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133
The control of the false discovery rate in multiple testing under dependency
 Annals of Statistics
, 2001
"... Benjamini and Hochberg suggest that the false discovery rate may be the appropriate error rate to control in many applied multiple testing problems. A simple procedure was given there as an FDR controlling procedure for independent test statistics and was shown to be much more powerful than comparab ..."
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Cited by 469 (8 self)
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Benjamini and Hochberg suggest that the false discovery rate may be the appropriate error rate to control in many applied multiple testing problems. A simple procedure was given there as an FDR controlling procedure for independent test statistics and was shown to be much more powerful than comparable procedures which control the traditional familywise error rate. We prove that this same procedure also controls the false discovery rate when the test statistics have positive regression dependency on each of the test statistics corresponding to the true null hypotheses. This condition for positive dependency is general enough to cover many problems of practical interest, including the comparisons of many treatments with a single control, multivariate normal test statistics with positive correlation matrix and multivariate t. Furthermore, the test statistics may be discrete, and the tested hypotheses composite without posing special difficulties. For all other forms of dependency, a simple conservative modification of the procedure controls the false discovery rate. Thus the range of problems for which
Nonparametric Permutation Tests for Functional Neuroimaging: A Primer with Examples. Human Brain Mapping
, 2001
"... The statistical analyses of functional mapping experiments usually proceeds at the voxel level, involving the formation and assessment of a statistic image: at each voxel a statistic indicating evidence of the experimental effect of interest, at that voxel, is computed, giving an image of statistics ..."
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Cited by 145 (6 self)
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The statistical analyses of functional mapping experiments usually proceeds at the voxel level, involving the formation and assessment of a statistic image: at each voxel a statistic indicating evidence of the experimental effect of interest, at that voxel, is computed, giving an image of statistics, a statistic
An enhanced representation of time series which allows fast and accurate classification, clustering and relevance feedback
 In proceedings of the 4th Int'l Conference on Knowledge Discovery and Data Mining
"... We introduce an extended representation of time series that allows fast, accurate classification and clustering in addition to the ability to explore time series data in a relevance feedback framework. The representation consists of piecewise linear segments to represent shape and a weight vector th ..."
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Cited by 130 (24 self)
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We introduce an extended representation of time series that allows fast, accurate classification and clustering in addition to the ability to explore time series data in a relevance feedback framework. The representation consists of piecewise linear segments to represent shape and a weight vector that contains the relative importance of each individual linear segment. In the classification context, the weights are learned automatically as part of the training cycle. In the relevance feedback context, the weights are determined by an interactive and iterative process in which users rate various choices presented to them. Our representation allows a user to define a variety of similarity measures that can be tailored to specific domains. We demonstrate our approach on space telemetry, medical and synthetic data.
The sample average approximation method for stochastic discrete optimization
 SIAM Journal on Optimization
, 2001
"... Abstract. In this paper we study a Monte Carlo simulation based approach to stochastic discrete optimization problems. The basic idea of such methods is that a random sample is generated and consequently the expected value function is approximated by the corresponding sample average function. The ob ..."
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Cited by 127 (16 self)
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Abstract. In this paper we study a Monte Carlo simulation based approach to stochastic discrete optimization problems. The basic idea of such methods is that a random sample is generated and consequently the expected value function is approximated by the corresponding sample average function. The obtained sample average optimization problem is solved, and the procedure is repeated several times until a stopping criterion is satisfied. We discuss convergence rates and stopping rules of this procedure and present a numerical example of the stochastic knapsack problem. Key words. Stochastic programming, discrete optimization, Monte Carlo sampling, Law of Large Numbers, Large Deviations theory, sample average approximation, stopping rules, stochastic knapsack problem AMS subject classifications. 90C10, 90C15
Detecting group differences: Mining contrast sets
 Data Mining and Knowledge Discovery
, 2001
"... A fundamental task in data analysis is understanding the differences between several contrasting groups. These groups can represent different classes of objects, such as male or female students, or the same group over time, e.g. freshman students in 1993 through 1998. We present the problem of mini ..."
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Cited by 78 (3 self)
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A fundamental task in data analysis is understanding the differences between several contrasting groups. These groups can represent different classes of objects, such as male or female students, or the same group over time, e.g. freshman students in 1993 through 1998. We present the problem of mining contrast sets: conjunctions of attributes and values that differ meaningfully in their distribution across groups. We provide a search algorithm for mining contrast sets with pruning rules that drastically reduce the computational complexity. Once the contrast sets are found, we postprocess the results to present a subset that are surprising to the user given what we have already shown. We explicitly control the probability of Type I error (false positives) and guarantee a maximum error rate for the entire analysis by using Bonferroni corrections.
A linear nongaussian acyclic model for causal discovery
 J. Machine Learning Research
, 2006
"... In recent years, several methods have been proposed for the discovery of causal structure from nonexperimental data. Such methods make various assumptions on the data generating process to facilitate its identification from purely observational data. Continuing this line of research, we show how to ..."
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Cited by 54 (23 self)
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In recent years, several methods have been proposed for the discovery of causal structure from nonexperimental data. Such methods make various assumptions on the data generating process to facilitate its identification from purely observational data. Continuing this line of research, we show how to discover the complete causal structure of continuousvalued data, under the assumptions that (a) the data generating process is linear, (b) there are no unobserved confounders, and (c) disturbance variables have nonGaussian distributions of nonzero variances. The solution relies on the use of the statistical method known as independent component analysis, and does not require any prespecified timeordering of the variables. We provide a complete Matlab package for performing this LiNGAM analysis (short for Linear NonGaussian Acyclic Model), and demonstrate the effectiveness of the method using artificially generated data and realworld data.
A Fully Sequential Procedure for IndifferenceZone Selection in Simulation
 ACM TOMACS
, 1999
"... We present procedures for selecting the best or nearbest of a finite number of simulated systems when best is defined by maximum or minimum expected performance. The procedures are appropriate when it is possible to repeatedly obtain small, incremental samples from each simulated system. The goal o ..."
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Cited by 46 (11 self)
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We present procedures for selecting the best or nearbest of a finite number of simulated systems when best is defined by maximum or minimum expected performance. The procedures are appropriate when it is possible to repeatedly obtain small, incremental samples from each simulated system. The goal of such a sequential procedure is to eliminate, at an early stage of experimentation, those simulated systems that are clearly inferior, and thereby reduce the overall computational effort required to find the best. The procedures we present accommodate unequal variances across systems and the use of common random numbers. However, they are based on the assumption of normally distributed data, so we analyze the impact of batching (to achieve approximate normality or independence) on the performance of the procedures. Comparisons with existing procedures are also provided.
Simple Procedures for Selecting the Best Simulated System when the Number of Alternatives Is Large
 Operations Research
, 1999
"... In this paper we address the problem of finding the simulated system with the best (maximum or minimum) expected performance when the number of alternatives is finite, but large enough that rankingandselection (R&S) procedures may require too much computation to be practical. Our approach is to ..."
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Cited by 44 (9 self)
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In this paper we address the problem of finding the simulated system with the best (maximum or minimum) expected performance when the number of alternatives is finite, but large enough that rankingandselection (R&S) procedures may require too much computation to be practical. Our approach is to use the data provided by the first stage of sampling in an R&S procedure to screen out alternatives that are not competitive and thereby avoid the (typically much larger) secondstage sample for these systems. Our procedures represent a compromise between standard R&S proceduresthat are easy to implement, but can be computationally inefficientand fully sequential proceduresthat can be statistically efficient, but are more difficult to implement and depend on more restrictive assumptions. We present a general theory for constructing combined screening and indifferencezone selection procedures, several specific procedures and a portion of an extensive empirical evaluation. ...
Discovering Predictive Association Rules
 In Proc. of the 4th Int'l Conference on Knowledge Discovery in Databases and Data Mining
, 1998
"... Association rule algorithms can produce a very large number of output patterns. This has raised questions of whether the set of discovered rules "overfit" the data because all the patterns that satisfy some constraints are generated (the Bonferroni effect). In other words, the question is whether so ..."
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Cited by 40 (0 self)
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Association rule algorithms can produce a very large number of output patterns. This has raised questions of whether the set of discovered rules "overfit" the data because all the patterns that satisfy some constraints are generated (the Bonferroni effect). In other words, the question is whether some of the rules are "false discoveries" that are not statistically significant. We present a novel approach for estimating the number of "false discoveries" at any cutoff level. Empirical evaluation shows that on typical datasets the fraction of rules that may be false discoveries is very small. A bonus of this work is that the statistical significance measures we compute are a good basis for ordering the rules for presentation to users, since they correspond to the statistical "surprise" of the rule. We also show how to compute confidence intervals for the support and confidence of an association rule, enabling the rule to be used predictively on future data.
Generalizations of the familywise error rate
 Ann. Statist
, 2005
"... Consider the problem of simultaneously testing null hypotheses H1,...,Hs. The usual approach to dealing with the multiplicity problem is to restrict attention to procedures that control the familywise error rate (FWER), the probability of even one false rejection. In many applications, particularly ..."
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Cited by 33 (5 self)
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Consider the problem of simultaneously testing null hypotheses H1,...,Hs. The usual approach to dealing with the multiplicity problem is to restrict attention to procedures that control the familywise error rate (FWER), the probability of even one false rejection. In many applications, particularly if s is large, one might be willing to tolerate more than one false rejection provided the number of such cases is controlled, thereby increasing the ability of the procedure to detect false null hypotheses. This suggests replacing control of the FWER by controlling the probability of k or more false rejections, which we call the kFWER. We derive both singlestep and stepdown procedures that control the kFWER, without making any assumptions concerning the dependence structure of the pvalues of the individual tests. In particular, we derive a stepdown procedure that is quite simple to apply, and prove that it cannot be improved without violation of control of the kFWER. We also consider the false discovery proportion (FDP) defined by the number of false rejections divided by the total number of rejections (defined to be 0 if there are no rejections). The false discovery rate proposed by Benjamini