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Bernard De De Baets - One of the best experts on this subject based on the ideXlab platform.
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Transitive comparison of random variables
Logical Algebraic Analytic and Probabilistic Aspects of Triangular Norms, 2020Co-Authors: Bernard De De Baets, H. De Meyer, Bart De SchuymerAbstract:A general framework for describing the transitivity of Probabilistic Relations is presented. A procedure is established for expressing the pairwise comparison of independent random variables in terms of a Probabilistic Relation. The transitivity of this Relation is studied both in general and within popular parameterized families of distributions. It is shown how a copula can be entered into this comparison procedure and how this affects the transitivity of the Probabilistic Relation.
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On the transitivity of the comonotonic and countermonotonic comparison of random variables
Journal of Multivariate Analysis, 2020Co-Authors: H. De Meyer, Bernard De De Baets, Bart De SchuymerAbstract:A recently proposed method for the pairwise comparison of arbitrary independent random variables results in a Probabilistic Relation. When restricted to discrete random variables uniformly distributed on finite multisets of numbers, this Probabilistic Relation expresses the winning probabilities between pairs of hypothetical dice that carry these numbers and exhibits a particular type of transitivity called dice-transitivity. In case these multisets have equal cardinality, two alternative methods for statistically comparing the ordered lists of the numbers on the faces of the dice have been studied recently: the comonotonic method based upon the comparison of the numbers of the same rank when the lists are in increasing order, and the countermonotonic method, also based upon the comparison of only numbers of the same rank but with the lists in opposite order. In terms of the discrete random variables associated to these lists, these methods each turn out to be related to a particular copula that joins the marginal cumulative distribution functions into a bivariate cumulative distribution function. The transitivity of the generated Probabilistic Relation has been completely characterized. In this paper, the list comparison methods are generalized for the purpose of comparing arbitrary random variables. The transitivity properties derived in the case of discrete uniform random variables are shown to be generic. Additionally, it is shown that for a collection of normal random variables, both comparison methods lead to a Probabilistic Relation that is at least moderately stochastic transitive.
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EUSFLAT Conf. - Transitive comparison of marginal probability distributions
2020Co-Authors: H. De Meyer, Bernard De De Baets, Bart De SchuymerAbstract:A generalized dice model for the pairwise comparison of non-necessarily independent random variables is established. It is shown how the transitivity of the Probabilistic Relation generated by the model depends on the copula defining the coupling of the marginal distribution functions in the joint distribution function.
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On the cycle-transitive comparison of artificially coupled random variables
International Journal of Approximate Reasoning, 2008Co-Authors: Bernard De De Baets, H. De MeyerAbstract:Given a collection of random variables, we build a Probabilistic Relation that, in the case of continuous random variables, expresses for each couple of random variables the probability that the first one takes a greater value than the second one. In order to compute this probability, the random variables are artificially coupled by means of a fixed commutative copula. The main result of this paper pertains to the transitivity of this Probabilistic Relation. Provided the commutative copula satisfies some additional condition, this transitivity can be described elegantly within the cycle-transitivity framework. It ranges between two known types of transitivity: T"L-transitivity and partial stochastic transitivity.
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Extreme Copulas and the Comparison of Ordered Lists
Theory and Decision, 2007Co-Authors: B. De Schuymer, H. De Meyer, Bernard De De BaetsAbstract:We introduce two extreme methods to pairwisely compare ordered lists of the same length, viz. the comonotonic and the countermonotonic comparison method, and show that these methods are, respectively, related to the copula T _ M (the minimum operator) and the Ł ukasiewicz copula T _ L used to join marginal cumulative distribution functions into bivariate cumulative distribution functions. Given a collection of ordered lists of the same length, we generate by means of T _ M and T _ L two Probabilistic Relations Q ^ M and Q ^ L and identify their type of transitivity. Finally, it is shown that any Probabilistic Relation with rational elements on a 3-dimensional space of alternatives which possesses one of these types of transitivity, can be generated by three ordered lists and at least one of the two extreme comparison methods.
Mathew Magimai.-doss - One of the best experts on this subject based on the ideXlab platform.
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Acoustic data-driven grapheme-to-phoneme conversion using KL-HMM
2012 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2012Co-Authors: Ramya Rasipuram, Mathew Magimai.-dossAbstract:This paper proposes a novel grapheme-to-phoneme (G2P) conversion approach where first the Probabilistic Relation between graphemes and phonemes is captured from acoustic data using Kullback-Leibler divergence based hidden Markov model (KL-HMM) system. Then, through a simple decoding framework the information in this Probabilistic Relation is integrated with the sequence information in the orthographic transcription of the word to infer the phoneme sequence. One of the main application of the proposed G2P approach is in the area of low linguistic resource based automatic speech recognition or text-to-speech systems. We demonstrate this potential through a simulation study where linguistic resources from one domain is used to create linguistic resources for a different domain.
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ICASSP - Acoustic data-driven grapheme-to-phoneme conversion using KL-HMM
2012 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2012Co-Authors: Ramya Rasipuram, Mathew Magimai.-dossAbstract:This paper proposes a novel grapheme-to-phoneme (G2P) conversion approach where first the Probabilistic Relation between graphemes and phonemes is captured from acoustic data using Kullback-Leibler divergence based hidden Markov model (KL-HMM) system. Then, through a simple decoding framework the information in this Probabilistic Relation is integrated with the sequence information in the orthographic transcription of the word to infer the phoneme sequence. One of the main application of the proposed G2P approach is in the area of low linguistic resource based automatic speech recognition or text-to-speech systems. We demonstrate this potential through a simulation study where linguistic resources from one domain is used to create linguistic resources for a different domain.
Susana Díaz - One of the best experts on this subject based on the ideXlab platform.
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Interpretation of Statistical Preference in Terms of Location Parameters
Infor, 2020Co-Authors: Ignacio Montes, Davide Martinetti, Susana Díaz, Susana MontesAbstract:Stochastic orders are methods that allow the comparison of random quantities. One of the most used stochastic orders is stochastic dominance. This method is based on the direct comparison of the cumulative distribution functions of the random variables, and it is characterized by comparing the expectations of the adequate transformation of the variables. Statistical preference is another alternative based on a Probabilistic Relation that provides preference degrees between the variables. This paper proves that statistical preference is connected to another location parameter different from the expectation: the median. Then, both stochastic orders have different interpretations, in the same way as mean and median are two different location parameters for describing random samples. Nevertheless, we prove that stochastic dominance and statistical preference are connected when the random variables are independent.
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Graded comparison of imprecise fitness values
Expert Systems With Applications, 2016Co-Authors: Ignacio Montes, Susana Díaz, Susana MontesAbstract:We establish a new way to compare two randomness values of two KBs, which allow us to compare any pair.We compare this new method with the previous ones.We study the behavior for the particular and important cases of uniformity and beta distribution. Genetic algorithms can be used to construct knowledge bases. They are based on the idea of "survival of the fittest" in the same way as natural evolution. Nature chooses the fittest ones in real life. In artificial intelligence we need a method that carries out the comparison and choice. Traditionally, this choice is based on fitness functions. Each alternative or possible solution is given a fitness score. If there is no ambiguity and those scores are numbers, it is easy to order individuals according to those values and determine the fittest ones. However, the process of assessing degrees of optimality usually involves uncertainty or imprecision.In this contribution we discuss the comparison among fitness scores when they are known to be in an interval, but the exact value is not given. Random variables are used to represent fitness values in this situation. Some of the most usual approaches that can be found in the literature for the comparison of those kinds of intervals are the strong dominance and the Probabilistic prior method. In this contribution we consider an alternative procedure to order vague fitness values: statistical preference. We first study the connection among the three methods previously mentioned. Despite they appear to be completely different approaches, we will prove some Relations among them. We will then focus on statistical preference since it takes into consideration the information about the Relation between the fitness values to compare them. We will provide the explicit expression of the Probabilistic Relation associated to statistical preference when the fitness values are defined by uniform and beta distributions when they are independent, comonotone and countermonotone.
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A study on the transitivity of Probabilistic and fuzzy Relations
Fuzzy Sets and Systems, 2011Co-Authors: Davide Martinetti, Ignacio Montes, Susana Díaz, Susana MontesAbstract:Given a set of alternatives we consider a fuzzy Relation and a Probabilistic Relation defined on such a set. We investigate the Relation between the T-transitivity of the fuzzy Relation and the cycle-transitivity of the associated Probabilistic Relation. We provide a general result, valid for any t-norm and we later provide explicit expressions for important particular cases. We also apply the results obtained to explore the transitivity satisfied by the Probabilistic Relation defined on a set of random variables. We focus on uniform continuous random variables.
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Min-transitivity of graded comparisons for random variables
International Conference on Fuzzy Systems, 2010Co-Authors: Susana Montes, Davide Martinetti, Ignacio Montes, Susana DíazAbstract:Classically, the comparison of random variables have been done by means of a crisp order, which is known as stochastic dominance. In the last years, the classical stochastic dominance have been extended to a graded version by means of a Probabilistic Relation. In this work we propose different ways of measuring the gradual order among random variables by using fuzzy Relations instead of Probabilistic Relations. The connection between the cycle-transitivity of the Probabilistic Relation and the T-transitivity of the associated fuzzy weak preference Relation is characterized in the particular case of the minimum t-norm.
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FUZZ-IEEE - Min-transitivity of graded comparisons for random variables
International Conference on Fuzzy Systems, 2010Co-Authors: Susana Montes, Davide Martinetti, Ignacio Montes, Susana DíazAbstract:Classically, the comparison of random variables have been done by means of a crisp order, which is known as stochastic dominance. In the last years, the classical stochastic dominance have been extended to a graded version by means of a Probabilistic Relation. In this work we propose different ways of measuring the gradual order among random variables by using fuzzy Relations instead of Probabilistic Relations. The connection between the cycle-transitivity of the Probabilistic Relation and the T-transitivity of the associated fuzzy weak preference Relation is characterized in the particular case of the minimum t-norm.
Bart De Schuymer - One of the best experts on this subject based on the ideXlab platform.
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Transitive comparison of random variables
Logical Algebraic Analytic and Probabilistic Aspects of Triangular Norms, 2020Co-Authors: Bernard De De Baets, H. De Meyer, Bart De SchuymerAbstract:A general framework for describing the transitivity of Probabilistic Relations is presented. A procedure is established for expressing the pairwise comparison of independent random variables in terms of a Probabilistic Relation. The transitivity of this Relation is studied both in general and within popular parameterized families of distributions. It is shown how a copula can be entered into this comparison procedure and how this affects the transitivity of the Probabilistic Relation.
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On the transitivity of the comonotonic and countermonotonic comparison of random variables
Journal of Multivariate Analysis, 2020Co-Authors: H. De Meyer, Bernard De De Baets, Bart De SchuymerAbstract:A recently proposed method for the pairwise comparison of arbitrary independent random variables results in a Probabilistic Relation. When restricted to discrete random variables uniformly distributed on finite multisets of numbers, this Probabilistic Relation expresses the winning probabilities between pairs of hypothetical dice that carry these numbers and exhibits a particular type of transitivity called dice-transitivity. In case these multisets have equal cardinality, two alternative methods for statistically comparing the ordered lists of the numbers on the faces of the dice have been studied recently: the comonotonic method based upon the comparison of the numbers of the same rank when the lists are in increasing order, and the countermonotonic method, also based upon the comparison of only numbers of the same rank but with the lists in opposite order. In terms of the discrete random variables associated to these lists, these methods each turn out to be related to a particular copula that joins the marginal cumulative distribution functions into a bivariate cumulative distribution function. The transitivity of the generated Probabilistic Relation has been completely characterized. In this paper, the list comparison methods are generalized for the purpose of comparing arbitrary random variables. The transitivity properties derived in the case of discrete uniform random variables are shown to be generic. Additionally, it is shown that for a collection of normal random variables, both comparison methods lead to a Probabilistic Relation that is at least moderately stochastic transitive.
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EUSFLAT Conf. - Transitive comparison of marginal probability distributions
2020Co-Authors: H. De Meyer, Bernard De De Baets, Bart De SchuymerAbstract:A generalized dice model for the pairwise comparison of non-necessarily independent random variables is established. It is shown how the transitivity of the Probabilistic Relation generated by the model depends on the copula defining the coupling of the marginal distribution functions in the joint distribution function.
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Cycle-transitive comparison of independent random variables
Journal of Multivariate Analysis, 2005Co-Authors: Bart De Schuymer, H. De Meyer, Bernard De De BaetsAbstract:The discrete dice model, previously introduced by the present authors, essentially amounts to the pairwise comparison of a collection of independent discrete random variables that are uniformly distributed on finite integer multisets. This pairwise comparison results in a Probabilistic Relation that exhibits a particular type of transitivity, called dice-transitivity. In this paper, the discrete dice model is generalized with the purpose of pairwisely comparing independent discrete or continuous random variables with arbitrary probability distributions. It is shown that the Probabilistic Relation generated by a collection of arbitrary independent random variables is still dice-transitive. Interestingly, this Probabilistic Relation can be seen as a graded alternative to the concept of stochastic dominance. Furthermore, when the marginal distributions of the random variables belong to the same parametric family of distributions, the Probabilistic Relation exhibits interesting types of isostochastic transitivity, such as multiplicative transitivity. Finally, the Probabilistic Relation generated by a collection of independent normal random variables is proven to be moderately stochastic transitive.
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Transitive comparison of random variables
Logical, Algebraic, Analytic and Probabilistic Aspects of Triangular Norms, 2005Co-Authors: Bernard De De Baets, Hans De De Meyer, Bart De SchuymerAbstract:This chapter presents a general framework for describing the transitivity of Probabilistic Relations. It discusses a procedure for expressing the pairwise comparison of independent random variables in terms of a Probabilistic Relation. The transitivity of this Relation is studied both in general and within popular parameterized families of distributions. The chapter also explains how a copula can be entered into this comparison procedure and how this affects the transitivity of the Probabilistic Relation. A collection of generalized dice together with the Probabilistic Relation made of the winning probabilities among these dice is called a discrete dice model. The chapter generalizes the discrete dice model to collections of independent discrete or continuous random variables with arbitrary probability distributions and illustrates that the generated Probabilistic Relations that provide an alternative to the concept of stochastic dominance are still dice-transitive. A further generalization consists of allowing the random variables to be dependent. For the pairwise comparison of such random variables, the two-dimensional marginal distributions are needed. A copula is called stable if it coincides with its survival copula. © 2005 Elsevier B.V. All rights reserved.
Susana Montes - One of the best experts on this subject based on the ideXlab platform.
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Interpretation of Statistical Preference in Terms of Location Parameters
Infor, 2020Co-Authors: Ignacio Montes, Davide Martinetti, Susana Díaz, Susana MontesAbstract:Stochastic orders are methods that allow the comparison of random quantities. One of the most used stochastic orders is stochastic dominance. This method is based on the direct comparison of the cumulative distribution functions of the random variables, and it is characterized by comparing the expectations of the adequate transformation of the variables. Statistical preference is another alternative based on a Probabilistic Relation that provides preference degrees between the variables. This paper proves that statistical preference is connected to another location parameter different from the expectation: the median. Then, both stochastic orders have different interpretations, in the same way as mean and median are two different location parameters for describing random samples. Nevertheless, we prove that stochastic dominance and statistical preference are connected when the random variables are independent.
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Graded comparison of imprecise fitness values
Expert Systems With Applications, 2016Co-Authors: Ignacio Montes, Susana Díaz, Susana MontesAbstract:We establish a new way to compare two randomness values of two KBs, which allow us to compare any pair.We compare this new method with the previous ones.We study the behavior for the particular and important cases of uniformity and beta distribution. Genetic algorithms can be used to construct knowledge bases. They are based on the idea of "survival of the fittest" in the same way as natural evolution. Nature chooses the fittest ones in real life. In artificial intelligence we need a method that carries out the comparison and choice. Traditionally, this choice is based on fitness functions. Each alternative or possible solution is given a fitness score. If there is no ambiguity and those scores are numbers, it is easy to order individuals according to those values and determine the fittest ones. However, the process of assessing degrees of optimality usually involves uncertainty or imprecision.In this contribution we discuss the comparison among fitness scores when they are known to be in an interval, but the exact value is not given. Random variables are used to represent fitness values in this situation. Some of the most usual approaches that can be found in the literature for the comparison of those kinds of intervals are the strong dominance and the Probabilistic prior method. In this contribution we consider an alternative procedure to order vague fitness values: statistical preference. We first study the connection among the three methods previously mentioned. Despite they appear to be completely different approaches, we will prove some Relations among them. We will then focus on statistical preference since it takes into consideration the information about the Relation between the fitness values to compare them. We will provide the explicit expression of the Probabilistic Relation associated to statistical preference when the fitness values are defined by uniform and beta distributions when they are independent, comonotone and countermonotone.
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A study on the transitivity of Probabilistic and fuzzy Relations
Fuzzy Sets and Systems, 2011Co-Authors: Davide Martinetti, Ignacio Montes, Susana Díaz, Susana MontesAbstract:Given a set of alternatives we consider a fuzzy Relation and a Probabilistic Relation defined on such a set. We investigate the Relation between the T-transitivity of the fuzzy Relation and the cycle-transitivity of the associated Probabilistic Relation. We provide a general result, valid for any t-norm and we later provide explicit expressions for important particular cases. We also apply the results obtained to explore the transitivity satisfied by the Probabilistic Relation defined on a set of random variables. We focus on uniform continuous random variables.
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Min-transitivity of graded comparisons for random variables
International Conference on Fuzzy Systems, 2010Co-Authors: Susana Montes, Davide Martinetti, Ignacio Montes, Susana DíazAbstract:Classically, the comparison of random variables have been done by means of a crisp order, which is known as stochastic dominance. In the last years, the classical stochastic dominance have been extended to a graded version by means of a Probabilistic Relation. In this work we propose different ways of measuring the gradual order among random variables by using fuzzy Relations instead of Probabilistic Relations. The connection between the cycle-transitivity of the Probabilistic Relation and the T-transitivity of the associated fuzzy weak preference Relation is characterized in the particular case of the minimum t-norm.
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FUZZ-IEEE - Min-transitivity of graded comparisons for random variables
International Conference on Fuzzy Systems, 2010Co-Authors: Susana Montes, Davide Martinetti, Ignacio Montes, Susana DíazAbstract:Classically, the comparison of random variables have been done by means of a crisp order, which is known as stochastic dominance. In the last years, the classical stochastic dominance have been extended to a graded version by means of a Probabilistic Relation. In this work we propose different ways of measuring the gradual order among random variables by using fuzzy Relations instead of Probabilistic Relations. The connection between the cycle-transitivity of the Probabilistic Relation and the T-transitivity of the associated fuzzy weak preference Relation is characterized in the particular case of the minimum t-norm.
