Journal articles: 'Variable Order Markov Model'

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Shirgave, Suresh, Prakash Kulkarni, and José Borges. "Semantically Enriched Variable Length Markov Chain Model for Analysis of User Web Navigation Sessions." International Journal of Information Technology & Decision Making 13, no. 04 (July 2014): 721–53. http://dx.doi.org/10.1142/s0219622014500643.

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The rapid growth of the World Wide Web has resulted in intricate Web sites, demanding enhanced user skills to find the required information and more sophisticated tools that are able to generate apt recommendations. Markov Chains have been widely used to generate next-page recommendations; however, accuracy of such models is limited. Herein, we propose the novel Semantic Variable Length Markov Chain Model (SVLMC) that combines the fields of Web Usage Mining and Semantic Web by enriching the Markov transition probability matrix with rich semantic information extracted from Web pages. We show that the method is able to enhance the prediction accuracy relatively to usage-based higher order Markov models and to semantic higher order Markov models based on ontology of concepts. In addition, the proposed model is able to handle the problem of ambiguous predictions. An extensive experimental evaluation was conducted on two real-world data sets and on one partially generated data set. The results show that the proposed model is able to achieve 15–20% better accuracy than the usage-based Markov model, 8–15% better than the semantic ontology Markov model and 7–12% better than semantic-pruned Selective Markov Model. In summary, the SVLMC is the first work proposing the integration of a rich set of detailed semantic information into higher order Web usage Markov models and experimental results reveal that the inclusion of detailed semantic data enhances the prediction ability of Markov models.

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Begleiter, R., R. El-Yaniv, and G. Yona. "On Prediction Using Variable Order Markov Models." Journal of Artificial Intelligence Research 22 (December 1, 2004): 385–421. http://dx.doi.org/10.1613/jair.1491.

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This paper is concerned with algorithms for prediction of discrete sequences over a finite alphabet, using variable order Markov models. The class of such algorithms is large and in principle includes any lossless compression algorithm. We focus on six prominent prediction algorithms, including Context Tree Weighting (CTW), Prediction by Partial Match (PPM) and Probabilistic Suffix Trees (PSTs). We discuss the properties of these algorithms and compare their performance using real life sequences from three domains: proteins, English text and music pieces. The comparison is made with respect to prediction quality as measured by the average log-loss. We also compare classification algorithms based on these predictors with respect to a number of large protein classification tasks. Our results indicate that a ``decomposed'' CTW (a variant of the CTW algorithm) and PPM outperform all other algorithms in sequence prediction tasks. Somewhat surprisingly, a different algorithm, which is a modification of the Lempel-Ziv compression algorithm, significantly outperforms all algorithms on the protein classification problems.

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Tengke Xiong, Shengrui Wang, Qingshan Jiang, and Joshua Zhexue Huang. "A Novel Variable-order Markov Model for Clustering Categorical Sequences." IEEE Transactions on Knowledge and Data Engineering 26, no. 10 (October 2014): 2339–53. http://dx.doi.org/10.1109/tkde.2013.104.

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Cunial, Fabio, Jarno Alanko, and Djamal Belazzougui. "A framework for space-efficient variable-order Markov models." Bioinformatics 35, no. 22 (April 20, 2019): 4607–16. http://dx.doi.org/10.1093/bioinformatics/btz268.

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Abstract Motivation Markov models with contexts of variable length are widely used in bioinformatics for representing sets of sequences with similar biological properties. When models contain many long contexts, existing implementations are either unable to handle genome-scale training datasets within typical memory budgets, or they are optimized for specific model variants and are thus inflexible. Results We provide practical, versatile representations of variable-order Markov models and of interpolated Markov models, that support a large number of context-selection criteria, scoring functions, probability smoothing methods, and interpolations, and that take up to four times less space than previous implementations based on the suffix array, regardless of the number and length of contexts, and up to ten times less space than previous trie-based representations, or more, while matching the size of related, state-of-the-art data structures from Natural Language Processing. We describe how to further compress our indexes to a quantity related to the redundancy of the training data, saving up to 90% of their space on very repetitive datasets, and making them become up to 60 times smaller than previous implementations based on the suffix array. Finally, we show how to exploit constraints on the length and frequency of contexts to further shrink our compressed indexes to half of their size or more, achieving data structures that are a hundred times smaller than previous implementations based on the suffix array, or more. This allows variable-order Markov models to be used with bigger datasets and with longer contexts on the same hardware, thus possibly enabling new applications. Availability and implementation https://github.com/jnalanko/VOMM Supplementary information Supplementary data are available at Bioinformatics online.

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POSCH, STEFAN, JAN GRAU, ANDRE GOHR, IRAD BEN-GAL, ALEXANDER E. KEL, and IVO GROSSE. "RECOGNITION OF CIS-REGULATORY ELEMENTS WITH VOMBAT." Journal of Bioinformatics and Computational Biology 05, no. 02b (April 2007): 561–77. http://dx.doi.org/10.1142/s0219720007002886.

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Variable order Markov models and variable order Bayesian trees have been proposed for the recognition of cis-regulatory elements, and it has been demonstrated that they outperform traditional models such as position weight matrices, Markov models, and Bayesian trees for the recognition of binding sites in prokaryotes. Here, we study to which degree variable order models can improve the recognition of eukaryotic cis-regulatory elements. We find that variable order models can improve the recognition of binding sites of all the studied transcription factors. To ease a systematic evaluation of different model combinations based on problem-specific data sets and allow genomic scans of cis-regulatory elements based on fixed and variable order Markov models and Bayesian trees, we provide the VOMBATserver to the public community.

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Xiao Li, Yuhao Wang, and Yuan Liu. "A Channel Cognitive Method for Local Fading Characteristics using Variable-Order Markov Model." Journal of Communications and Information Sciences 1, no. 2 (2011): 1–12. http://dx.doi.org/10.4156/jcis.vol1.issue2.1.

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Saadani, A., P. Gelpi, and P. Tortelier. "A Variable-Order Markov-Chain-Based Model for Rayleigh Fading and Rake Receiver." IEEE Signal Processing Letters 11, no. 3 (March 2004): 356–58. http://dx.doi.org/10.1109/lsp.2003.822915.

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Qi, Zhang, Wen Guang, Chen Zhixin, Zhou Qin, Xiang Guoqi, Yang Guangchun, and Zhang Xuegang. "Contact stress reliability analysis based on first order second moment for variable hyperbolic circular arc gear." Advances in Mechanical Engineering 14, no. 7 (July 2022): 168781322211112. http://dx.doi.org/10.1177/16878132221111210.

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Aiming at the contact strength reliability of variable hyperbolic circular arc gear, a reliability analysis method for contact strength of variable hyperbolic circular arc gear based on Kriging model and advanced first-order and second-moment algorithm is proposed. Kriging model was used to establish the limit state equation of the contact stress reliability analysis of variable hyperbolic circular arc gear, and the advanced first-order second-moment method was used to analyze the contact stress reliability of variable hyperbolic circular arc gear based on the limit state equation of the contact stress. In order to verify the effectiveness of the proposed algorithm, a Markov Chain Monte Carlo reliability analysis method based on Important Sampling was proposed. Markov Chain and Important Sampling were exploited to improve the accuracy of contact reliability analysis based on Monte Carlo method for variable hyperbolic circular arc gear. The comparison between the analysis results of Markov Chain Monte Carlo with Important Sampling method and first order second moment shows that it is feasible to analyze the reliability of variable hyperbolic circular arc gear by first-order second-moment method.

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Melikov, A. Z., L. A. Ponomarenko, and S. A. Bagirova. "Markov Models of Queueing–Inventory Systems with Variable Order Size." Cybernetics and Systems Analysis 53, no. 3 (May 2017): 373–86. http://dx.doi.org/10.1007/s10559-017-9937-3.

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Kohli, Amit Kumar, Amrita Rai, and Meher Krishna Patel. "Variable Forgetting Factor LS Algorithm for Polynomial Channel Model." ISRN Signal Processing 2011 (December 30, 2011): 1–4. http://dx.doi.org/10.5402/2011/915259.

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Variable forgetting factor (VFF) least squares (LS) algorithm for polynomial channel paradigm is presented for improved tracking performance under nonstationary environment. The main focus is on updating VFF when each time-varying fading channel is considered to be a first-order Markov process. In addition to efficient tracking under frequency-selective fading channels, the incorporation of proposed numeric variable forgetting factor (NVFF) in LS algorithm reduces the computational complexity.

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Nagata, Yuichi. "High-Order Entropy-Based Population Diversity Measures in the Traveling Salesman Problem." Evolutionary Computation 28, no. 4 (December 2020): 595–619. http://dx.doi.org/10.1162/evco_a_00268.

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To maintain the population diversity of genetic algorithms (GAs), we are required to employ an appropriate population diversity measure. However, commonly used population diversity measures designed for permutation problems do not consider the dependencies between the variables of the individuals in the population. We propose three types of population diversity measures that address high-order dependencies between the variables to investigate the effectiveness of considering high-order dependencies. The first is formulated as the entropy of the probability distribution of individuals estimated from the population based on an [Formula: see text]-th--order Markov model. The second is an extension of the first. The third is similar to the first, but it is based on a variable order Markov model. The proposed population diversity measures are incorporated into the evaluation function of a GA for the traveling salesman problem to maintain population diversity. Experimental results demonstrate the effectiveness of the three types of high-order entropy-based population diversity measures against the commonly used population diversity measures.

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Chen, Juan. "A Novel Variable Order Markov Model Based Wireless Service Prediction Algorithm with User Similarity." Journal of Information and Computational Science 12, no. 17 (November 20, 2015): 6267–76. http://dx.doi.org/10.12733/jics20106976.

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Wu, Shih-Lin, Jen-Jee Chen, and Wen-Chiang Chou. "Cell-related location area planning for 4G PCS networks with variable-order Markov model." Journal of Systems and Software 86, no. 10 (October 2013): 2688–99. http://dx.doi.org/10.1016/j.jss.2013.05.031.

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Al-Shatnawi, Mufleh, M. Omair Ahmad, and M. N. S. Swamy. "Prediction of Indel flanking regions in protein sequences using a variable-order Markov model." Bioinformatics 31, no. 1 (August 31, 2014): 40–47. http://dx.doi.org/10.1093/bioinformatics/btu556.

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Apsel, Udi, and Ronen Brafman. "Lifted MEU by Weighted Model Counting." Proceedings of the AAAI Conference on Artificial Intelligence 26, no. 1 (September 20, 2021): 1861–67. http://dx.doi.org/10.1609/aaai.v26i1.8396.

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Recent work in the field of probabilistic inference demonstrated the efficiency of weighted model counting (WMC) enginesfor exact inference in propositional and, very recently, first order models. To date, these methods have not been applied to decision making models, propositional or first order, such as influence diagrams, and Markov decision networks (MDN). In this paper we show how this technique can be applied to such models. First, we show how WMC can be used to solve (propositional) MDNs. Then, we show how this can be extended to handle a first-order model — the Markov Logic Decision Network (MLDN). WMC offers two central benefits: it is a very simple and very efficient technique. This is particularly true for the first-order case, where the WMC approach is simpler conceptually, and, in many cases, more effective computationally than the existing methods for solving MLDNs via first-order variable elimination, or via propositionalization. We demonstrate the above empirically.

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Chen, Haiying, Haiyan Chen, Wei Zhang, Chaodan Yang, and Hongxiu Cui. "Research on Marketing Prediction Model Based on Markov Prediction." Wireless Communications and Mobile Computing 2021 (December 15, 2021): 1–9. http://dx.doi.org/10.1155/2021/4535181.

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Many activities in modern business marketing management are random and repetitive. The marketing effect is constantly influenced by a variety of factors such as changing market supply and demand, customers’ purchase intentions, and national financial policy. As a result, Markov analysis can be used to analyze the status and trend of some variables, that is, to predict the future status and trend of a variable based on its current status and trend, in order to forecast possible changes in the future and take appropriate countermeasures. The mathematical model of product marketing prediction is presented in this paper by establishing the probability matrix of product state transition and analyzing and calculating with the Markov chain, resulting in a practical and reliable theoretical basis for economic prediction. After using the Markov analysis method, a suitable mathematical model can be created based on market investigation and statistics, which is extremely useful for making reasonable predictions about the market’s future development trend and improving marketing effectiveness.

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Meng, Jingxiang. "Comparison of Statistical Estimators for Estimating the Orders of Markov Chains." Journal of Physics: Conference Series 2386, no. 1 (December 1, 2022): 012004. http://dx.doi.org/10.1088/1742-6596/2386/1/012004.

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Abstract High order discrete Markov chain is essential to analyze the dependency structure of data sets. To apply Markov chain correctly, even though the true order is an unknown parameter, statisticians have developed multiple order estimators. It is natural to identify the strongest order estimators under different parameter combinations. Aim for evaluating the performance of estimators, we study four of them in this paper: Akaike information criteria (AIC), Bayesian information criteria (BIC), Maximal fluctuation estimation method (PS), and approximate χ 2 − distribution method (Dk ). We simulated Cr × C transition matrices to generate word-count-based Markov sequences with the most straightforward initial distribution. We found PS and Dk give more accurate discrete Markov order estimation. Although AIC and BIC are commonly applied, their performances are not the most accurate. The accuracy declines approximately exponentially as the Markov model gets more complex, i.e. r ≥ 1 and C ≥ 3. AIC’s accuracy is higher when the Markov chain length is relatively small, but Dk yields a slightly higher accuracy under the same setting. PS give a more reasonable estimation when Markov order is the variable, i.e. 1 ≥ r ≥ 3. Dk gives more reasonable estimations when the length L and alphabet size C are variable, i.e. 150 ≥ L ≥ 800 and 3 ≥ C ≥ 5.

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Herkenrath, Ulrich. "On the uniform ergodicity of Markov processes of order 2." Journal of Applied Probability 40, no. 2 (June 2003): 455–72. http://dx.doi.org/10.1239/jap/1053003556.

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We study the uniform ergodicity of Markov processes (Zn, n ≥ 1) of order 2 with a general state space (Z, 𝒵). Markov processes of order higher than 1 were defined in the literature long ago, but scarcely treated in detail. We take as the basis for our considerations the natural transition probability Q of such a process. A Markov process of order 2 is transformed into one of order 1 by combining two consecutive variables Z2n–1 and Z2n into one variable Yn with values in the Cartesian product space (Z × Z, 𝒵 ⊗ 𝒵). Thus, a Markov process (Yn, n ≥ 1) of order 1 with transition probability R is generated. Uniform ergodicity for the process (Zn, n ≥ 1) is defined in terms of the same property for (Yn, n ≥ 1). We give some conditions on the transition probability Q which transfer to R and thus ensure the uniform ergodicity of (Zn, n ≥ 1). We apply the general results to study the uniform ergodicity of Markov processes of order 2 which arise in some nonlinear time series models and as sequences of smoothed values in sequential smoothing procedures of Markovian observations. As for the time series models, Markovian noise sequences are covered.

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Herkenrath, Ulrich. "On the uniform ergodicity of Markov processes of order 2." Journal of Applied Probability 40, no. 02 (June 2003): 455–72. http://dx.doi.org/10.1017/s0021900200019422.

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We study the uniform ergodicity of Markov processes (Z n , n ≥ 1) of order 2 with a general state space (Z, 𝒵). Markov processes of order higher than 1 were defined in the literature long ago, but scarcely treated in detail. We take as the basis for our considerations the natural transition probability Q of such a process. A Markov process of order 2 is transformed into one of order 1 by combining two consecutive variables Z 2n–1 and Z 2n into one variable Y n with values in the Cartesian product space (Z × Z, 𝒵 ⊗ 𝒵). Thus, a Markov process (Y n , n ≥ 1) of order 1 with transition probability R is generated. Uniform ergodicity for the process (Z n , n ≥ 1) is defined in terms of the same property for (Y n , n ≥ 1). We give some conditions on the transition probability Q which transfer to R and thus ensure the uniform ergodicity of (Z n , n ≥ 1). We apply the general results to study the uniform ergodicity of Markov processes of order 2 which arise in some nonlinear time series models and as sequences of smoothed values in sequential smoothing procedures of Markovian observations. As for the time series models, Markovian noise sequences are covered.

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Wang, Xing, Xinhua Jiang, Lifei Chen, and Yi Wu. "KVLMM: A Trajectory Prediction Method Based on a Variable-Order Markov Model With Kernel Smoothing." IEEE Access 6 (2018): 25200–25208. http://dx.doi.org/10.1109/access.2018.2829545.

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Guseva, Maria, and Andrey Silaev. "Applying Bayesian methods for macroeconomic modeling of business cycle phases." St Petersburg University Journal of Economic Studies 37, no. 2 (2021): 298–317. http://dx.doi.org/10.21638/spbu05.2021.205.

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In the present research, the features of applying two models for estimating macroeconomic dynamic in the USA are investigated: Bayesian vector autoregression and Bayesian vector autoregression with Markov switching. The research goal is to identify periods, structure of fluctuations and the main directions of interaction of the variables (real US GDP and employment) using Bayesian vector autoregression models. Models with Markov chains include many equations (structures). The switching mechanisms between these structures are controlled by an unobservable variable that follows a first-order Markov process. The analyzed variables were taken from the first quarter of 1953 to the third quarter of 2015. The model parameters were estimated on the basis of a prior for the multivariate normal distribution — the inverse Wishart distribution (a generalization of the Minnesota a priori distribution). Basing on the results of the estimation of the two-dimensional model with Markov Switching the average GDP growth rate and expected duration of phases was calculated. The estimated model is acceptable for describing the US economy and with high accuracy describes the probability of being in a particular phase in different periods of time. On the basis of medium-term forecasts, root mean squared errors of the forecast are calculated and a conclusion is made about the most appropriate model. Within the framework of this paper, impulse response functions are built allowing to evaluate how variables in the model react on fluctuations, shocks.

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Kasse, Irwan, Didiharyono Didiharyono, and Maulidina Maulidina. "Metode Markov Chain untuk Menghitung Premi Asuransi pada Pasien Penderita Penyakit Demam Berdarah Dengue." Al-Khwarizmi: Jurnal Pendidikan Matematika dan Ilmu Pengetahuan Alam 7, no. 2 (March 29, 2020): 151–60. http://dx.doi.org/10.24256/jpmipa.v7i2.1251.

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Abstract:This paper discusses the Markov Chain method in calculating insurance premiums for patients with dengue hemorrhagic fever (DHF) at Labuang Baji Hospital. The Markov Chain Model is a method that studies the characteristics of a variable in the present that depends on its properties in the past in an attempt to estimate the properties of these variables in the future. This paper aims to determine the transition probability model for each circumstance using the Markov multistate model and to determine insurance premiums using the Markov Method. Based on the results of research and discussion, obtained a probability transition model matrix with the order 5 x 5. Next calculate the transition rate matrix, calculate the transition opportunity, calculate the density function, and calculate the premium of each event. With a large one-year term life insurance premium paid to patients with Dengue Hemorrhagic Fever (DHF) at each transition opportunity adjusted to the state of each gradient I, II, and III, with the maximum value of the premium paid that is at the state of the gradient I that moves to die with the value Ax.a|04=Rp.1.372.500.. Abstrak:Tulisan ini membahas tentang metode Markov Chain dalam menghitung premi asuransi pada penderita penyakit demam berdarah dengue (DBD) di Rumah Sakit Labuang Baji. Model Markov Chain merupakan salah satu metode yang mengkaji sifat-sifat suatu variabel saat sekarang bergantung pada sifat-sifat variabel di masa terdahulu untuk mengestimasi sifat-sifat variabel tersebut untuk keperluan di masa mendatang. Tulisan ini bertujuan untuk mengetahui model probabilitas transisi dari setiap keadaan dengan menggunakan model multistatus Markov dan untuk menentukan premi Asuransi menggunakan Metode Markov. Berdasarkan hasil penelitian diperoleh model matriks probabilitas transisi berordo 5 x 5 . Selanjutnya menghitung matriks laju transisi, menghitung peluang transisi, menghitung fungsi densitas, dan menghitung premi dari setiap kejadian. Dengan Besar premi asuransi jiwa berjangka satu tahun yang dibayarkan pada pasien Demam Berdarah Dengue (DBD) pada setiap peluang transisi disesuaikan dengan keadaan masing-masing gradiasi I, II, dan III, dengan nilai maksimal premi yang di bayarkan yaitu pada keadaan gradiasi I yang berpindah ke meninggal dengan nilai Ax.a|04=Rp.1.372.500..

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Xia, Ying, Yu Gong, Xu Zhang, and Hae-young Bae. "Location Prediction based on Variable-order Markov Model with Time Feature and User’s Spatio-temporal Rule." Advances in Science, Technology and Engineering Systems Journal 4, no. 2 (2019): 351–56. http://dx.doi.org/10.25046/aj040244.

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BORGES, JOSÉ, and MARK LEVENE. "A COMPARISON OF SCORING METRICS FOR PREDICTING THE NEXT NAVIGATION STEP WITH MARKOV MODEL-BASED SYSTEMS." International Journal of Information Technology & Decision Making 09, no. 04 (July 2010): 547–73. http://dx.doi.org/10.1142/s0219622010003956.

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The problem of predicting the next request during a user's navigation session has been extensively studied. In this context, higher-order Markov models have been widely used to model navigation sessions and to predict the next navigation step, while prediction accuracy has been mainly evaluated with the hit and miss score. We claim that this score, although useful, is not sufficient for evaluating next link prediction models with the aim of finding a sufficient order of the model, the size of a recommendation set, and assessing the impact of unexpected events on the prediction accuracy. Herein, we make use of a variable length Markov model to compare the usefulness of three alternatives to the hit and miss score: the Mean Absolute Error, the Ignorance Score, and the Brier score. We present an extensive evaluation of the methods on real data sets and a comprehensive comparison of the scoring methods.

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Zhu, Yunsheng, Jinxu Chen, Kaifeng Wang, Yong Liu, and Yanting Wang. "Research on Performance Prediction of Highway Asphalt Pavement Based on Grey–Markov Model." Transportation Research Record: Journal of the Transportation Research Board 2676, no. 4 (November 29, 2021): 194–209. http://dx.doi.org/10.1177/03611981211057527.

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Reasonable and accurate forecasts can be used by the highway maintenance management department to determine the best maintenance timing and strategy, which can keep the highway performing well and maximize its social and economic benefits. A Grey–Markov combination model is established in this paper to predict highway pavement performance accurately based on the Grey GM (1, 1) model (a single-variable Grey prediction model with a first-order difference equation) and revised by the Markov model. The advantages of the short-term forecast Grey model and the probabilistic Markov model, which considers the fate of pavement performance prediction, are comprehensively applied to the combined forecasting model. The Grey GM (1, 1), Grey–Markov model and Liu-Yao model are adopted to predict the pavement condition index (PCI) based on the actual PCI values measured in Shanxi, Chongqing, and Shaoguan. The average relative errors of the above three models’ predicted values in Shanxi are 0.73%, 1.18%, and 0.67%, respectively, from 2012 to 2014. Thus, the prediction errors of the three models are relatively close. The average relative errors of the prediction values predicted by the three models are 3.89%, 0.67%, and 0.50%, respectively, from 2015 to 2019. The latter two errors are more minor than the Grey GM (1, 1) model. Two other regions have similar conclusions. The results show that the prediction accuracy of the combination Grey–Markov prediction model established in this paper is feasible to predict asphalt pavement performance in China.

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Zhang, Weibin, Yong Qi, Zhuping Zhou, Salvatore A. Biancardo, and Yinhai Wang. "Method of speed data fusion based on Bayesian combination algorithm and high-order multi-variable Markov model." IET Intelligent Transport Systems 12, no. 10 (December 1, 2018): 1312–21. http://dx.doi.org/10.1049/iet-its.2018.5020.

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Berchtold, André. "The Predictive Power of Transition Matrices." Symmetry 13, no. 11 (November 5, 2021): 2096. http://dx.doi.org/10.3390/sym13112096.

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When working with Markov chains, especially if they are of order greater than one, it is often necessary to evaluate the respective contribution of each lag of the variable under study on the present. This is particularly true when using the Mixture Transition Distribution model to approximate the true fully parameterized Markov chain. Even if it is possible to evaluate each transition matrix using a standard association measure, these measures do not allow taking into account all the available information. Therefore, in this paper, we introduce a new class of so-called "predictive power" measures for transition matrices. These measures address the shortcomings of traditional association measures, so as to allow better estimation of high-order models.

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Paluszkiewicz, Theresa, and Charles F. Marshall. "COMPARISON OF TECHNIQUES FOR FORCING AN OIL SPILL TRAJECTORY MODEL." International Oil Spill Conference Proceedings 1989, no. 1 (February 1, 1989): 547–53. http://dx.doi.org/10.7901/2169-3358-1989-1-547.

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ABSTRACT The Oil Spill Risk Analysis model used by the U.S. Department of the Interior simulates trajectories of hypothetical oil spills on the outer continental shelf. The trajectories are calculated from surface current fields provided by a general circulation model with a superimposed wind-drift simulation. This paper compares two techniques for driving the wind-drift portion of the trajectory model. In this comparison, a statistical model of the wind, utilizing a first-order Markov approach, is used to simulate wind records to drive the model; these results are compared with trajectories forced by the observed winds. The comparison shows that trajectories resulting from the two forcing techniques differ; the trajectories forced by the observed winds are more variable and have directional differences as compared with the trajectories forced by modeled winds. The differences appear to be due to the inability of the first-order Markov approach to simulate wind history and the duration of wind events.

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Zhao, Kun, Hongwei Ding, Kai Ye, and Xiaohui Cui. "A Transformer-Based Hierarchical Variational AutoEncoder Combined Hidden Markov Model for Long Text Generation." Entropy 23, no. 10 (September 29, 2021): 1277. http://dx.doi.org/10.3390/e23101277.

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The Variational AutoEncoder (VAE) has made significant progress in text generation, but it focused on short text (always a sentence). Long texts consist of multiple sentences. There is a particular relationship between each sentence, especially between the latent variables that control the generation of the sentences. The relationships between these latent variables help in generating continuous and logically connected long texts. There exist very few studies on the relationships between these latent variables. We proposed a method for combining the Transformer-Based Hierarchical Variational AutoEncoder and Hidden Markov Model (HT-HVAE) to learn multiple hierarchical latent variables and their relationships. This application improves long text generation. We use a hierarchical Transformer encoder to encode the long texts in order to obtain better hierarchical information of the long text. HT-HVAE’s generation network uses HMM to learn the relationship between latent variables. We also proposed a method for calculating the perplexity for the multiple hierarchical latent variable structure. The experimental results show that our model is more effective in the dataset with strong logic, alleviates the notorious posterior collapse problem, and generates more continuous and logically connected long text.

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Li, RuiChang. "Joint Modeling of User Behaviors Based on Variable-Order Additive Markov Chain for POI Recommendation." Wireless Communications and Mobile Computing 2021 (November 23, 2021): 1–13. http://dx.doi.org/10.1155/2021/4359369.

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The POI recommendation system has become an important means to help people discover attractive and interesting places. Based on our data analysis, we observe that users pay equal attention to conservatism and curiosity. In particular, adopting analysis corresponding to different time intervals, we find that users lean towards old POIs in the short term and look for new POIs with the increase of the time interval. However, existing approaches usually neglect users’ conservatism and curiosity preferences. Therefore, they are confronted with a bottleneck of depicting accurate user needs, making it difficult to improve the recommendation performance further. Besides, we further find that the number of user daily check-ins has uneven distribution, which is not conducive to capture the accurate transition patterns of user behaviors. In light of the above, we design a single POI sequential method. On this basis, we propose a recommendation method of the variable additive Markov chain. We consider the user sequential preferences, especially liking old and pursuing new features. In addition, our model exploits the geographical tendency of user behaviors. Finally, we conduct abundant experiments on four cities in the two real datasets, i.e., Foursquare and Jiepang. The experimental results show its superiority over other competitors.

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Haviv, Avery. "Technical Note—Cyclic Variables and Markov Decision Processes." Operations Research 68, no. 4 (July 2020): 1231–37. http://dx.doi.org/10.1287/opre.2019.1913.

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Markov decision processes are commonly used to model forward-looking behavior. However, cyclic terms, including seasonality, are often omitted from these models because of the increase in computational burden. This paper develops a cyclic value function iteration (CVFI), an adjustment to the standard value function iteration. By updating states in a specific order, CVFI allows cyclic variables to be included in the state space with no increase in the computational cost. This result is proved theoretically and shown to hold closely in Monte Carlo simulations.

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Liu, Zhenpeng, Dewei Miao, Ruilin Li, Yi Liu, and Xiaofei Li. "Cache-Based Privacy Protection Scheme for Continuous Location Query." Entropy 25, no. 2 (January 19, 2023): 201. http://dx.doi.org/10.3390/e25020201.

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Users who initiate continuous location queries are prone to trajectory information leakage, and the obtained query information is not effectively utilized. To address these problems, we propose a continuous location query protection scheme based on caching and an adaptive variable-order Markov model. When a user initiates a query request, we first query the cache information to obtain the required data. When the local cache cannot satisfy the user’s demand, we use a variable-order Markov model to predict the user’s future query location and generate a k-anonymous set based on the predicted location and cache contribution. We perturb the location set using differential privacy, then send the perturbed location set to the location service provider to obtain the service. We cache the query results returned by the service provider to the local device and update the local cache results according to time. By comparing the experiment with other schemes, the proposed scheme in this paper reduces the number of interactions with location providers, improves the local cache hit rate, and effectively ensures the security of the users’ location privacy.

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Barska, Magdalena. "Analysis of demand in steel and iron industry – latent variables model." Przegląd Statystyczny 66, no. 4 (April 30, 2020): 247–69. http://dx.doi.org/10.5604/01.3001.0014.0951.

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Demand in the steel and iron industry is influenced by multiple factors. Not all of them can be identified and measured. The paper presents the results of the analysis of the levels of demand achieved by a selected enterprise from this sector in the years 2010–2014. The aim of the study is to build a hidden Markov model which would reflect the turning points of this demand, thus making it possible to forecast its future levels. The model’s forecasting properties and stability have been examined. A simulation has been carried out that involved generating a high number of series for selected model parameters and checking their properties. This demonstrated that a three-state second order hidden Markov model was most relevant to the purpose of the study. Thanks to the model’s application, it was possible to describe states which could potentially shape the demand. Moreover, taking the transition state into consideration allowed spotting the signal about the upcoming replacement of the growth phase with the decline phase, and vice versa. The presented second order hidden Markov model can serve as an alternative to the traditional methods of the analysis of time series. The forecast generated by the model informs about the shaping of a trend in demand and serves as an indication of the shifts in economic cycles.

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Dalevi, D., D. Dubhashi, and M. Hermansson. "Bayesian classifiers for detecting HGT using fixed and variable order markov models of genomic signatures." Bioinformatics 22, no. 5 (January 10, 2006): 517–22. http://dx.doi.org/10.1093/bioinformatics/btk029.

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Mardiati, Rina, Bambang R Trilaksono, Yudi S Gondokaryono, and Sony S Wibowo. "Motorcycle Movement Model Based on Markov Chain Process in Mixed Traffic." International Journal of Electrical and Computer Engineering (IJECE) 8, no. 5 (October 1, 2018): 3149. http://dx.doi.org/10.11591/ijece.v8i5.pp3149-3157.

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<p>Mixed traffic systems are dynamically complex since there are many parameters and variables that influence the interactions between the different kinds of vehicles. Modeling the behavior of vehicles, especially motorcycle which has erratic behavior is still being developed continuously, especially in developing countries which have heterogeneous traffic. To get a better understanding of motorcycle behavior, one can look at maneuvers performed by drivers. In this research, we tried to build a model of motorcycle movement which only focused on maneuver action to avoid the obstacle along with the trajectories using a Markov Chain approach. In Markov Chain, the maneuver of motorcycle will described by state transition. The state transition model is depend on probability function which will use for determine what action will be executed next. The maneuver of motorcycle using Markov Chain model was validated by comparing the analytical result with the naturalistic data, with similarity is calculated using MSE. In order to know how good our proposed method can describe the maneuver of motorcycle, we try to compare the MSE of the trajectory based on Markov Chain model with those using polynomial approach. The MSE results showed the performance of Markov Chain Model give the smallest MSE which 0.7666 about 0.24 better than 4th order polynomial.</p>

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Ramesh, Nadarajah I., Gayatri Rode, and Christian Onof. "A Cox Process with State-Dependent Exponential Pulses to Model Rainfall." Water Resources Management 36, no. 1 (November 29, 2021): 297–313. http://dx.doi.org/10.1007/s11269-021-03028-6.

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AbstractA point process model based on a class of Cox processes is developed to analyse precipitation data at a point location. The model is constructed using state-dependent exponential pulses that are governed by an unobserved underlying Markov chain. The mathematical formulation of the model where both the arrival rate of the rain cells and the initial pulse depth are determined by the Markov chain is presented. Second-order properties of the rainfall depth process are derived and utilised in model assessment. A method of moment estimation is employed in model fitting. The proposed model is used to analyse 69 years of sub-hourly rainfall data from Germany and 15 years of English rainfall data. The results of the analysis using variants of the proposed model with fixed pulse lifetime and variable pulse duration are presented. The performance of the proposed model, in reproducing second-moment characteristics of the rainfall, is compared with that of two stochastic models where one has exponential pulses and the other has rectangular pulses. The proposed model is found to capture most of the empirical rainfall properties well and outperform the two alternative models considered in our analysis.

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Wang, Yuanhong, Timothy van Bremen, Yuyi Wang, and Ondřej Kuželka. "Domain-Lifted Sampling for Universal Two-Variable Logic and Extensions." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 9 (June 28, 2022): 10070–79. http://dx.doi.org/10.1609/aaai.v36i9.21246.

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Given a first-order sentence ? and a domain size n, how can one sample a model of ? on the domain {1, . . . , n} efficiently as n scales? We consider two variants of this problem: the uniform sampling regime, in which the goal is to sample a model uniformly at random, and the symmetric weighted sampling regime, in which models are weighted according to the number of groundings of each predicate appearing in them. Solutions to this problem have applications to the scalable generation of combinatorial structures, as well as sampling in several statistical-relational models such as Markov logic networks and probabilistic logic programs. In this paper, we identify certain classes of sentences that are domain-liftable under sampling, in the sense that they admit a sampling algorithm that runs in time polynomial in n. In particular, we prove that every sentence of the form ∀x∀y: ?(x, y) for some quantifier-free formula ?(x,y) is domain-liftable under sampling. We then further show that this result continues to hold in the presence of one or more cardinality constraints as well as a single tree axiom constraint.

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Friedmann, Roberto, and Richard Fox. "On the Internal Organization of Consumers' Cognitive Schemata." Psychological Reports 65, no. 1 (August 1989): 115–26. http://dx.doi.org/10.2466/pr0.1989.65.1.115.

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An operational definition for internal-based versus external-based schema variables via the tangible versus intangible dichotomy is provided. Using strings of one-word associations made in response to a verbal stimulus, the stochastic structure associated with the use of these variables is investigated. Analysis shows that a first-order Markov chain model which allows for dependence between two consecutive schema variables is more appropriate than a Bernoulli model in the description of the internal organization of cognitive schemata. The phenomena of “chunking” and tangible versus intangible dominance are expressed in the context of the parameters associated with a first-order Markov chain.

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Tong, You Cheng, Yang Zhang, and Jun Zhou Yao. "Texture Segmentation of Jacquard Fabric Image Based on Multiresolution Markov Random Field." Applied Mechanics and Materials 101-102 (September 2011): 496–99. http://dx.doi.org/10.4028/www.scientific.net/amm.101-102.496.

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In order to develop an automated segmentation system for jacquard fabric images, a new approach based on MRMRF algorithm with variable weighing parameter is proposed in this paper. Firstly the variable weighting parameter different to the one in traditional MRMRF is described, which can provide a more accurate vector. The next step is MAP estimation and the model for texture segmentation. During this iterative process the initial value is big enough to learn more accurate parameters of feature energy. With the iterative number going on, the value will decrease and stop decreasing when the iterative number comes to some degree. Lastly the experiment results show that the new approach works better than the traditional method with constant weighing parameter.

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Wanke, Peter, Otávio Henrique dos Santos Figueiredo, and Jorge Junio Moreira Antunes. "Unveiling endogeneity and temporal dependence between tourism revenues/expenditures and macroeconomic variables in Brazil: A stochastic hidden Markov model approach." Tourism Economics 25, no. 1 (July 12, 2018): 3–21. http://dx.doi.org/10.1177/1354816618787578.

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Thus far, a comprehensive analysis on the feedback processes that may exist between macroeconomic variables and tourism activity in Brazil is still missing. This article fills this literature gap by analyzing the endogenous and temporally dependent pattern between Brazilian monthly tourism revenue/expenditures and macroeconomic variables over 20 years. A novel stochastic hidden Markov model approach reveals the feedback processes that exist between them. While tourism revenues are autocorrelated and impacted by gross domestic product (GDP) growth, tourism expenditures are detached from any macroeconomic variable, but are rather directly dependent on tourism revenues past performance, which also exert an impact on exchange rates and GDP growth, thus indirectly benefiting tourism expenditures abroad. Policy implications in terms of a specific tourism exchange rate for Brazil are derived in order to sustain tourism expenditures apart from tourism revenue flows.

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Wang, Xi Jie, and Xiao Fan Zhao. "Texture Image Segmentation Based on MRMRF in Contourlet Domain." Advanced Materials Research 532-533 (June 2012): 732–37. http://dx.doi.org/10.4028/www.scientific.net/amr.532-533.732.

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This paper presents a new multi-resolution Markov random field model in Contourlet domain for unsupervised texture image segmentation. In order to make full use of the merits of Contourlet transformation, we introduce the taditional MRMRF model into Contourlet domain, in a manner of variable interation between two components in the tradtional MRMRF model. Using this method, the new model can automatically estimate model parameters and produce accurate unsupervised segmentation results. The results obtained on synthetic texture images and remote sensing images demonstrate that a better segmentation is achieved by our model than the traditional MRMRF model.

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Muhirwa, J. P., S. I. Mbalawata, and V. G. Masanja. "Markov Chain Monte Carlo Analysis of the Variable-Volume Exothermic Model for a Continuously Stirred Tank Reactor." Engineering, Technology & Applied Science Research 11, no. 2 (April 11, 2021): 6919–29. http://dx.doi.org/10.48084/etasr.3962.

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In this paper, a variable-volume Continuously Stirred Tank Reactor (CSTR) deterministic exothermic model has been formulated based on the Reynold Transport Theorem. The numerical analysis of the formulated model and the identifiability of its physical parameters are done by using the least squares and the Delayed-Rejection Adaptive Metropolis (DRAM) method. The least square estimates provide the prior information for the DRAM method. The overall numerical results show that the model gives an insight in describing the dynamics of CSTR processes, and 14 parameters of the CSTR are well identified through DRAM convergence diagnostic tests, such as trace, scatter, autocorrelation, histograms, and marginal density plots. Global sensitivity analysis was further performed, by using the partial rank correlation coefficients obtained from the Latin hypercube sampling method, in order to study and quantify the impact of estimated parameters, uncertainties on the model outputs. The results showed that 7 among the 14 estimated model parameters are very sensitive to the model outcomes and so those parameters need to be handled and treated carefully.

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FRANK, T. D. "COLLECTIVE BEHAVIOR OF BIOPHYSICAL SYSTEMS WITH THERMODYNAMIC FEEDBACK LOOPS: A CASE STUDY FOR A NONLINEAR MARKOV MODEL — THE TAKATSUJI SYSTEM." Modern Physics Letters B 25, no. 08 (March 30, 2011): 551–68. http://dx.doi.org/10.1142/s0217984911025845.

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We study order–disorder transitions and the emergence of collective behavior using a particular mean field model: the dynamic Takatsuji system. This model satisfies linear non-equilibrium thermodynamics and can be described in terms of a nonlinear Markov process defined by a nonlinear Fokker–Planck equation, that is, an evolution equation that is nonlinear with respect to its probability density. We discuss quantitatively the impact of a feedback loop that involves a macroscopic, thermodynamic variable. We demonstrate by means of semi-analytical methods and numerical simulations that the feedback loop increases the magnitude of order, increases the gap between the free energy of the ordered and disordered states, and increases the maximal rate of entropy production that can be observed during the order–disorder transition.

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Nuijten, Mark J. C., and Pieter H. A. J. M. Van Gelder. "A Concise Equation That Captures the Essential Elements of One-Way Sensitivity Analyses in Health Economic Models." Medical Decision Making 31, no. 4 (January 20, 2011): 642–49. http://dx.doi.org/10.1177/0272989x10393975.

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Objective: Sensitivity analyses are often performed on only a limited number of variables without justification of the choice of variables and range of each variable. External parties such as health authorities are increasingly requiring submission of the actual model, often in order to test the robustness of the outcomes of the model by performing additional sensitivity analyses. The objective of this work was to develop an alternative method to capture the critical issues of a sensitivity analysis in a health economic model, especially regarding the selection of variables and determining the range for each variable. Apart from external parties such as health authorities, journal readers who want to perform their own sensitivity analysis but do not have access to the model may find this useful. Methods and Results: Statistical methods based on Markov chain modeling and regression analysis, using the framework of the Taylor series expansion around a point, are used to derive an equation for 1-way sensitivity analyses. In particular, equations for costs and effects are being developed, from which the cost-effectiveness ratio is built. The article shows the feasibility of such equations for the execution of 1-way sensitivity analyses. Conclusion: An equation that can be derived in the manner described in this article provides a substantial amount of information. The inclusion of such an equation in a report may increase transparency of the reporting of outcomes of health economic models.

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Lamine, Benrais, and Baha Nadia. "Object-Based Scene Classification Modeled by Hidden Markov Models Architecture." International Journal of Cognitive Informatics and Natural Intelligence 15, no. 4 (October 2021): 1–30. http://dx.doi.org/10.4018/ijcini.20211001.oa6.

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Multiclass classification problems such as document classification, medical diagnosis or scene classification are very challenging to address due to similarities between mutual classes. The use of reliable tools is necessary to get good classification results. This paper addresses the scene classification problem using objects as attributes. The process of classification is modeled by a famous mathematical tool: The Hidden Markov Models. We introduce suitable relations that scale the parameters of the Hidden Markov Model into variables of scene classification. The construction of Hidden Markov Chains is supported with weight measures and sorting functions. Lastly, inference algorithms extract most suitable scene categories from the Discrete Markov Chain. A parallelism approach constructs several Discrete Markov Chains in order to improve the accuracy of the classification process. We provide numerous tests on different datasets and compare classification accuracies with some state of the art methods. The proposed approach distinguishes itself by outperforming the other.

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Et.al, Dr R. Rooba. "Webpage Recommendation System Based on the Social Media Semantic Details of the Website." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 6 (April 10, 2021): 237–43. http://dx.doi.org/10.17762/turcomat.v12i6.1358.

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The web page recommendation is generated by using the navigational history from web server log files. Semantic Variable Length Markov Chain Model (SVLMC) is a web page recommendation system used to generate recommendation by combining a higher order Markov model with rich semantic data. The problem of state space complexity and time complexity in SVLMC was resolved by Semantic Variable Length confidence pruned Markov Chain Model (SVLCPMC) and Support vector machine based SVLCPMC (SSVLCPMC) meth-ods respectively. The recommendation accuracy was further improved by quickest change detection using Kullback-Leibler Divergence method. In this paper, socio semantic information is included with the similarity score which improves the recommendation accuracy. The social information from the social websites such as twitter is considered for web page recommendation. Initially number of web pages is collected and the similari-ty between web pages is computed by comparing their semantic information. The term frequency and inverse document frequency (tf-idf) is used to produce a composite weight, the most important terms in the web pages are extracted. Then the Pointwise Mutual Information (PMI) between the most important terms and the terms in the twitter dataset are calculated. The PMI metric measures the closeness between the twitter terms and the most important terms in the web pages. Then this measure is added with the similarity score matrix to provide the socio semantic search information for recommendation generation. The experimental results show that the pro-posed method has better performance in terms of prediction accuracy, precision, F1 measure, R measure and coverage.

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Wang, Weiwei, and Xiaoping Hu. "Pricing Israeli Option with Time-changed Compensation by an FFT-Based High-order Multinomial Tree in Lévy Markets." Computational Intelligence and Neuroscience 2022 (June 29, 2022): 1–8. http://dx.doi.org/10.1155/2022/9682292.

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The problem for pricing the Israel option with time-changed compensation was studied based on the high-order recombined multinomial tree by using a fast Fourier transform to approximate a Lévy process. First, the Lévy option pricing model and Fourier transform are introduced. Then, a network model based on FFT (Markov chain) is presented. After that, an FFT-based multinomial tree construction method is given to solve the problem of difficult parameter estimation when approximating the Lévy process with high-order multinomial trees. It is proved that the discrete random variables corresponding to the multinomial tree converge to the Lévy-distributed continuous random variable. Next, an algorithm based on a reverse recursion algorithm for pricing the Israel option with time-changed compensation was presented. Finally, an example was illustrated, and the relationship between the price of the Israel option and the time-changed compensation was discussed. The results show that the method of constructing a high-order recombined multinomial tree based on FFT has very high calculation precision and calculation speed, which can solve the problem of traditional risk-neutral multinomial tree construction, and it is a promising pricing method for pricing Israel options.

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De Nijs, Roderick Sebastiaan, Christian Landsiedel, Dirk Wollherr, and Martin Buss. "Quadratization and Roof Duality of Markov Logic Networks." Journal of Artificial Intelligence Research 55 (March 25, 2016): 685–714. http://dx.doi.org/10.1613/jair.5023.

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This article discusses the quadratization of Markov Logic Networks, which enables efficient approximate MAP computation by means of maximum flows. The procedure relies on a pseudo-Boolean representation of the model, and allows handling models of any order. The employed pseudo-Boolean representation can be used to identify problems that are guaranteed to be solvable in low polynomial-time. Results on common benchmark problems show that the proposed approach finds optimal assignments for most variables in excellent computational time and approximate solutions that match the quality of ILP-based solvers.

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De Blasis, Riccardo, Giovanni Batista Masala, and Filippo Petroni. "A Multivariate High-Order Markov Model for the Income Estimation of a Wind Farm." Energies 14, no. 2 (January 12, 2021): 388. http://dx.doi.org/10.3390/en14020388.

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The energy produced by a wind farm in a given location and its associated income depends both on the wind characteristics in that location—i.e., speed and direction—and the dynamics of the electricity spot price. Because of the evidence of cross-correlations between wind speed, direction and price series and their lagged series, we aim to assess the income of a hypothetical wind farm located in central Italy when all interactions are considered. To model these cross and auto-correlations efficiently, we apply a high-order multivariate Markov model which includes dependencies from each time series and from a certain level of past values. Besides this, we used the Raftery Mixture Transition Distribution model (MTD) to reduce the number of parameters to get a more parsimonious model. Using data from the MERRA-2 project and from the electricity market in Italy, we estimate the model parameters and validate them through a Monte Carlo simulation. The results show that the simulated income faithfully reproduces the empirical income and that the multivariate model also closely reproduces the cross-correlations between the variables. Therefore, the model can be used to predict the income generated by a wind farm.

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Zufryden, Fred S. "Multibrand Transition Probabilities as a Function of Explanatory Variables: Estimation by a Least-Squares-Based Approach." Journal of Marketing Research 23, no. 2 (May 1986): 177–83. http://dx.doi.org/10.1177/002224378602300210.

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A model is formulated to express the relationship between first-order Markov transition probabilities for a multibrand market and explanatory variables. The author shows that the parameters of the model can be estimated through a proposed restricted weighted least squares procedure. An empirical implementation of the estimation procedure illustrates the structure, goodness of fit, and predictive validity of the proposed model.

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Journal articles on the topic 'Variable Order Markov Model'

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