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28
Mixed memory Markov models: decomposing complex stochastic processes as mixtures of simpler ones
, 1998
"... . We study Markov models whose state spaces arise from the Cartesian product of two or more discrete random variables. We show how to parameterize the transition matrices of these models as a convex combinationor mixtureof simpler dynamical models. The parameters in these models admit a simple ..."
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Cited by 62 (1 self)
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. We study Markov models whose state spaces arise from the Cartesian product of two or more discrete random variables. We show how to parameterize the transition matrices of these models as a convex combinationor mixtureof simpler dynamical models. The parameters in these models admit a simple probabilistic interpretation and can be fitted iteratively by an ExpectationMaximization (EM) procedure. We derive a set of generalized BaumWelch updates for factorial hidden Markov models that make use of this parameterization. We also describe a simple iterative procedure for approximately computing the statistics of the hidden states. Throughout, we give examples where mixed memory models provide a useful representation of complex stochastic processes. Keywords: Markov models, mixture models, discrete time series 1. Introduction The modeling of time series is a fundamental problem in machine learning, with widespread applications. These include speech recognition (Rabiner, 1989), natu...
Computer Intrusion: Detecting Masquerades
 Statistical Science
, 2001
"... Masqueraders in computer intrusion detection are people who use somebody else's computer account. We investigate a number of statistical approaches for detecting masqueraders. To evaluate them, we collected UNIX command data from 50 users and then contaminated the data with masqueraders. The experim ..."
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Cited by 58 (1 self)
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Masqueraders in computer intrusion detection are people who use somebody else's computer account. We investigate a number of statistical approaches for detecting masqueraders. To evaluate them, we collected UNIX command data from 50 users and then contaminated the data with masqueraders. The experiment was blinded. We show results from our methods and two approaches from the computer science community.
A Hybrid Highorder Markov Chain Model for Computer Intrusion Detection
, 1999
"... A hybrid model based mostly on a highorder Markovchain and occasionally on an independence model is proposed for pro#ling the commandsequence of a computer user in order to identify a "signature behavior" for that user. Based on the model, an estimation procedure for such a signature behavior driv ..."
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Cited by 20 (3 self)
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A hybrid model based mostly on a highorder Markovchain and occasionally on an independence model is proposed for pro#ling the commandsequence of a computer user in order to identify a "signature behavior" for that user. Based on the model, an estimation procedure for such a signature behavior driven by Maximum Likelihood #ML# considerations is devised. The formal ML estimates are numerically intractable, but the MLoptimization problem can be substituted by a linear inverse problem with positivity constraints #LININPOS#, for which the EM algorithm can be used as an equation solver to produce an approximate MLestimate. A user's commandsequence is then compared to his and others' estimated signaturebehavior in real time, by means of statistical hypothesis testing. A form of the likelihoodratio test is used to test if a given sequence of commands is from the proclaimed user, with the alternative hypothesis being masquerader user. Data from a reallife experiment, conducted at a research lab, is used to assess the method. Key Words: Anomaly Detection; Unix; Mixture Transition Distribution #MTD#; LININPOS; EM. 1
The mixture transition distribution model for highorder Markov chains and nonGaussian time series
 Statistical Science
, 2002
"... Abstract. The mixture transition distribution model (MTD) was introduced in 1985 by Raftery for the modeling of highorder Markov chains with a finite state space. Since then it has been generalized and successfully applied to a range of situations, including the analysis of wind directions, DNA seq ..."
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Cited by 19 (2 self)
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Abstract. The mixture transition distribution model (MTD) was introduced in 1985 by Raftery for the modeling of highorder Markov chains with a finite state space. Since then it has been generalized and successfully applied to a range of situations, including the analysis of wind directions, DNA sequences and social behavior. Here we review the MTD model and the developments since 1985. We first introduce the basic principle and then we present several extensions, including general state spaces and spatial statistics. Following that, we review methods for estimating the model parameters. Finally, a review of different types of applications shows the practical interest of the MTD model. Key words and phrases: Mixture transition distribution (MTD) model, Markov chains, highorder dependences, time series, GMTD model, EM algorithm,
The double chain Markov model
 Comm Stat Theor Meths
, 1999
"... Among the class of discrete time Markovian processes, two models are widely used, the Markov chain and the Hidden Markov Model. A major di erence between these two models lies in the relation between successive outputs of the observed variable. In a visible Markov chain, these are directly correlate ..."
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Cited by 13 (2 self)
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Among the class of discrete time Markovian processes, two models are widely used, the Markov chain and the Hidden Markov Model. A major di erence between these two models lies in the relation between successive outputs of the observed variable. In a visible Markov chain, these are directly correlated while in hidden models they are not. However, in some situations it is possible to observe both a hidden Markov chain and a direct relation between successive observed outputs. Unfortunately, the use of either a visible or a hidden model implies the suppression of one of these hypothesis. This paper presents a Markovian model called the Double Chain Markov Model which takes into account the main features of both visible and hidden models. Its main purpose is the modeling of nonhomogeneous timeseries. It is very exible and can be estimated with traditional methods. The model is applied on a sequence of wind speeds and it appears to
Change Point and Change Curve Modeling in Stochastic Processes and Spatial Statistics
 Journal of Applied Statistical Science
, 1993
"... In simple onedimensional stochastic processes it is feasible to model change points explicitly and to make inference about them. I have found that the Bayesian approach produces results more easily than nonBayesian approaches. It has the advantages of relative technical simplicity, theoretical opt ..."
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Cited by 9 (4 self)
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In simple onedimensional stochastic processes it is feasible to model change points explicitly and to make inference about them. I have found that the Bayesian approach produces results more easily than nonBayesian approaches. It has the advantages of relative technical simplicity, theoretical optimality, and of allowing a formal comparison between abrupt and gradual descriptions of change. When it can be assumed that there is at most one changepoint, this is especially simple. This is illustrated in the context of Poisson point processes. A simple approximation is introduced that is applicable to a wide range of problems in which the change point model can be written as a regression or generalized linear model. When the number of change points is unknown, the Bayesian approach proceeds most naturally by statespace modeling or "hidden Markov chains". The general ideas of this are briefly reviewed, particularly the multiprocess Kalman filter. I then describe the application of these...
Estimation of the Mixture Transition Distribution Model
, 1999
"... This paper introduces a new iterative algorithm for the estimation of the Mixture Transition Distribution model (MTD). It does not require the use of any speci c external optimization procedure and can therefore be programmed in any computing language. Comparisons with previously published results s ..."
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Cited by 9 (4 self)
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This paper introduces a new iterative algorithm for the estimation of the Mixture Transition Distribution model (MTD). It does not require the use of any speci c external optimization procedure and can therefore be programmed in any computing language. Comparisons with previously published results show that this new algorithm performs at least as good or better than other methods. The choice of initial values is also discussed. The MTD model was designed for the modeling of highorder Markov chains and already proved to be a useful tool for the analysis of di erenttypes of timeseries such as wind speeds and wind directions. In this paper, we also propose to use this it for the modeling of onedimensional spatial data. An application using a DNA sequence shows that this approach
Highorder extensions of the double chain Markov model
 Stoch. Models
, 2002
"... The Double Chain Markov Model is a fully Markovian model for the representation of timeseries in random environment. In this article, we showthat it can handle transitions of highorder between both a set of obsevations and a set of hidden states. In order to reduce the number of parameters, each t ..."
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Cited by 9 (4 self)
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The Double Chain Markov Model is a fully Markovian model for the representation of timeseries in random environment. In this article, we showthat it can handle transitions of highorder between both a set of obsevations and a set of hidden states. In order to reduce the number of parameters, each transition matrix can be replaced by a Mixture Transition Model. We provide a complete derivation of the algorithms needed to compute the model. Three applications, the analysis of a sequence of DNA, the song of the wood pewee and the behavior of young monkeys, show that this model is of great interest for the representation of data which can be decomposed
DISTRIBUTIONS ASSOCIATED WITH GENERAL RUNS AND PATTERNS IN HIDDEN MARKOV MODELS
, 706
"... This paper gives a method for computing distributions associated with patterns in the state sequence of a hidden Markov model, conditional on observing all or part of the observation sequence. Probabilities are computed for very general classes of patterns (competing patterns and generalized later p ..."
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Cited by 3 (2 self)
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This paper gives a method for computing distributions associated with patterns in the state sequence of a hidden Markov model, conditional on observing all or part of the observation sequence. Probabilities are computed for very general classes of patterns (competing patterns and generalized later patterns), and thus, the theory includes as special cases results for a large class of problems that have wide application. The unobserved state sequence is assumed to be Markovian with a general order of dependence. An auxiliary Markov chain is associated with the state sequence and is used to simplify the computations. Two examples are given to illustrate the use of the methodology. Whereas the first application is more to illustrate the basic steps in applying the theory, the second is a more detailed application to DNA sequences, and shows that the methods can be adapted to include restrictions related to biological knowledge. 1. Introduction. Hidden Markov models (HMMs) provide a rich structure