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28
A bayesian framework for word segmentation: Exploring the effects of context
 In 46th Annual Meeting of the ACL
, 2009
"... Since the experiments of Saffran et al. (1996a), there has been a great deal of interest in the question of how statistical regularities in the speech stream might be used by infants to begin to identify individual words. In this work, we use computational modeling to explore the effects of differen ..."
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Cited by 52 (12 self)
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Since the experiments of Saffran et al. (1996a), there has been a great deal of interest in the question of how statistical regularities in the speech stream might be used by infants to begin to identify individual words. In this work, we use computational modeling to explore the effects of different assumptions the learner might make regarding the nature of words – in particular, how these assumptions affect the kinds of words that are segmented from a corpus of transcribed childdirected speech. We develop several models within a Bayesian ideal observer framework, and use them to examine the consequences of assuming either that words are independent units, or units that help to predict other units. We show through empirical and theoretical results that the assumption of independence causes the learner to undersegment the corpus, with many two and threeword sequences (e.g. what’s that, do you, in the house) misidentified as individual words. In contrast, when the learner assumes that words are predictive, the resulting segmentation is far more accurate. These results indicate that taking context into account is important for a statistical word segmentation strategy to be successful, and raise the possibility that even young infants may be able to exploit more subtle statistical patterns than have usually been considered. 1
Bayesian Inference for Semiparametric Binary Regression
 JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
, 1996
"... We propose a regression model for binary response data which places no structural restrictions on the link function except monotonicity and known location and scale. Predictors enter linearly. We demonstrate Bayesian inference calculations in this model. By modifying the Dirichlet process, we obtain ..."
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Cited by 24 (2 self)
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We propose a regression model for binary response data which places no structural restrictions on the link function except monotonicity and known location and scale. Predictors enter linearly. We demonstrate Bayesian inference calculations in this model. By modifying the Dirichlet process, we obtain a natural prior measure over this semiparametric model, and we use Polya sequence theory to formulate this measure in terms of a finite number of unobserved variables. A Markov chain Monte Carlo algorithm is designed for posterior simulation, and the methodology is applied to data on radiotherapy treatments for cancer.
Probabilistic bounds on the coefficients of polynomials with only real zeros
 J. Combin. Theory Ser. A
, 1997
"... ..."
The Probabilistic Relationship between the Assignment and Asymmetric Traveling Salesman Problems
, 2001
"... this paper, c0, cl,... are positive absolute constants whose precise values are not too important to us ..."
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Cited by 14 (1 self)
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this paper, c0, cl,... are positive absolute constants whose precise values are not too important to us
Asymptotics of Poisson approximation to random discrete distributions: an analytic approach
 Advances in Applied Probability
, 1998
"... this paper, we shall describe the asymptotic behaviors of several distances of Poisson approximation to a wide class of discrete distributions covering many examples from number theory, combinatorics and arithmetic semigroups. Our aim is to show that whenever (analytic) generating functions of the r ..."
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Cited by 13 (9 self)
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this paper, we shall describe the asymptotic behaviors of several distances of Poisson approximation to a wide class of discrete distributions covering many examples from number theory, combinatorics and arithmetic semigroups. Our aim is to show that whenever (analytic) generating functions of the random variables in question are available, complexanalytic methods can be used to derive precise asymptotic results for the five distances above. Actually, we shall consider the following generalized distances: let ff ? 0 be a fixed positive number, (X; Y ) = FM (X; Y ) = (X; Y ) = sup K (X; Y ) = sup M (X; Y ) = jP(X = j) \Gamma P(Y = j) Note that d TV = d M . Besides the case ff = 1 (and ff = 1=2 for d M ), only the case d TV was previously studied by Franken [39] for Poisson approximation to the sum of independent but not identically distributed Bernoulli random variables. We take these quantities as our measures of degree of nearness of Poisson approximation, some of which may be interpreted as certain norms in suitable space as many authors did (cf. [12, 22, 23, 74, 96]). For a large class of discrete distributions, we shall derive an asymptotic main term together with an error estimate for each of these distances. Our results are thus "approximation theorems" rather than "limit theorems". The common form of the underlying structure of these distributions suggests the study of an analytic scheme as we did previously for normal approximation and large deviations (cf. [53, 54]). Many concrete examples from probabilistic number theory and combinatorial structures will justify the study of this scheme. Our treatment being completely general, many extensions can be further pursued with essentially the same line of methods. We shall di...
Computational aspects of nonparametric bayesian analysis with applications to the modelling of multiple binary sequences
 Journal of Computational and Graphical Statistics
, 2000
"... ..."
Nonparametric Bayesian Analysis for Assessing Homogeneity in k×l Contingency TABLES WITH FIXED RIGHT MARGIN TOTALS
 JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
, 1996
"... In this work we postulate a nonparametric Bayesian model for data that can be accommodated in a contingency table with fixed right margin totals. This data structure usually arises when comparing different groups regarding classification probabilities for a number of categories. We assume cell count ..."
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Cited by 10 (1 self)
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In this work we postulate a nonparametric Bayesian model for data that can be accommodated in a contingency table with fixed right margin totals. This data structure usually arises when comparing different groups regarding classification probabilities for a number of categories. We assume cell count vectors for each group to be conditionally independent, and with multinomial distribution given vectors of classification probabilities. In turn, these vectors of probabilities are assumed to be a sample from a distribution F , and the prior distribution of F is assumed to be a Dirichlet process, centered on a probability measure ff and with weight c. We also assume a prior distribution for c, as a way of obtaining a better control on the clustering structure induced by the Dirichlet process. We use this setting to assess homogeneity of classification probabilities, and a "Bayes factor" is proposed. We derive exact expressions for the relevant quantities. These can be directly computed wh...
A predictive view of Bayesian clustering
 J. Statist. Planning and Inference
, 2006
"... This work considers probability models for partitions of a set of n elements using a predictive approach, i.e., models that are specified in terms of the conditional probability of either joining an already existing cluster or forming a new one. The inherent structure can be motivated by resorting t ..."
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Cited by 9 (0 self)
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This work considers probability models for partitions of a set of n elements using a predictive approach, i.e., models that are specified in terms of the conditional probability of either joining an already existing cluster or forming a new one. The inherent structure can be motivated by resorting to hierarchical models of either parametric or nonparametric nature. Parametric examples include the product partition models (PPMs) and the modelbased approach of Dasgupta and Raftery (1998), while nonparametric alternatives include the Dirichlet Process, and more generally, the Species Sampling Models (SSMs). Under exchangeability, PPMs and SSMs induce the same type of partition structure. The methods are discussed in the context of outlier detection in normal linear regression models and of (univariate) density estimation.