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28
Learning HighDimensional Markov Forest Distributions: Analysis of Error Rates
, 1005
"... The problem of learning foreststructured discrete graphical models from i.i.d. samples is considered. An algorithm based on pruning of the ChowLiu tree through adaptive thresholding is proposed. It is shown that this algorithm is both structurally consistent and risk consistent and the error proba ..."
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Cited by 14 (8 self)
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The problem of learning foreststructured discrete graphical models from i.i.d. samples is considered. An algorithm based on pruning of the ChowLiu tree through adaptive thresholding is proposed. It is shown that this algorithm is both structurally consistent and risk consistent and the error probability of structure learning decays faster than any polynomial in the number of samples under fixed model size. For the highdimensional scenario where the size of the model d and the number of edges k scale with the number of samples n, sufficient conditions on (n,d,k) are given for the algorithm to satisfy structural and risk consistencies. In addition, the extremal structures for learning are identified; we prove that the independent (resp. tree) model is the hardest (resp. easiest) to learn using the proposed algorithm in terms of error rates for structure learning.
Estimating and testing the order of a model
, 2002
"... This paper deals with order identification for nested models in the i.i.d. framework. We study the asymptotic efficiency of two generalized likelihood ratio tests of the order. They are based on two estimators which are proved to be strongly consistent. A version of Stein’s lemma yields an optimal u ..."
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Cited by 11 (1 self)
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This paper deals with order identification for nested models in the i.i.d. framework. We study the asymptotic efficiency of two generalized likelihood ratio tests of the order. They are based on two estimators which are proved to be strongly consistent. A version of Stein’s lemma yields an optimal underestimation error exponent. The lemma also implies that the overestimation error exponent is necessarily trivial. Our tests admit nontrivial underestimation error exponents. The optimal underestimation error exponent is achieved in some situations. The overestimation error can decay exponentially with respect to a positive power of the number of observations. These results are proved under mild assumptions by relating the underestimation (resp. overestimation) error to large (resp. moderate) deviations of the loglikelihood process. In particular, it is not necessary that the classical Cramér condition be satisfied; namely, the logdensities are not required to admit every exponential moment. Three benchmark examples with specific difficulties (location mixture of normal distributions, abrupt changes and various regressions) are detailed so as to illustrate the generality of our results.
HMMBased semantic Learning for a mobile robot
, 2004
"... We are developing a intelligent robot and attempting to teach it language. While there are many aspects of this research, for the purposes of this dissertation the most important are the following ideas. Language is primarily based on semantics, not syntax, which is the focus in speech recognition r ..."
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Cited by 8 (2 self)
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We are developing a intelligent robot and attempting to teach it language. While there are many aspects of this research, for the purposes of this dissertation the most important are the following ideas. Language is primarily based on semantics, not syntax, which is the focus in speech recognition research these days. To truly learn meaning, a language engine cannot simply be a computer program running on a desktop computer analyzing speech. It must be part of a more general, embodied intelligent system, one capable of using associative learning to form concepts from the perception of experiences in the world, and further capable of manipulating those concepts symbolically. This dissertation explores the use of hidden Markov models (HMMs) in this capacity. HMMs are capable of automatically learning and extracting the underlying structure of continuousvalued inputs and representing that structure in the states of the model. These states can then be treated as symbolic representations of the inputs. We show how a model consisting of a cascade of HMMs can be embedded in a small mobile robot and used to learn correlations among sensory inputs to create symbolic concepts, which can eventually be manipulated linguistically and used for decision making.
Order Estimation for a Special Class of Hidden Markov Sources and Binary Renewal Processes
 IEEE Trans. Inform. Theory
, 2002
"... We consider the estimation of the order, i.e., the number of hidden states, of a special class of discretetime finitealphabet hidden Markov sources. This class can be characterized in terms of equivalent renewal processes. No a priori bound is assumed on the maximum permissible order. An order est ..."
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Cited by 8 (0 self)
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We consider the estimation of the order, i.e., the number of hidden states, of a special class of discretetime finitealphabet hidden Markov sources. This class can be characterized in terms of equivalent renewal processes. No a priori bound is assumed on the maximum permissible order. An order estimator based on renewal types is constructed, and is shown to be strongly consistent by computing the precise asymptotics of the probability of estimation error. The probability of underestimation of the true order decays exponentially in the number of observations while the probability of overestimation goes to zero sufficiently fast. It is further shown that this estimator has the best possible error exponent in a large class of estimators. Our results are also valid for the general class of binary independentrenewal processes with finite mean renewal times.
Predictive Robot Programming: Theoretical and Experimental Analysis
 in Proceedings of the IEEE International Conference on Robotics and Automation April 26  May 1, 2004
, 2004
"... As the capabilities of manipulator robots increase, they are performing more complex tasks. The cumbersome nature of conventional programming methods limits robotic automation due to the lengthy programming time. We present a novel method for reducing the time needed to program a manipulator robot: ..."
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Cited by 7 (1 self)
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As the capabilities of manipulator robots increase, they are performing more complex tasks. The cumbersome nature of conventional programming methods limits robotic automation due to the lengthy programming time. We present a novel method for reducing the time needed to program a manipulator robot: Predictive Robot Programming (PRP). The PRP system constructs a statistical model of the user by incorporating information from previously completed tasks. Using this model, the PRP system computes predictions about where the user will move the robot. The user can reduce programming time by allowing the PRP system to complete the task automatically. In this paper, we derive a learning algorithm that estimates the structure of continuousdensity hidden Markov models from tasks the user has already completed. We analyze the performance of the PRP system on two sets of data. The first set is based on data from complex, realworld robotic tasks. We show that the PRP system is able to compute predictions for about 25% of the waypoints with a median prediction error less than 0:5% of the distance traveled during prediction. We also present laboratory experiments showing that the PRP system results in a significant reduction in programming time, with users completing simple robotprogramming tasks over 30% faster when using the PRP system to compute predictions of future positions.
Recursive filters for partially observable finite Markov chains
 J. Appl. Probab
, 2005
"... In this note, we consider discretetime finite Markov Chains and assume that they are only partly observed. We obtain finitedimensional normalized filters for basic statistics associated with such processes. Recursive equations for these filters are derived by means of simple computations involving ..."
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Cited by 3 (3 self)
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In this note, we consider discretetime finite Markov Chains and assume that they are only partly observed. We obtain finitedimensional normalized filters for basic statistics associated with such processes. Recursive equations for these filters are derived by means of simple computations involving conditional expectations. An application to the estimation of parameters for the socalled discretetime Batch Markovian Arrival Processes is outlined.
NUMBER OF HIDDEN STATES AND MEMORY: A JOINT ORDER ESTIMATION PROBLEM FOR MARKOV CHAINS WITH MARKOV REGIME
"... Abstract. This paper deals with order identification for Markov chains with Markov regime (MCMR) in the context of finite alphabets. We define the joint order of a MCMR process in terms of the number k of states of the hidden Markov chain and the memory m of the conditional Markov chain. We study th ..."
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Abstract. This paper deals with order identification for Markov chains with Markov regime (MCMR) in the context of finite alphabets. We define the joint order of a MCMR process in terms of the number k of states of the hidden Markov chain and the memory m of the conditional Markov chain. We study the properties of penalized maximum likelihood estimators for the unknown order (k, m) of an observed MCMR process, relying on information theoretic arguments. The novelty of our work relies in the joint estimation of two structural parameters. Furthermore, the different models in competition are not nested. In an asymptotic framework, we prove that a penalized maximum likelihood estimator is strongly consistent without prior bounds on k and m. We complement our theoretical work with a simulation study of its behaviour. We also study numerically the behaviour of the BIC criterion. A theoretical proof of its consistency seems to us presently out of reach for MCMR, as such a result does not yet exist in the simpler case where m = 0 (that is for hidden Markov models). Résumé. Ce travail porte sur l’identification de l’ordre d’une chaîne de Markov à régime Markovien (MCMR) sur un alphabet fini. L’ordre d’une MCMR est défini comme le couple (k, m) où k est le nombre d’états de la chaîne cachée et m la mémoire de la chaîne de Markov conditionnelle. Nous étudions des estimateurs du maximum de vraisemblance pénalisée en utilisant des techniques issues de
About the posterior distribution in hidden Markov models with unknown number of states
 Bernoulli
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Order Estimation and Model Selection
, 2003
"... reason why source coding concepts and techniques have become a standard tool in the area. This chapter presents four kinds of results: a rst very general consistency result in a Bayesian setting provides hints about the ideal penalties that could be used in penalized maximum likelihood order estimat ..."
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Cited by 2 (0 self)
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reason why source coding concepts and techniques have become a standard tool in the area. This chapter presents four kinds of results: a rst very general consistency result in a Bayesian setting provides hints about the ideal penalties that could be used in penalized maximum likelihood order estimation. Then we provide a general construction for strongly consistent order estimators based on universal coding arguments. The third main result reports a recent tour de force by Csiszar and Shields (2000) who show that the Bayesian Information Criterion provides a strongly consistent Markov order estimator. We conclude by presenting a general framework for analyzing the Bahadur eciency of order estimation procedures following the line Gassiat and Boucheron (to appear). LRI UMR 8623 CNRS, Universite ParisSud Mathematiques, Universite ParisSud 2.1 Model Order Identi cation: what is it about ? In the preceding chapters, we have been concerned with inference problems in HMMs where th
Free Energy of Stochastic Context Free Grammar on Variational Bayes
"... Abstract. Variational Bayesian learning is proposed for approximation method of Bayesian learning. In spite of efficiency and experimental good performance, their mathematical property has not yet been clarified. In this paper we analyze variational Bayesian Stochastic Context Free Grammar which inc ..."
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Abstract. Variational Bayesian learning is proposed for approximation method of Bayesian learning. In spite of efficiency and experimental good performance, their mathematical property has not yet been clarified. In this paper we analyze variational Bayesian Stochastic Context Free Grammar which includes the true distribution thus the model is nonidentifiable. We derive their asymptotic free energy. It is shown that in some prior conditions, the free energy is much smaller than identifiable models and satisfies eliminating redundant nonterminals. 1