Markov and Semi‐Markov Switching Linear Mixed Models Used to Identify Forest Tree Growth Components

Chaubert-Pereira, Florence; Guédon, Yann; Lavergne, Christian; Trottier, Catherine

doi:10.1111/j.1541-0420.2009.01338.x

Cited by 17 publications

(21 citation statements)

References 27 publications

(40 reference statements)

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“…Thus, we reveal that a similar structural effect as with the error exponent for hidden Markov processes occurs here as well [21], [24]. This result is of immediate interest for inference in HSMM, as it allows extension and application to HSMM of certain algorithms designed for HMM that specifically rely on matrix product representation of the likelihood, see [20], [39]. Further, using the introduced transition matrix for the semi-Markov model, we find explicitly an upper bound on the error exponent, equal to the expected SNR of the process.…”

Section: Introductionsupporting

confidence: 64%

“…Further examples from econometrics are time to currency alignment or time to transactions in stock market [19]. In biometrics, HSMM is used to model forest tree growth and identify individual growth components [20]. In communication systems theory, pulse-duration modulated (PDM) signals for transmitting information encoded into the pulse duration have two possible signal states: the positive value state is a pulse whose duration is proportional to the information symbol to be encoded, and the zero-value state in between any two pulses.…”

Section: Introductionmentioning

confidence: 99%

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Optimal Detection and Error Exponents for Hidden Semi-Markov Models

Bajović

Stanković

et al. 2018

IEEE J. Sel. Top. Signal Process.

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Abstract. We study detection of random signals corrupted by noise that over time switch their values (states) between a finite set of possible values, where the switchings occur at unknown points in time. We model such signals as hidden semi-Markov signals (HSMS), which generalize classical Markov chains by introducing explicit (possibly non-geometric) distribution for the time spent in each state. Assuming two possible signal states and Gaussian noise, we derive optimal likelihood ratio test and show that it has a computationally tractable form of a matrix product, with the number of matrices involved in the product being the number of process observations. The product matrices are independent and identically distributed, constructed by a simple measurement modulation of the sparse semi-Markov model transition matrix that we define in the paper. Using this result, we show that the Neyman-Pearson error exponent is equal to the top Lyapunov exponent for the corresponding random matrices. Using theory of large deviations, we derive a lower bound on the error exponent. Finally, we show that this bound is tight by means of numerical simulations.

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Section: Introductionsupporting

confidence: 64%

Section: Introductionmentioning

confidence: 99%

Optimal Detection and Error Exponents for Hidden Semi-Markov Models

Bajović

Stanković

et al. 2018

IEEE J. Sel. Top. Signal Process.

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“…Now the forward recursion is given by (27) and (29), and the backward recursion by (28), (30) and (25).…”

Section: Computational Complexitymentioning

confidence: 99%

Hidden Semi-Markov Models

2016

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As an extension to the popular hidden Markov model (HMM), a hidden semi-Markov model (HSMM) allows the underlying stochastic process to be a semi-Markov chain. Each state has variable duration and a number of observations being produced while in the state. This makes it suitable for use in a wider range of applications. Its forwardbackward algorithms can be used to estimate/update the model parameters, determine the predicted, filtered and smoothed probabilities, evaluate goodness of an observation sequence fitting to the model, and find the best state sequence of the underlying stochastic process. Since the HSMM was initially introduced in 1980 for machine recognition of speech, it has been applied in thirty scientific and engineering areas, such as speech recognition/synthesis, human activity recognition/prediction, handwriting recognition, functional MRI brain mapping, and network anomaly detection. There are about three hundred papers published in the literature. An overview of HSMMs is presented in this paper, including modelling, inference, estimation, implementation and applications. It first provides a unified description of various HSMMs and discusses the general issues behind them. The boundary conditions of HSMM are extended. Then the conventional models, including the explicit duration, variable transition, and residential time of HSMM, are discussed. Various duration distributions and observation models are presented. Finally, the paper draws an outline of the applications.

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“…However, a strict recursive application of rules leads to self-similar structures and thus, to enhance realism, irregularities may be generated through probabilistic approaches [5,1]. Adjusting stochastic parameters to achieve realistic models requires intensive botanical knowledge [6]. Another approach consists in modelling plant irregularities as a result of the competition for space between the different organs of the plants [7].…”

mentioning

confidence: 99%

Reconstructing Plants in 3D from a Single Image Using Analysis-by-Synthesis

Guénard¹,

Morin²,

Boudon³

et al. 2013

Advances in Visual Computing

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Abstract. Mature computer vision techniques allow the reconstruction of challenging 3D objects from images. However, due to high complexity of plant topology, dedicated methods for generating 3D plant models must be devised. We propose to generate a 3D model of a plant, using an analysis-by-synthesis method mixing information from a single image and a priori knowledge of the plant species. First, our dedicated skeletonisation algorithm generates a possible branching structure from the foliage segmentation. Then, a 3D generative model, based on a parametric model of branching systems that takes into account botanical knowledge is built. The resulting skeleton follows the hierarchical organisation of natural branching structures. An instance of a 3D model can be generated. Moreover, varying parameter values of the generative model (main branching structure of the plant and foliage), we produce a series of candidate models. The reconstruction is improved by selecting the model among these proposals based on a matching criterion with the image. Realistic results obtained on different species of plants illustrate the performance of the proposed method. Fig. 1. On the left, an original image of Ginkgo tree. In the middle, a possible architecture of the branching extracted with our skeletonisation method. On the right, a 3D model of this tree with the same viewpoint.

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Markov and Semi‐Markov Switching Linear Mixed Models Used to Identify Forest Tree Growth Components

Abstract: Markov switching linear mixed models used to identify forest tree growth components.. Biometrics, Wiley, 2010, 66 (3), pp.753-762. 10.1111/j.1541-0420.2009.01338.x. inria-00488100

Cited by 17 publications

References 27 publications

Optimal Detection and Error Exponents for Hidden Semi-Markov Models

Optimal Detection and Error Exponents for Hidden Semi-Markov Models

Hidden Semi-Markov Models

Reconstructing Plants in 3D from a Single Image Using Analysis-by-Synthesis

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