Results 1  10
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65
Missing value estimation methods for DNA microarrays
, 2001
"... Motivation: Gene expression microarray experiments can generate data sets with multiple missing expression values. Unfortunately, many algorithms for gene expression analysis require a complete matrix of gene array values as input. For example, methods such as hierarchical clustering and Kmeans clu ..."
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Cited by 477 (24 self)
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Motivation: Gene expression microarray experiments can generate data sets with multiple missing expression values. Unfortunately, many algorithms for gene expression analysis require a complete matrix of gene array values as input. For example, methods such as hierarchical clustering and Kmeans clustering are not robust to missing data, and may lose effectiveness even with a few missing values. Methods for imputing missing data are needed, therefore, to minimize the effect of incomplete data sets on analyses, and to increase the range of data sets to which these algorithms can be applied. In this report, we investigate automated methods for estimating missing data.
Sliced inverse regression for dimension reduction
 J. AMER. STATIST. ASSOC
, 1991
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A Comparison of Prediction Accuracy, Complexity, and Training Time of Thirtythree Old and New Classification Algorithms
, 2000
"... . Twentytwo decision tree, nine statistical, and two neural network algorithms are compared on thirtytwo datasets in terms of classication accuracy, training time, and (in the case of trees) number of leaves. Classication accuracy is measured by mean error rate and mean rank of error rate. Both cr ..."
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Cited by 234 (8 self)
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. Twentytwo decision tree, nine statistical, and two neural network algorithms are compared on thirtytwo datasets in terms of classication accuracy, training time, and (in the case of trees) number of leaves. Classication accuracy is measured by mean error rate and mean rank of error rate. Both criteria place a statistical, splinebased, algorithm called Polyclass at the top, although it is not statistically signicantly dierent from twenty other algorithms. Another statistical algorithm, logistic regression, is second with respect to the two accuracy criteria. The most accurate decision tree algorithm is Quest with linear splits, which ranks fourth and fth, respectively. Although splinebased statistical algorithms tend to have good accuracy, they also require relatively long training times. Polyclass, for example, is third last in terms of median training time. It often requires hours of training compared to seconds for other algorithms. The Quest and logistic regression algor...
Unbiased recursive partitioning: a conditional inference framework
, 2004
"... Recursive binary partitioning is a popular tool for regression analysis. Two fundamental problems of exhaustive search procedures usually applied to fit such models have been known for a long time: Overfitting and a selection bias towards covariates with many possible splits or missing values. While ..."
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Cited by 165 (12 self)
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Recursive binary partitioning is a popular tool for regression analysis. Two fundamental problems of exhaustive search procedures usually applied to fit such models have been known for a long time: Overfitting and a selection bias towards covariates with many possible splits or missing values. While pruning procedures are able to solve the overfitting problem, the variable selection bias still seriously effects the interpretability of treestructured regression models. For some special cases unbiased procedures have been suggested, however lacking a common theoretical foundation. We propose a unified framework for recursive partitioning which embeds treestructured regression models into a well defined theory of conditional inference procedures. Stopping criteria based on multiple test procedures are implemented and it is shown that the predictive performance of the resulting trees is as good as the performance of established exhaustive search procedures. It turns out that the partitions and therefore the models induced by both approaches are structurally different, indicating the need for an unbiased variable selection. The methodology presented here is applicable to all kinds of regression problems, including nominal, ordinal, numeric, censored as well as multivariate response variables and arbitrary measurement scales of the covariates. Data from studies on animal abundance, glaucoma classification, node positive breast cancer and mammography experience are reanalyzed.
Split Selection Methods for Classification Trees
 STATISTICA SINICA
, 1997
"... Classification trees based on exhaustive search algorithms tend to be biased towards selecting variables that afford more splits. As a result, such trees should be interpreted with caution. This article presents an algorithm called QUEST that has negligible bias. Its split selection strategy shares ..."
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Cited by 130 (10 self)
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Classification trees based on exhaustive search algorithms tend to be biased towards selecting variables that afford more splits. As a result, such trees should be interpreted with caution. This article presents an algorithm called QUEST that has negligible bias. Its split selection strategy shares similarities with the FACT method, but it yields binary splits and the final tree can be selected by a direct stopping rule or by pruning. Real and simulated data are used to compare QUEST with the exhaustive search approach. QUEST is shown to be substantially faster and the size and classification accuracy of its trees are typically comparable to those of exhaustive search.
RainForest  a Framework for Fast Decision Tree Construction of Large Datasets
 In VLDB
, 1998
"... Classification of large datasets is an important data mining problem. Many classification algorithms have been proposed in the literature, but studies have shown that so far no algorithm uniformly outperforms all other algorithms in terms of quality. In this paper, we present a unifying framework fo ..."
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Cited by 120 (8 self)
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Classification of large datasets is an important data mining problem. Many classification algorithms have been proposed in the literature, but studies have shown that so far no algorithm uniformly outperforms all other algorithms in terms of quality. In this paper, we present a unifying framework for decision tree classifiers that separates the scalability aspects of algorithms for constructing a decision tree from the central features that determine the quality of the tree. This generic algorithm is easy to instantiate with specific algorithms from the literature (including C4.5, CART,
Regression Trees With Unbiased Variable Selection and Interaction Detection
 STATISTICA SINICA
, 2002
"... We propose an algorithm for regression tree construction called GUIDE. It is specifically designed to eliminate variable selection bias, a problem that can undermine the reliability of inferences from a tree structure. GUIDE controls bias by employing chisquare analysis of residuals and bootstrap c ..."
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Cited by 86 (15 self)
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We propose an algorithm for regression tree construction called GUIDE. It is specifically designed to eliminate variable selection bias, a problem that can undermine the reliability of inferences from a tree structure. GUIDE controls bias by employing chisquare analysis of residuals and bootstrap calibration of significance probabilities. This approach allows fast computation speed, natural extension to data sets with categorical variables, and direct detection of local twovariable interactions. Previous algorithms are not unbiased and are insensitive to local interactions during split selection. The speed of GUIDE enables two further enhancements—complex modeling at the terminal nodes, such as polynomial or best simple linear models, and bagging. In an experiment with real data sets, the prediction mean square error of the piecewise constant GUIDE model is within ±20 % of that of CART�. Piecewise linear GUIDE models are more accurate; with bagging they can outperform the splinebased MARS � method.
Classification trees with unbiased multiway splits
 Journal of the American Statistical Association
, 2001
"... Two univariate split methods and one linear combination split method are proposed for the construction of classification trees with multiway splits. Examples are given where the trees are more compact and hence easier to interpret than binary trees. A major strength of the univariate split methods i ..."
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Cited by 74 (11 self)
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Two univariate split methods and one linear combination split method are proposed for the construction of classification trees with multiway splits. Examples are given where the trees are more compact and hence easier to interpret than binary trees. A major strength of the univariate split methods is that they have negligible bias in variable selection, both when the variables differ in the number of splits they offer and when they differ in number of missing values. This is an advantage because inferences from the tree structures can be adversely affected by selection bias. The new methods are shown to be highly competitive in terms of computational speed and classification accuracy of future observations. Key words and phrases: Decision tree, linear discriminant analysis, missing value, selection bias. 1
Top–Down Induction of Decision Trees Classifiers–A survey
 Systems, Man, and Cybernetics, Part C: Applications and Reviews, IEEE Transactions on
, 2005
"... Abstract—Decision trees are considered to be one of the most popular approaches for representing classifiers. Researchers from various disciplines such as statistics, machine learning, pattern recognition, and data mining considered the issue of growing a decision tree from available data. This pape ..."
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Cited by 52 (4 self)
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Abstract—Decision trees are considered to be one of the most popular approaches for representing classifiers. Researchers from various disciplines such as statistics, machine learning, pattern recognition, and data mining considered the issue of growing a decision tree from available data. This paper presents an updated survey of current methods for constructing decision tree classifiers in a topdown manner. The paper suggests a unified algorithmic framework for presenting these algorithms and describes the various splitting criteria and pruning methodologies. Index Terms—Classification, decision trees, pruning methods, splitting criteria. I.
Piecewisepolynomial regression trees
 Statistica Sinica
, 1994
"... A nonparametric function 1 estimation method called SUPPORT (“Smoothed and Unsmoothed PiecewisePolynomial Regression Trees”) is described. The estimate is typically made up of several pieces, each piece being obtained by fitting a polynomial regression to the observations in a subregion of the data ..."
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Cited by 51 (8 self)
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A nonparametric function 1 estimation method called SUPPORT (“Smoothed and Unsmoothed PiecewisePolynomial Regression Trees”) is described. The estimate is typically made up of several pieces, each piece being obtained by fitting a polynomial regression to the observations in a subregion of the data space. Partitioning is carried out recursively as in a treestructured method. If the estimate is required to be smooth, the polynomial pieces may be glued together by means of weighted averaging. The smoothed estimate is thus obtained in three steps. In the first step, the regressor space is recursively partitioned until the data in each piece are adequately fitted by a polynomial of a fixed order. Partitioning is guided by analysis of the distributions of residuals and crossvalidation estimates of prediction mean square error. In the second step, the data within a neighborhood of each partition are fitted by a polynomial. The final estimate of the regression function is obtained by averaging the polynomial pieces, using smooth weight functions each of which diminishes rapidly to zero outside its associated partition. Estimates of derivatives of the regression function may be