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18,951
Proof verification and hardness of approximation problems
 IN PROC. 33RD ANN. IEEE SYMP. ON FOUND. OF COMP. SCI
, 1992
"... We show that every language in NP has a probablistic verifier that checks membership proofs for it using logarithmic number of random bits and by examining a constant number of bits in the proof. If a string is in the language, then there exists a proof such that the verifier accepts with probabilit ..."
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Cited by 797 (39 self)
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with probability 1 (i.e., for every choice of its random string). For strings not in the language, the verifier rejects every provided “proof " with probability at least 1/2. Our result builds upon and improves a recent result of Arora and Safra [6] whose verifiers examine a nonconstant number of bits
Fast probabilistic algorithms for verification of polynomial identities
 J. ACM
, 1980
"... ABSTRACT The starthng success of the RabmStrassenSolovay pnmahty algorithm, together with the intriguing foundattonal posstbthty that axtoms of randomness may constttute a useful fundamental source of mathemaucal truth independent of the standard axmmaUc structure of mathemaUcs, suggests a wgorous ..."
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Cited by 520 (1 self)
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wgorous search for probabdisuc algonthms In dlustratmn of this observaUon, vanous fast probabdlsttc algonthms, with probability of correctness guaranteed a prion, are presented for testing polynomial ldentmes and propemes of systems of polynomials. Ancdlary fast algorithms for calculating resultants
Solving multiclass learning problems via errorcorrecting output codes
 JOURNAL OF ARTIFICIAL INTELLIGENCE RESEARCH
, 1995
"... Multiclass learning problems involve nding a de nition for an unknown function f(x) whose range is a discrete set containing k>2values (i.e., k \classes"). The de nition is acquired by studying collections of training examples of the form hx i;f(x i)i. Existing approaches to multiclass l ..."
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Cited by 726 (8 self)
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thatlike the other methodsthe errorcorrecting code technique can provide reliable class probability estimates. Taken together, these results demonstrate that errorcorrecting output codes provide a generalpurpose method for improving the performance of inductive learning programs on multiclass
Divergence measures based on the Shannon entropy
 IEEE Transactions on Information theory
, 1991
"... AbstractA new class of informationtheoretic divergence measures based on the Shannon entropy is introduced. Unlike the wellknown Kullback divergences, the new measures do not require the condition of absolute continuity to be satisfied by the probability distributions involved. More importantly, ..."
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Cited by 666 (0 self)
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, their close relationship with the variational distance and the probability of misclassification error are established in terms of bounds. These bounds are crucial in many applications of divergence measures. The new measures are also well characterized by the properties of nonnegativity, finiteness
Probabilistic Outputs for Support Vector Machines and Comparisons to Regularized Likelihood Methods
 ADVANCES IN LARGE MARGIN CLASSIFIERS
, 1999
"... The output of a classifier should be a calibrated posterior probability to enable postprocessing. Standard SVMs do not provide such probabilities. One method to create probabilities is to directly train a kernel classifier with a logit link function and a regularized maximum likelihood score. Howev ..."
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Cited by 1051 (0 self)
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. However, training with a maximum likelihood score will produce nonsparse kernel machines. Instead, we train an SVM, then train the parameters of an additional sigmoid function to map the SVM outputs into probabilities. This chapter compares classification error rate and likelihood scores for an SVM plus
Bandera: Extracting Finitestate Models from Java Source Code
 IN PROCEEDINGS OF THE 22ND INTERNATIONAL CONFERENCE ON SOFTWARE ENGINEERING
, 2000
"... Finitestate verification techniques, such as model checking, have shown promise as a costeffective means for finding defects in hardware designs. To date, the application of these techniques to software has been hindered by several obstacles. Chief among these is the problem of constructing a fini ..."
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Cited by 654 (33 self)
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finitestate model that approximates the executable behavior of the software system of interest. Current bestpractice involves handconstruction of models which is expensive (prohibitive for all but the smallest systems), prone to errors (which can result in misleading verification results
The model checker SPIN.
 IEEE Trans. on Software Eng.
, 1997
"... AbstractSPIN is an efficient verification system for models of distributed software systems. It has been used to detect design errors in applications ranging from highlevel descriptions of distributed algorithms to detailed code for controlling telephone exchanges. This paper gives an overview of ..."
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Cited by 1516 (26 self)
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AbstractSPIN is an efficient verification system for models of distributed software systems. It has been used to detect design errors in applications ranging from highlevel descriptions of distributed algorithms to detailed code for controlling telephone exchanges. This paper gives an overview
Extended Static Checking for Java
, 2002
"... Software development and maintenance are costly endeavors. The cost can be reduced if more software defects are detected earlier in the development cycle. This paper introduces the Extended Static Checker for Java (ESC/Java), an experimental compiletime program checker that finds common programming ..."
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Cited by 638 (24 self)
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programming errors. The checker is powered by verificationcondition generation and automatic theoremproving techniques. It provides programmers with a simple annotation language with which programmer design decisions can be expressed formally. ESC/Java examines the annotated software and warns
A direct approach to false discovery rates
, 2002
"... Summary. Multiplehypothesis testing involves guarding against much more complicated errors than singlehypothesis testing. Whereas we typically control the type I error rate for a singlehypothesis test, a compound error rate is controlled for multiplehypothesis tests. For example, controlling the ..."
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Cited by 775 (14 self)
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and then estimate its corresponding error rate. This new approach offers increased applicability, accuracy and power. We apply the methodology to both the positive false discovery rate pFDR and FDR, and provide evidence for its benefits. It is shown that pFDR is probably the quantity of interest over FDR. Also
Approximate Statistical Tests for Comparing Supervised Classification Learning Algorithms
, 1998
"... This article reviews five approximate statistical tests for determining whether one learning algorithm outperforms another on a particular learning task. These tests are compared experimentally to determine their probability of incorrectly detecting a difference when no difference exists (type I err ..."
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Cited by 723 (8 self)
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error). Two widely used statistical tests are shown to have high probability of type I error in certain situations and should never be used: a test for the difference of two proportions and a paireddifferences t test based on taking several random traintest splits. A third test, a paired
Results 1  10
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18,951