Results 1  10
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19
SEMIRING FRAMEWORKS AND ALGORITHMS FOR SHORTESTDISTANCE PROBLEMS
, 2002
"... We define general algebraic frameworks for shortestdistance problems based on the structure of semirings. We give a generic algorithm for finding singlesource shortest distances in a weighted directed graph when the weights satisfy the conditions of our general semiring framework. The same algorit ..."
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Cited by 72 (20 self)
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We define general algebraic frameworks for shortestdistance problems based on the structure of semirings. We give a generic algorithm for finding singlesource shortest distances in a weighted directed graph when the weights satisfy the conditions of our general semiring framework. The same algorithm can be used to solve efficiently classical shortest paths problems or to find the kshortest distances in a directed graph. It can be used to solve singlesource shortestdistance problems in weighted directed acyclic graphs over any semiring. We examine several semirings and describe some specific instances of our generic algorithms to illustrate their use and compare them with existing methods and algorithms. The proof of the soundness of all algorithms is given in detail, including their pseudocode and a full analysis of their running time complexity.
Parameter Estimation for Probabilistic FiniteState Transducers
 Proc. of the Annual Meeting of the Association for Computational Linguistics
, 2002
"... Weighted finitestate transducers suffer from the lack of a training algorithm. Training is even harder for transducers that have been assembled via finitestate operations such as composition, minimization, union, concatenation, and closure, as this yields tricky parameter tying. We formulate a "pa ..."
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Cited by 49 (4 self)
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Weighted finitestate transducers suffer from the lack of a training algorithm. Training is even harder for transducers that have been assembled via finitestate operations such as composition, minimization, union, concatenation, and closure, as this yields tricky parameter tying. We formulate a "parameterized FST" paradigm and give training algorithms for it, including a general bookkeeping trick ("expectation semirings") that cleanly and efficiently computes expectations and gradients.
The correspondence principle for Idempotent Calculus and some computer applications // Gunawardena
 Idempotency: Publ. of the I. Newton Institute
, 1998
"... This paper is devoted to heuristic aspects of the socalled idempotent calculus. There is a correspondence between important, useful and interesting constructions and results over the field of real (or complex) numbers ..."
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Cited by 37 (16 self)
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This paper is devoted to heuristic aspects of the socalled idempotent calculus. There is a correspondence between important, useful and interesting constructions and results over the field of real (or complex) numbers
Graph Kernels
, 2007
"... We present a unified framework to study graph kernels, special cases of which include the random walk (Gärtner et al., 2003; Borgwardt et al., 2005) and marginalized (Kashima et al., 2003, 2004; Mahé et al., 2004) graph kernels. Through reduction to a Sylvester equation we improve the time complexit ..."
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Cited by 37 (4 self)
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We present a unified framework to study graph kernels, special cases of which include the random walk (Gärtner et al., 2003; Borgwardt et al., 2005) and marginalized (Kashima et al., 2003, 2004; Mahé et al., 2004) graph kernels. Through reduction to a Sylvester equation we improve the time complexity of kernel computation between unlabeled graphs with n vertices from O(n 6) to O(n 3). We find a spectral decomposition approach even more efficient when computing entire kernel matrices. For labeled graphs we develop conjugate gradient and fixedpoint methods that take O(dn 3) time per iteration, where d is the size of the label set. By extending the necessary linear algebra to Reproducing Kernel Hilbert Spaces (RKHS) we obtain the same result for ddimensional edge kernels, and O(n 4) in the infinitedimensional case; on sparse graphs these algorithms only take O(n 2) time per iteration in all cases. Experiments on graphs from bioinformatics and other application domains show that these techniques can speed up computation of the kernel by an order of magnitude or more. We also show that certain rational kernels (Cortes et al., 2002, 2003, 2004) when specialized to graphs reduce to our random walk graph kernel. Finally, we relate our framework to Rconvolution kernels (Haussler, 1999) and provide a kernel that is close to the optimal assignment kernel of Fröhlich et al. (2006) yet provably positive semidefinite.
Algorithmic Aspects of Symbolic Switch Network Analysis
 IEEE Trans. CAD/IC
, 1987
"... A network of switches controlled by Boolean variables can be represented as a system of Boolean equations. The solution of this system gives a symbolic description of the conducting paths in the network. Gaussian elimination provides an efficient technique for solving sparse systems of Boolean eq ..."
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Cited by 16 (5 self)
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A network of switches controlled by Boolean variables can be represented as a system of Boolean equations. The solution of this system gives a symbolic description of the conducting paths in the network. Gaussian elimination provides an efficient technique for solving sparse systems of Boolean equations. For the class of networks that arise when analyzing digital metaloxide semiconductor (MOS) circuits, a simple pivot selection rule guarantees that most s switch networks encountered in practice can be solved with O(s) operations. When represented by a directed acyclic graph, the set of Boolean formulas generated by the analysis has total size bounded by the number of operations required by the Gaussian elimination. This paper presents the mathematical basis for systems of Boolean equations, their solution by Gaussian elimination, and data structures and algorithms for representing and manipulating Boolean formulas.
Efficient Computation of the Relative Entropy of Probabilistic Automata
 In Proceedings of LATIN 2006, volume 3887 of LNCS
, 2006
"... Abstract. The problem of the efficient computation of the relative entropy of two distributions represented by deterministic weighted automata arises in several machine learning problems. We show that this problem can be naturally formulated as a shortestdistance problem over an intersection automa ..."
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Cited by 9 (6 self)
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Abstract. The problem of the efficient computation of the relative entropy of two distributions represented by deterministic weighted automata arises in several machine learning problems. We show that this problem can be naturally formulated as a shortestdistance problem over an intersection automaton defined on an appropriate semiring. We describe simple and efficient novel algorithms for its computation and report the results of experiments demonstrating the practicality of our algorithms for very large weighted automata. Our algorithms apply to unambiguous weighted automata, a class of weighted automata that strictly includes deterministic weighted automata. These are also the first algorithms extending the computation of entropy or of relative entropy beyond the class of deterministic weighted automata. 1
On the computation of the Relative Entropy of Probabilistic Automata
 International Journal of Foundations of Computer Science
, 2007
"... We present an exhaustive analysis of the problem of computing the relative entropy of two probabilistic automata. We show that the problem of computing the relative entropy of unambiguous probabilistic automata can be formulated as a shortestdistance problem over an appropriate semiring, give effic ..."
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Cited by 8 (5 self)
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We present an exhaustive analysis of the problem of computing the relative entropy of two probabilistic automata. We show that the problem of computing the relative entropy of unambiguous probabilistic automata can be formulated as a shortestdistance problem over an appropriate semiring, give efficient exact and approximate algorithms for its computation in that case, and report the results of experiments demonstrating the practicality of our algorithms for very large weighted automata. We also prove that the computation of the relative entropy of arbitrary probabilistic automata is PSPACEcomplete. The relative entropy is used in a variety of machine learning algorithms and applications to measure the discrepancy of two distributions. We examine the use of the symmetrized relative entropy in machine learning algorithms and show that, contrarily to what is suggested by a number of publications, the symmetrized relative entropy is neither positive definite symmetric nor negative definite symmetric, which limits its use and application in kernel methods. In particular, the convergence of training for learning algorithms is not guaranteed when the symmetrized relative entropy is used directly as a kernel, or as the operand of an exponential as in the case of Gaussian Kernels. Finally, we show that our algorithm for the computation of the entropy of an unambiguous probabilistic automaton can be generalized to the computation of the norm of an unambiguous probabilistic automaton by using a monoid morphism. In particular, this yields efficient algorithms for the computation of the Lpnorm of a probabilistic automaton. 1
Weighted FiniteState Transducer Algorithms: An Overview
 Formal Languages and Applications, volume 148, VIII
, 2004
"... Weighted finitestate transducers are used in many applications such as text, speech and image processing. This chapter gives an overview of several recent weighted transducer algorithms, including composition of weighted transducers, determinization of weighted automata, a weight pushing algorithm, ..."
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Cited by 7 (1 self)
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Weighted finitestate transducers are used in many applications such as text, speech and image processing. This chapter gives an overview of several recent weighted transducer algorithms, including composition of weighted transducers, determinization of weighted automata, a weight pushing algorithm, and minimization of weighted automata. It briefly describes these algorithms, discusses their running time complexity and conditions of application, and shows examples illustrating their application. 1
A Unified Construction of the Glushkov, Follow, and Antimirov Automata
 Proc. of MFCS’06, LNCS 4162
, 2006
"... Abstract. A number of different techniques have been introduced in the last few decades to create ɛfree automata representing regular expressions such as the Glushkov automata, follow automata, or Antimirov automata. This paper presents a simple and unified view of all these construction methods bo ..."
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Cited by 6 (0 self)
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Abstract. A number of different techniques have been introduced in the last few decades to create ɛfree automata representing regular expressions such as the Glushkov automata, follow automata, or Antimirov automata. This paper presents a simple and unified view of all these construction methods both for unweighted and weighted regular expressions. It describes simpler algorithms with time complexities at least as favorable as that of the best previously known techniques, and provides a concise proof of their correctness. Our algorithms are all based on two standard automata operations: epsilonremoval and minimization. This contrasts with the multitude of complicated and specialpurpose techniques previously described in the literature, and makes it straightforward to generalize these algorithms to the weighted case. In particular, we extend the definition and construction of follow automata to the case of weighted regular expressions over a closed semiring and present the first algorithm to compute weighted Antimirov automata. 1