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12,330
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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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
Probabilistic Algorithms in Robotics
 AI Magazine vol
"... This article describes a methodology for programming robots known as probabilistic robotics. The probabilistic paradigm pays tribute to the inherent uncertainty in robot perception, relying on explicit representations of uncertainty when determining what to do. This article surveys some of the progr ..."
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Cited by 199 (6 self)
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This article describes a methodology for programming robots known as probabilistic robotics. The probabilistic paradigm pays tribute to the inherent uncertainty in robot perception, relying on explicit representations of uncertainty when determining what to do. This article surveys some
Probabilistic Algorithms In Finite Fields
 SIAM J. Comput
, 1979
"... We present probabilistic algorithms for the problems of finding an irreducible polynomial of degree n over a finite field, finding roots of a polynomial, and factoring a polynomial into its irreducible factors over a finite field. All of these problems are of importance in algebraic coding theor ..."
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Cited by 98 (1 self)
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We present probabilistic algorithms for the problems of finding an irreducible polynomial of degree n over a finite field, finding roots of a polynomial, and factoring a polynomial into its irreducible factors over a finite field. All of these problems are of importance in algebraic coding
Formal Verification of Probabilistic Algorithms
, 2002
"... This thesis shows how probabilistic algorithms can be formally verified using a mechanical theorem prover. We begin with an extensive foundational development of probability, creating a higherorder logic formalization of mathematical measure theory. This allows the definition of the probability spac ..."
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Cited by 53 (3 self)
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This thesis shows how probabilistic algorithms can be formally verified using a mechanical theorem prover. We begin with an extensive foundational development of probability, creating a higherorder logic formalization of mathematical measure theory. This allows the definition of the probability
Probabilistic Algorithms for Geometric Elimination
 in Engineering, Communication and Computing
, 1999
"... We develop probabilistic algorithms that solve problems of geometric elimination theory using small memory resources. These algorithms are obtained by means of the adaptation of a general transformation due to A. Borodin which converts uniform boolean circuit depth into sequential (Turing machine) s ..."
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Cited by 11 (4 self)
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We develop probabilistic algorithms that solve problems of geometric elimination theory using small memory resources. These algorithms are obtained by means of the adaptation of a general transformation due to A. Borodin which converts uniform boolean circuit depth into sequential (Turing machine
Probabilistic Principal Component Analysis
 JOURNAL OF THE ROYAL STATISTICAL SOCIETY, SERIES B
, 1999
"... Principal component analysis (PCA) is a ubiquitous technique for data analysis and processing, but one which is not based upon a probability model. In this paper we demonstrate how the principal axes of a set of observed data vectors may be determined through maximumlikelihood estimation of paramet ..."
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Cited by 709 (5 self)
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of parameters in a latent variable model closely related to factor analysis. We consider the properties of the associated likelihood function, giving an EM algorithm for estimating the principal subspace iteratively, and discuss, with illustrative examples, the advantages conveyed by this probabilistic approach
Bisimulation through probabilistic testing
 in â€śConference Record of the 16th ACM Symposium on Principles of Programming Languages (POPL
, 1989
"... We propose a language for testing concurrent processes and examine its strength in terms of the processes that are distinguished by a test. By using probabilistic transition systems as the underlying semantic model, we show how a testing algorithm can distinguish, with a probability arbitrarily clos ..."
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Cited by 529 (14 self)
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We propose a language for testing concurrent processes and examine its strength in terms of the processes that are distinguished by a test. By using probabilistic transition systems as the underlying semantic model, we show how a testing algorithm can distinguish, with a probability arbitrarily
Probabilistic Latent Semantic Indexing
, 1999
"... Probabilistic Latent Semantic Indexing is a novel approach to automated document indexing which is based on a statistical latent class model for factor analysis of count data. Fitted from a training corpus of text documents by a generalization of the Expectation Maximization algorithm, the utilized ..."
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Cited by 1225 (10 self)
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Probabilistic Latent Semantic Indexing is a novel approach to automated document indexing which is based on a statistical latent class model for factor analysis of count data. Fitted from a training corpus of text documents by a generalization of the Expectation Maximization algorithm, the utilized
FINDING STRUCTURE WITH RANDOMNESS: PROBABILISTIC ALGORITHMS FOR CONSTRUCTING APPROXIMATE MATRIX DECOMPOSITIONS
"... Lowrank matrix approximations, such as the truncated singular value decomposition and the rankrevealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which demonstrates that randomization offers a powerful tool for ..."
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Cited by 253 (6 self)
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for performing lowrank matrix approximation. These techniques exploit modern computational architectures more fully than classical methods and open the possibility of dealing with truly massive data sets. This paper presents a modular framework for constructing randomized algorithms that compute partial matrix
A Probabilistic Analysis of the Rocchio Algorithm with TFIDF for Text Categorization
, 1997
"... The Rocchio relevance feedback algorithm is one of the most popular and widely applied learning methods from information retrieval. Here, a probabilistic analysis of this algorithm is presented in a text categorization framework. The analysis gives theoretical insight into the heuristics used in the ..."
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Cited by 456 (1 self)
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The Rocchio relevance feedback algorithm is one of the most popular and widely applied learning methods from information retrieval. Here, a probabilistic analysis of this algorithm is presented in a text categorization framework. The analysis gives theoretical insight into the heuristics used
Results 1  10
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