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On the Computation of Some Standard Distances between Probabilistic Automata
 In Proceedings of the 11th International Conference on Implementation and Application of Automata (CIAA 2006
, 2006
"... Abstract. The problem of the computation of a distance between two probabilistic automata arises in a variety of statistical learning problems. This paper presents an exhaustive analysis of the problem of computing the Lp distance between two automata. We give efficient exact and approximate algorit ..."
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Abstract. The problem of the computation of a distance between two probabilistic automata arises in a variety of statistical learning problems. This paper presents an exhaustive analysis of the problem of computing the Lp distance between two automata. We give efficient exact and approximate algorithms for computing these distances for p even and prove the problem to be NPhard for all odd values of p, thereby completing previously known hardness results. We also give an efficient algorithm for computing the Hellinger distance between unambiguous probabilistic automata. Our results include a general algorithm for the computation of the norm of an unambiguous probabilistic automaton based on a monoid morphism and efficient algorithms for the specific case of the computation of the Lp norm. Finally, we also describe an efficient algorithm for testing the equivalence of two arbitrary probabilistic automata A1 and A2 based on Schützenberger’s standardization with a running time complexity of O(Σ  (A1+A2) 3), a significant improvement over the previously best algorithm reported for this problem. 1
General algorithms for testing the ambiguity of finite automata
 In Developments in Language Theory, 12th International Conference, volume 5257 of Lecture Notes in Computer Science
, 2008
"... Abstract. This paper presents efficient algorithms for testing the finite, polynomial, and exponential ambiguity of finite automata with ǫtransitions. It gives an algorithm for testing the exponential ambiguity of an automaton A in time O(A  2 E), and finite or polynomial ambiguity in time O(A  ..."
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Abstract. This paper presents efficient algorithms for testing the finite, polynomial, and exponential ambiguity of finite automata with ǫtransitions. It gives an algorithm for testing the exponential ambiguity of an automaton A in time O(A  2 E), and finite or polynomial ambiguity in time O(A  3 E), where AE denotes the number of transitions of A. These complexities significantly improve over the previous best complexities given for the same problem. Furthermore, the algorithms presented are simple and based on a general algorithm for the composition or intersection of automata. We also give an algorithm to determine in time O(A  3 E) the degree of polynomial ambiguity of a polynomially ambiguous automaton A. Finally, we present an application of our algorithms to an approximate computation of the entropy of a probabilistic automaton. 1
Measuring the confusability of pronunciations in speech recognition
"... In this work, we define a measure aimed at assessing how well a pronunciation model will function when used as a component of a speech recognition system. This measure, pronunciation entropy, fuses information from both the pronunciation model and the language model. We show how to compute this scor ..."
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Cited by 1 (0 self)
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In this work, we define a measure aimed at assessing how well a pronunciation model will function when used as a component of a speech recognition system. This measure, pronunciation entropy, fuses information from both the pronunciation model and the language model. We show how to compute this score by effectively composing the output of a phoneme recognizer with a pronunciation dictionary and a language model, and investigate its role as predictor of pronunciation model performance. We present results of this measure for different dictionaries with and without pronunciation variants and counts. 1
Products of Weighted Logic Programs
"... www.lti.cs.cmu.edu © 2008, Shay B. Cohen and Robert J. Simmons and Noah A. SmithAbstract. Weighted logic programming, a generalization of bottomup logic programming, is a successful framework for specifying dynamic programming algorithms. In this setting, proofs correspond to the algorithm’s output ..."
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www.lti.cs.cmu.edu © 2008, Shay B. Cohen and Robert J. Simmons and Noah A. SmithAbstract. Weighted logic programming, a generalization of bottomup logic programming, is a successful framework for specifying dynamic programming algorithms. In this setting, proofs correspond to the algorithm’s output space, such as a path through a graph or a grammatical derivation, and are given a weighted score, often interpreted as a probability, that depends on the score of the base axioms used in the proof. The desired output is a function over all possible proofs, such as a sum of scores or an optimal score. We describe the PRODUCT transformation, which can merge two weighted logic programs into a new one. The resulting program optimizes a product of proof scores from the original programs, constituting a scoring function known in machine learning as a “product of experts. ” Through the addition of intuitive constraining side conditions, we show that several important dynamic programming algorithms can be derived by applying PRODUCT to weighted logic programs corresponding to simpler weighted logic programs. This report is an extended version of [3]. 1 1
TR2007908 General Algorithms for Testing the Ambiguity of Finite Automata
"... Abstract. This paper presents efficient algorithms for testing the finite, polynomial, and exponential ambiguity of finite automata with ǫtransitions. It gives an algorithm for testing the exponential ambiguity of an automaton A in time O(A  2 E), and finite or polynomial ambiguity in time O(A  ..."
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Abstract. This paper presents efficient algorithms for testing the finite, polynomial, and exponential ambiguity of finite automata with ǫtransitions. It gives an algorithm for testing the exponential ambiguity of an automaton A in time O(A  2 E), and finite or polynomial ambiguity in time O(A  3 E). These complexities significantly improve over the previous best complexities given for the same problem. Furthermore, the algorithms presented are simple and are based on a general algorithm for the composition or intersection of automata. We also give an algorithm to determine the degree of polynomial ambiguity of a finite automaton A that is polynomially ambiguous in time O(A  3 E). Finally, we present an application of our algorithms to an approximate computation of the entropy of a probabilistic automaton. 1
On the construction of probabilistic diagnosers ⋆
"... Abstract: This paper revisits the notions of observer and diagnoser, and adapts them to probabilistic automata, in a setting of weighted automata computations. In the non stochastic case, observers and diagnosers are obtained by standard elementary steps, as state augmentation, epsilonreduction and ..."
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Abstract: This paper revisits the notions of observer and diagnoser, and adapts them to probabilistic automata, in a setting of weighted automata computations. In the non stochastic case, observers and diagnosers are obtained by standard elementary steps, as state augmentation, epsilonreduction and determinization. It is shown that these steps can be adapted to probabilistic automata, and algorithms to perform them efficiently are provided. In particular, the determinization is related to a standard filtering equation that recursively computes the conditional distribution of the current state given past observations. New notions of probabilistic observers and diagnosers are provided and compared to previous constructions, and simpler derivations of the latter are proposed. 1.