clustering; a special algorithm is formulated for the row–column interactions, which are displayed in clusterwise biplots. The method is illustrated via an empirical example and interpreting the interaction biplots are discussed. Supplemental materials for this paper are available online, which includes the dedicated R package, lsbclust.
      PubDate: 2022-12-01
      DOI: 10.1007/s11634-021-00475-2
       
  • A comparison of two dissimilarity functions for mixed-type predictor
           variables in the $$\delta $$ -machine

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      Abstract: Abstract The \(\delta \) -machine is a statistical learning tool for classification based on dissimilarities or distances between profiles of the observations to profiles of a representation set, which was proposed by Yuan et al. (J Claasif 36(3): 442–470, 2019). So far, the \(\delta \) -machine was restricted to continuous predictor variables only. In this article, we extend the \(\delta \) -machine to handle continuous, ordinal, nominal, and binary predictor variables. We utilized a tailored dissimilarity function for mixed type variables which was defined by Gower. This measure has properties of a Manhattan distance. We develop, in a similar vein, a Euclidean dissimilarity function for mixed type variables. In simulation studies we compare the performance of the two dissimilarity functions and we compare the predictive performance of the \(\delta \) -machine to logistic regression models. We generated data according to two population distributions where the type of predictor variables, the distribution of categorical variables, and the number of predictor variables was varied. The performance of the \(\delta \) -machine using the two dissimilarity functions and different types of representation set was investigated. The simulation studies showed that the adjusted Euclidean dissimilarity function performed better than the adjusted Gower dissimilarity function; that the \(\delta \) -machine outperformed logistic regression; and that for constructing the representation set, K-medoids clustering achieved fewer active exemplars than the one using K-means clustering while maintaining the accuracy. We also applied the \(\delta \) -machine to an empirical example, discussed its interpretation in detail, and compared the classification performance with five other classification methods. The results showed that the \(\delta \) -machine has a good balance between accuracy and interpretability.
      PubDate: 2022-12-01
      DOI: 10.1007/s11634-021-00463-6
       
  • Sparse dimension reduction based on energy and ball statistics

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      Abstract: Abstract Two new methods for sparse dimension reduction are introduced, based on martingale difference divergence and ball covariance, respectively. These methods can be utilized straightforwardly as sufficient dimension reduction (SDR) techniques to estimate a sufficient dimension reduced subspace, which contains all information sufficient to explain a dependent variable. Moreover, owing to their sparsity, they intrinsically perform sufficient variable selection (SVS) and present two attractive new approaches to variable selection in a context of nonlinear dependencies that require few model assumptions. The two new methods are compared to a similar existing approach for SDR and SVS based on distance covariance, as well as to classical and robust sparse partial least squares. A simulation study shows that each of the new estimators can achieve correct variable selection in highly nonlinear contexts, yet are sensitive to outliers and computationally intensive. The study sheds light on the subtle differences between the methods. Two examples illustrate how they can be applied in practice, with a slight preference for the option based on martingale difference divergence in a bioinformatics example.
      PubDate: 2022-12-01
      DOI: 10.1007/s11634-021-00470-7
       
  • Quantile composite-based path modeling: algorithms, properties and
           applications

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      Abstract: Abstract Composite-based path modeling aims to study the relationships among a set of constructs, that is a representation of theoretical concepts. Such constructs are operationalized as composites (i.e. linear combinations of observed or manifest variables). The traditional partial least squares approach to composite-based path modeling focuses on the conditional means of the response distributions, being based on ordinary least squares regressions. Several are the cases where limiting to the mean could not reveal interesting effects at other locations of the outcome variables. Among these: when response variables are highly skewed, distributions have heavy tails and the analysis is concerned also about the tail part, heteroscedastic variances of the errors is present, distributions are characterized by outliers and other extreme data. In such cases, the quantile approach to path modeling is a valuable tool to complement the traditional approach, analyzing the entire distribution of outcome variables. Previous research has already shown the benefits of Quantile Composite-based Path Modeling but the methodological properties of the method have never been investigated. This paper offers a complete description of Quantile Composite-based Path Modeling, illustrating in details the method, the algorithms, the partial optimization criteria along with the machinery for validating and assessing the models. The asymptotic properties of the method are investigated through a simulation study. Moreover, an application on chronic kidney disease in diabetic patients is used to provide guidelines for the interpretation of results and to show the potentialities of the method to detect heterogeneity in the variable relationships.
      PubDate: 2022-12-01
      DOI: 10.1007/s11634-021-00469-0
       
  • The minimum weighted covariance determinant estimator for high-dimensional
           data

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      Abstract: Abstract In a variety of diverse applications, it is very desirable to perform a robust analysis of high-dimensional measurements without being harmed by the presence of a possibly larger percentage of outlying measurements. The minimum weighted covariance determinant (MWCD) estimator, based on implicit weights assigned to individual observations, represents a promising and flexible extension of the popular minimum covariance determinant (MCD) estimator of the expectation and scatter matrix of mlutivariate data. In this work, a regularized version of the MWCD denoted as the minimum regularized weighted covariance determinant (MRWCD) estimator is proposed. At the same time, it is accompanied by an outlier detection procedure. The novel MRWCD estimator is able to outperform other available robust estimators in several simulation scenarios, especially in estimating the scatter matrix of contaminated high-dimensional data.
      PubDate: 2022-12-01
      DOI: 10.1007/s11634-021-00471-6
       
  • Is there a role for statistics in artificial intelligence'

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      Abstract: Abstract The research on and application of artificial intelligence (AI) has triggered a comprehensive scientific, economic, social and political discussion. Here we argue that statistics, as an interdisciplinary scientific field, plays a substantial role both for the theoretical and practical understanding of AI and for its future development. Statistics might even be considered a core element of AI. With its specialist knowledge of data evaluation, starting with the precise formulation of the research question and passing through a study design stage on to analysis and interpretation of the results, statistics is a natural partner for other disciplines in teaching, research and practice. This paper aims at highlighting the relevance of statistical methodology in the context of AI development. In particular, we discuss contributions of statistics to the field of artificial intelligence concerning methodological development, planning and design of studies, assessment of data quality and data collection, differentiation of causality and associations and assessment of uncertainty in results. Moreover, the paper also discusses the equally necessary and meaningful extensions of curricula in schools and universities to integrate statistical aspects into AI teaching.
      PubDate: 2022-12-01
      DOI: 10.1007/s11634-021-00455-6
       
  • SUBiNN: a stacked uni- and bivariate kNN sparse ensemble

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      Abstract: Abstract Nearest Neighbor classification is an intuitive distance-based classification method. It has, however, two drawbacks: (1) it is sensitive to the number of features, and (2) it does not give information about the importance of single features or pairs of features. In stacking, a set of base-learners is combined in one overall ensemble classifier by means of a meta-learner. In this manuscript we combine univariate and bivariate nearest neighbor classifiers that are by itself easily interpretable. Furthermore, we combine these classifiers by a Lasso method that results in a sparse ensemble of nonlinear main and pairwise interaction effects. We christened the new method SUBiNN: Stacked Uni- and Bivariate Nearest Neighbors. SUBiNN overcomes the two drawbacks of simple nearest neighbor methods. In extensive simulations and using benchmark data sets, we evaluate the predictive performance of SUBiNN and compare it to other nearest neighbor ensemble methods as well as Random Forests and Support Vector Machines. Results indicate that SUBiNN often outperforms other nearest neighbor methods, that SUBiNN is well capable of identifying noise features, but that Random Forests is often, but not always, the best classifier.
      PubDate: 2022-12-01
      DOI: 10.1007/s11634-021-00462-7
       
  • A power-controlled reliability assessment for multi-class probabilistic
           classifiers

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      Abstract: Abstract In multi-class classification, the output of a probabilistic classifier is a probability distribution of the classes. In this work, we focus on a statistical assessment of the reliability of probabilistic classifiers for multi-class problems. Our approach generates a Pearson \(\chi ^2\) statistic based on the k-nearest-neighbors in the prediction space. Further, we develop a Bayesian approach for estimating the expected power of the reliability test that can be used for an appropriate sample size k. We propose a sampling algorithm and demonstrate that this algorithm obtains a valid prior distribution. The effectiveness of the proposed reliability test and expected power is evaluated through a simulation study. We also provide illustrative examples of the proposed methods with practical applications.
      PubDate: 2022-11-17
      DOI: 10.1007/s11634-022-00528-0
       
  • A dual subspace parsimonious mixture of matrix normal distributions

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      Abstract: Abstract We present a parsimonious dual-subspace clustering approach for a mixture of matrix-normal distributions. By assuming certain principal components of the row and column covariance matrices are equally important, we express the model in fewer parameters without sacrificing discriminatory information. We derive update rules for an ECM algorithm and set forth necessary conditions to ensure identifiability. We use simulation to demonstrate parameter recovery, and we illustrate the parsimony and competitive performance of the model through two data analyses.
      PubDate: 2022-11-16
      DOI: 10.1007/s11634-022-00526-2
       
  • Editorial for ADAC issue 4 of volume 16 (2022)

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      PubDate: 2022-10-31
      DOI: 10.1007/s11634-022-00525-3
       
 
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