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18
Assessment of school performance through a multilevel latent Markov Rash model
 Journal of Educational and Behavioral Statistics
, 2011
"... An extension of the latent Markov Rasch model is described for the analysis of binary longitudinal data with covariates when subjects are collected in clusters, such as students clustered in classes. For each subject, a latent process is used to represent the characteristic of interest (e.g., abilit ..."
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An extension of the latent Markov Rasch model is described for the analysis of binary longitudinal data with covariates when subjects are collected in clusters, such as students clustered in classes. For each subject, a latent process is used to represent the characteristic of interest (e.g., ability) conditional on the effect of the cluster to which he or she belongs. The latter effect is modeled by a discrete latent variable associated to each cluster. For the maximum likelihood estimation of the model parameters, an ExpectationMaximization algorithm is outlined. Through the analysis of a data set collected in the Lombardy Region (Italy), it is shown how the proposed model may be used for assessing the development of cognitive achievement. The data set is based on test scores in mathematics observed over 3 years on middle school students attending public and nonstate schools.
Attributedriven Hidden Markov Model Trees for Intention Prediction
"... In this paper we introduce a novel approach for generating an intention prediction model of user interactions with systems. As part of this new approach, we include personal aspects such as user characteristics that can increase prediction accuracy. The model is automatically trained according to th ..."
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In this paper we introduce a novel approach for generating an intention prediction model of user interactions with systems. As part of this new approach, we include personal aspects such as user characteristics that can increase prediction accuracy. The model is automatically trained according to the user’s fixed attributes (e.g., demographic data such as age and gender) and the user’s sequences of actions in the system. The generated model has a tree structure. The building blocks of each node can be any probabilistic sequence model (such as hidden Markov models and conditional random fields)) and each node is split according to user attributes. Thus, we refer to this algorithm as an attributedriven model tree. The new model was first tested on simulated data in which users with different attributes (such as age, gender) behave differently when trying to accomplish various tasks. We then validated the ability of the algorithm to discover the relevant attributes. We tested our algorithm on two real datasets: from a Web application and a mobile application dataset. The results were encouraging and indicate the capability of the proposed method for discovering the correct user intention model and increasing intention prediction accuracy compared to single HMM or CRF models.
A modelbased approach to gene clustering with missing observations reconstruction in a Markov Random Field framework
 J. Comput. Biol
, 2009
"... The different measurement techniques that interrogate biological systems provide means for monitoring the behavior of virtually all cell components at different scales and from complementary angles. However, data generated in these experiments are difficult to interpret. A first difficulty arises f ..."
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The different measurement techniques that interrogate biological systems provide means for monitoring the behavior of virtually all cell components at different scales and from complementary angles. However, data generated in these experiments are difficult to interpret. A first difficulty arises from highdimensionality and inherent noise of such data. Organizing them into meaningful groups is then highly desirable to improve our knowledge of biological mechanisms. A more accurate picture can be obtained when accounting for dependencies between components (e.g., genes) under study. A second difficulty arises from the fact that biological experiments often produce missing values. When it is not ignored, the latter issue has been solved by imputing the expression matrix prior to applying traditional analysis methods. Although helpful, this practice can lead to unsound results. We propose in this paper a statistical methodology that integrates individual dependencies in a missing data framework. More explicitly, we present a clustering algorithm dealing with incomplete data in a Hidden Markov Random Field context. This tackles the missing value issue in a probabilistic framework and still allows us to reconstruct missing observations a posteriori without imposing any preprocessing of the data. Experiments on synthetic data validate the gain in using our method, and analysis of real biological data shows its potential to extract biological knowledge. Key words: biological interaction network, gene clustering, Markov random field, mean fieldlike approximation, missing data.
A Note on the Mixture Transition Distribution and Hidden Markov Models
"... We discuss an interpretation of the Mixture Transition Distribution (MTD) for discretevalued time series which is based on a sequence of independent latent variables which are occasionspecific. We show that, by assuming that this latent process follows a first order Markov Chain, MTD can be genera ..."
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We discuss an interpretation of the Mixture Transition Distribution (MTD) for discretevalued time series which is based on a sequence of independent latent variables which are occasionspecific. We show that, by assuming that this latent process follows a first order Markov Chain, MTD can be generalized in a sensible way. A class of models results which also includes the Hidden Markov Model (HMM). For these models we outline an EM algorithm for the maximum likelihood estimation which exploits recursions developed within the HMM literature. Some key words: Backwardforward Recursions; Discretevalued time series; EMalgorithm; Statespace models.
Semisupervised Learning with Data Calibration for LongTerm Time Series Forecasting
"... Many time series prediction methods have focused on single step or short term prediction problems due to the inherent difficulty in controlling the propagation of errors from one prediction step to the next step. Yet, there is a broad range of applications such as climate impact assessments and urba ..."
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Many time series prediction methods have focused on single step or short term prediction problems due to the inherent difficulty in controlling the propagation of errors from one prediction step to the next step. Yet, there is a broad range of applications such as climate impact assessments and urban growth planning that require long term forecasting capabilities for strategic decision making. Training an accurate model that produces reliable long term predictions would require an extensive amount of historical data, which are either unavailable or expensive to acquire. For some of these domains, there are alternative ways to generate potential scenarios for the future using computerdriven simulation models, such as global climate and traffic demand models. However, the data generated by these models are currently utilized in a supervised learning setting, where a predictive model trained on past observations is used to estimate the future values. In this paper, we present a semisupervised learning framework for longterm time series forecasting based on Hidden Markov Model Regression. A covariance alignment method is also developed to deal with the issue of inconsistencies between historical and model simulation data. We evaluated our approach on data sets from a variety of domains, including climate modeling. Our experimental results demonstrate the efficacy of the approach compared to other supervised learning methods for longterm time series forecasting.
Hidden Markov models with mixtures as emission distributions
 Statistics and Computing
, 2013
"... In unsupervised classification, Hidden Markov Models (HMM) are used to account for a neighborhood structure between observations. The emission distributions are often supposed to belong to some parametric family. In this paper, a semiparametric modeling where the emission distributions are a mixture ..."
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In unsupervised classification, Hidden Markov Models (HMM) are used to account for a neighborhood structure between observations. The emission distributions are often supposed to belong to some parametric family. In this paper, a semiparametric modeling where the emission distributions are a mixture of parametric distributions is proposed to get a higher flexibility. We show that the classical EM algorithm can be adapted to infer the model parameters. For the initialisation step, starting from a large number of components, a hierarchical method to combine them into the hidden states is proposed. Three likelihoodbased criteria to select the components to be combined are discussed. To estimate the number of hidden states, BIClike criteria are derived. A simulation study is carried out both to determine the best combination between the merging criteria and the model selection criteria and to evaluate the accuracy of classification. The proposed method is also illustrated using a biological dataset from the model plant Arabidopsis thaliana. A R package HMMmix is freely available on the CRAN. 1
Userfriendly power management algorithms
, 2009
"... This article addresses the optimal choice of the waiting period (or timeout) that a device should respect before entering sleep mode, so as to optimize a tradeoff between power consumption and user impact. The optimal timeout is inferred by appropriate statistical modeling of the times between user ..."
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This article addresses the optimal choice of the waiting period (or timeout) that a device should respect before entering sleep mode, so as to optimize a tradeoff between power consumption and user impact. The optimal timeout is inferred by appropriate statistical modeling of the times between user requests. In a test approach, these times are supposed independent, and a constant optimal timeout is inferred accordingly. In a second approach, some dependency is introduced through a hidden Markov chain, which also models specific activity states, like business hours or night periods. This model leads to a statistical framework for computing adaptive optimal timeout values. Different strategies are assessed using real datasets, on the basis of the power consumption, user impact and the frequency of wrong decisions. 1
Nonparametric inference in hidden Markov models via penalized likelihood methods, arXiv
, 2013
"... Hidden Markov models (HMMs) are flexible time series models in which the distributions of the observations depend on unobserved serially correlated states. The statedependent distributions in HMMs are usually taken from some class of parametrically specified distributions. The choice of this class ..."
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Hidden Markov models (HMMs) are flexible time series models in which the distributions of the observations depend on unobserved serially correlated states. The statedependent distributions in HMMs are usually taken from some class of parametrically specified distributions. The choice of this class can be difficult, and an unfortunate choice can have serious consequences for example on state estimates, on forecasts and generally on the resulting model complexity and interpretation, in particular with respect to the number of states. We develop a novel approach for estimating the statedependent distributions of an HMM in a nonparametric way, which is based on the idea of representing the corresponding densities as linear combinations of a large number of standardized Bspline basis functions, imposing a penalty term on nonsmoothness in order to maintain a good balance between goodnessoffit and smoothness. We illustrate the nonparametric modeling approach in a real data application concerned with vertical speeds of a diving beaked whale, demonstrating that compared to parametric counterparts it can lead to models that are more parsimonious in terms of the number of states yet fit the data equally well.