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Journal articles on the topic 'Robbins-Monro algorithm'

Author: Grafiati

Published: 21 September 2024

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1

Moler, José A., Fernando Plo, and Miguel San Miguel. "Adaptive designs and Robbins–Monro algorithm." Journal of Statistical Planning and Inference 131, no. 1 (April 2005): 161–74. http://dx.doi.org/10.1016/j.jspi.2003.12.018.

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2

Wardi, Y. "On a proof of a Robbins-Monro algorithm." Journal of Optimization Theory and Applications 64, no. 1 (January 1990): 217. http://dx.doi.org/10.1007/bf00940033.

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3

Lin, Siming, and Jennie Si. "Weight-Value Convergence of the SOM Algorithm for Discrete Input." Neural Computation 10, no. 4 (May 1, 1998): 807–14. http://dx.doi.org/10.1162/089976698300017485.

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Some insights on the convergence of the weight values of the self-organizing map (SOM) to a stationary state in the case of discrete input are provided. The convergence result is obtained by applying the Robbins-Monro algorithm and is applicable to input-output maps of any dimension.

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4

Moser, Barry Kurt, and Melinda H. McCann. "Algorithm AS 316: A Robbins-Monro-based Sequential Procedure." Journal of the Royal Statistical Society: Series C (Applied Statistics) 46, no. 3 (1997): 388–99. http://dx.doi.org/10.1111/1467-9876.00078.

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5

El Moumen, AbdelKader, Salim Benslimane, and Samir Rahmani. "Robbins–Monro Algorithm with $$\boldsymbol{\psi}$$-Mixing Random Errors." Mathematical Methods of Statistics 31, no. 3 (September 2022): 105–19. http://dx.doi.org/10.3103/s1066530722030024.

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6

XU, ZI, YINGYING LI, and XINGFANG ZHAO. "SIMULATION-BASED OPTIMIZATION BY NEW STOCHASTIC APPROXIMATION ALGORITHM." Asia-Pacific Journal of Operational Research 31, no. 04 (August 2014): 1450026. http://dx.doi.org/10.1142/s0217595914500262.

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This paper proposes one new stochastic approximation algorithm for solving simulation-based optimization problems. It employs a weighted combination of two independent current noisy gradient measurements as the iterative direction. It can be regarded as a stochastic approximation algorithm with a special matrix step size. The almost sure convergence and the asymptotic rate of convergence of the new algorithm are established. Our numerical experiments show that it outperforms the classical Robbins–Monro (RM) algorithm and several other existing algorithms for one noisy nonlinear function minimization problem, several unconstrained optimization problems and one typical simulation-based optimization problem, i.e., (s, S)-inventory problem.

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7

Cai, Li. "Metropolis-Hastings Robbins-Monro Algorithm for Confirmatory Item Factor Analysis." Journal of Educational and Behavioral Statistics 35, no. 3 (June 2010): 307–35. http://dx.doi.org/10.3102/1076998609353115.

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8

Chen, Han-Fu. "Stochastic approximation with non-additive measurement noise." Journal of Applied Probability 35, no. 2 (June 1998): 407–17. http://dx.doi.org/10.1239/jap/1032192856.

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The Robbins–Monro algorithm with randomly varying truncations for measurements with non-additive noise is considered. Assuming that the function under observation is locally Lipschitz-continuous in its first argument and that the noise is a φ-mixing process, strong consistency of the estimate is shown. Neither growth rate restriction on the function, nor the decreasing rate of the mixing coefficients are required.

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9

Chen, Han-Fu. "Stochastic approximation with non-additive measurement noise." Journal of Applied Probability 35, no. 02 (June 1998): 407–17. http://dx.doi.org/10.1017/s0021900200015035.

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The Robbins–Monro algorithm with randomly varying truncations for measurements with non-additive noise is considered. Assuming that the function under observation is locally Lipschitz-continuous in its first argument and that the noise is a φ-mixing process, strong consistency of the estimate is shown. Neither growth rate restriction on the function, nor the decreasing rate of the mixing coefficients are required.

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10

Buckland, S. T., and P. H. Garthwaite. "Algorithm AS 259: Estimating Confidence Intervals by the Robbins-Monro Search Process." Applied Statistics 39, no. 3 (1990): 413. http://dx.doi.org/10.2307/2347401.

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11

Qi, Anna, Lihua Yang, and Chao Huang. "Convergence of Markovian stochastic approximation for Markov random fields with hidden variables." Stochastics and Dynamics 20, no. 05 (November 18, 2019): 2050029. http://dx.doi.org/10.1142/s021949372050029x.

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This paper studies the convergence of the stochastic algorithm of the modified Robbins–Monro form for a Markov random field (MRF), in which some of the nodes are clamped to be observed variables while the others are hidden ones. Based on the theory of stochastic approximation, we propose proper assumptions to guarantee the Hölder regularity of both the update function and the solution of the Poisson equation. Under these assumptions, it is proved that the control parameter sequence is almost surely bounded and accordingly the algorithm converges to the stable point of the log-likelihood function with probability [Formula: see text].

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12

Barczy, Mátyás, Ábris Nagy, Csaba Noszály, and Csaba Vincze. "A Robbins–Monro-type algorithm for computing global minimizer of generalized conic functions." Optimization 64, no. 9 (May 19, 2014): 1999–2020. http://dx.doi.org/10.1080/02331934.2014.919499.

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13

Chen, Han-Fu, Lei Guo, and Ai-Jun Gao. "Convergence and robustness of the Robbins-Monro algorithm truncated at randomly varying bounds." Stochastic Processes and their Applications 27 (1987): 217–31. http://dx.doi.org/10.1016/0304-4149(87)90039-1.

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14

Cai, Li. "High-dimensional Exploratory Item Factor Analysis by A Metropolis–Hastings Robbins–Monro Algorithm." Psychometrika 75, no. 1 (July 28, 2009): 33–57. http://dx.doi.org/10.1007/s11336-009-9136-x.

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15

Gahbiche, Mouna, and Mariane Pelletier. "On the estimation of the asymptotic covariance matrix for the averaged Robbins–Monro algorithm." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 331, no. 3 (August 2000): 255–60. http://dx.doi.org/10.1016/s0764-4442(00)01595-0.

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16

Liu, Chen-Wei, Björn Andersson, and Anders Skrondal. "A Constrained Metropolis–Hastings Robbins–Monro Algorithm for Q Matrix Estimation in DINA Models." Psychometrika 85, no. 2 (June 2020): 322–57. http://dx.doi.org/10.1007/s11336-020-09707-4.

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17

Krasulina, T. P., and Yu O. Yatel. "A probability estimate for not exceeding the unknown threshold by the Robbins-Monro algorithm." Automation and Remote Control 66, no. 3 (March 2005): 422–26. http://dx.doi.org/10.1007/s10513-005-0071-8.

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18

Zhao, Wenxiao. "An Introduction to Development of Centralized and Distributed Stochastic Approximation Algorithm with Expanding Truncations." Algorithms 14, no. 6 (May 31, 2021): 174. http://dx.doi.org/10.3390/a14060174.

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The stochastic approximation algorithm (SAA), starting from the pioneer work by Robbins and Monro in 1950s, has been successfully applied in systems and control, statistics, machine learning, and so forth. In this paper, we will review the development of SAA in China, to be specific, the stochastic approximation algorithm with expanding truncations (SAAWET) developed by Han-Fu Chen and his colleagues during the past 35 years. We first review the historical development for the centralized algorithm including the probabilistic method (PM) and the ordinary differential equation (ODE) method for SAA and the trajectory-subsequence method for SAAWET. Then, we will give an application example of SAAWET to the recursive principal component analysis. We will also introduce the recent progress on SAAWET in a networked and distributed setting, named the distributed SAAWET (DSAAWET).

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19

Heidergott, Bernd. "A weak derivative approach to optimization of threshold parameters in a multicomponent maintenance system." Journal of Applied Probability 38, no. 2 (June 2001): 386–406. http://dx.doi.org/10.1239/jap/996986751.

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We consider a multicomponent maintenance system controlled by an age replacement policy: when one of the components fails, it is immediately replaced; all components older than a threshold age θ are preventively replaced. Costs are associated with each maintenance action, such as replacement after failure or preventive replacement. We derive a weak derivative estimator for the derivative of the cost performance with respect to θ. The technique is quite general and can be applied to many other threshold optimization problems in maintenance. The estimator is easy to implement and considerably increases the efficiency of a Robbins-Monro type of stochastic approximation algorithm. The paper is self-contained in the sense that it includes a proof of the correctness of the weak derivative estimation algorithm.

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20

Heidergott, Bernd. "A weak derivative approach to optimization of threshold parameters in a multicomponent maintenance system." Journal of Applied Probability 38, no. 02 (June 2001): 386–406. http://dx.doi.org/10.1017/s0021900200019926.

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We consider a multicomponent maintenance system controlled by an age replacement policy: when one of the components fails, it is immediately replaced; all components older than a threshold age θ are preventively replaced. Costs are associated with each maintenance action, such as replacement after failure or preventive replacement. We derive a weak derivative estimator for the derivative of the cost performance with respect to θ. The technique is quite general and can be applied to many other threshold optimization problems in maintenance. The estimator is easy to implement and considerably increases the efficiency of a Robbins-Monro type of stochastic approximation algorithm. The paper is self-contained in the sense that it includes a proof of the correctness of the weak derivative estimation algorithm.

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21

Fermin, Lisandro Javier, Ricardo Rios, and Luis Angel Rodriguez. "A Robbins-Monro Algorithm for Non-Parametric Estimation of NAR Process with Markov Switching: Consistency." Journal of Time Series Analysis 38, no. 6 (April 20, 2017): 809–37. http://dx.doi.org/10.1111/jtsa.12237.

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22

Godichon-Baggioni, Antoine, and Bruno Portier. "An averaged projected Robbins-Monro algorithm for estimating the parameters of a truncated spherical distribution." Electronic Journal of Statistics 11, no. 1 (2017): 1890–927. http://dx.doi.org/10.1214/17-ejs1276.

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23

Monroe, Scott, and Li Cai. "Estimation of a Ramsay-Curve Item Response Theory Model by the Metropolis–Hastings Robbins–Monro Algorithm." Educational and Psychological Measurement 74, no. 2 (September 3, 2013): 343–69. http://dx.doi.org/10.1177/0013164413499344.

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24

Montes, Francisco, and Jorge Mateu. "On the MLE for a spatial point pattern." Advances in Applied Probability 28, no. 2 (June 1996): 339. http://dx.doi.org/10.1017/s0001867800048382.

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Parameter estimation for a two-dimensional point pattern is difficult because most of the available stochastic models have intractable likelihoods ([2]). An exception is the class of Gibbs or Markov point processes ([1], [5]), where the likelihood typically forms an exponential family and is given explicitly up to a normalising constant. However, the latter is not known analytically, so parameter estimates must be based on approximations ([3], [6], [7]). In this paper we present comparisons amongst the different techniques available in the literature to obtain an approximation of the maximum likelihood estimate (MLE). Two stochastic methods are specifically illustrated: a Newton-Raphson algorithm ([7]) and the Robbins-Monro procedure ([8]). We use a very simple point process model, the Strauss process ([4]), to test and compare those approximations.

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25

Slaoui, Y., and A. Jmaei. "Recursive and non-recursive regression estimators using Bernstein polynomials." Theory of Stochastic Processes 26(42), no. 1 (December 27, 2022): 60–95. http://dx.doi.org/10.37863/tsp-2899660400-77.

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If a regression function has a bounded support, the kernel estimates often exceed the boundaries and are therefore biased on and near these limits. In this paper, we focus on mitigating this boundary problem. We apply Bernstein polynomials and the Robbins-Monro algorithm to construct a non-recursive and recursive regression estimator. We study the asymptotic properties of these estimators, and we compare them with those of the Nadaraya-Watson estimator and the generalized Révész estimator introduced by [21]. In addition, through some simulation studies, we show that our non-recursive estimator has the lowest integrated root mean square error (ISE) in most of the considered cases. Finally, using a set of real data, we demonstrate how our non-recursive and recursive regression estimators can lead to very satisfactory estimates, especially near the boundaries.

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26

Yang, Ji Seung, and Li Cai. "Estimation of Contextual Effects Through Nonlinear Multilevel Latent Variable Modeling With a Metropolis–Hastings Robbins–Monro Algorithm." Journal of Educational and Behavioral Statistics 39, no. 6 (December 2014): 550–82. http://dx.doi.org/10.3102/1076998614559972.

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27

Bashkov, Bozhidar M., and Christine E. DeMars. "Examining the Performance of the Metropolis–Hastings Robbins–Monro Algorithm in the Estimation of Multilevel Multidimensional IRT Models." Applied Psychological Measurement 41, no. 5 (February 1, 2017): 323–37. http://dx.doi.org/10.1177/0146621616688923.

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The purpose of this study was to examine the performance of the Metropolis–Hastings Robbins–Monro (MH-RM) algorithm in the estimation of multilevel multidimensional item response theory (ML-MIRT) models. The accuracy and efficiency of MH-RM in recovering item parameters, latent variances and covariances, as well as ability estimates within and between clusters (e.g., schools) were investigated in a simulation study, varying the number of dimensions, the intraclass correlation coefficient, the number of clusters, and cluster size, for a total of 24 conditions. Overall, MH-RM performed well in recovering the item, person, and group-level parameters of the model. Ratios of the empirical to analytical standard errors indicated that the analytical standard errors reported in flexMIRT were somewhat overestimated for the cluster-level ability estimates, a little too large for the person-level ability estimates, and essentially accurate for the other parameters. Limitations of the study, implications for educational measurement practice, and directions for future research are offered.

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28

Findley, David F. "Convergence of a Robbins-Monro Algorithm for Recursive Estimation with Non-Monotone Weights for a Function with a Restricted Domain and Multiple Zeros." Calcutta Statistical Association Bulletin 56, no. 1-4 (March 2005): 1–15. http://dx.doi.org/10.1177/0008068320050501.

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Summary Convergence properties are established for the output of a deterministic Robbins- Monro recursion whose function can have singularities and multiple zeros. Our analysis is built largely on slight adaptations of some lemmas and proofs of Fradkov published only in an untranslated Russian monograph (Derevitzkii and Fradkov , 1981). A gap in Fradkov's proof of the final lemma is fixed but only for the scalar case. Our results can be applied to results of Cantor (2001) to establish the convergence of two well-known time series model recursive estimation schemes in the case of an incorrect moving average model. For such models, it is known that maximum likelihood estimates can converge w .p.1 to a set of values rather than to a single value. When the limit set is finite, our results show that , on a given realization of the time series, the (recursive) estimates will converge to single value. This is the first result establishing that estimates of a moving average coefficient do not oscillate forever among different limit set values when there are more than one.

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29

Li, Menglin, Xueqiang Gu, Chengyi Zeng, and Yuan Feng. "Feasibility Analysis and Application of Reinforcement Learning Algorithm Based on Dynamic Parameter Adjustment." Algorithms 13, no. 9 (September 22, 2020): 239. http://dx.doi.org/10.3390/a13090239.

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Reinforcement learning, as a branch of machine learning, has been gradually applied in the control field. However, in the practical application of the algorithm, the hyperparametric approach to network settings for deep reinforcement learning still follows the empirical attempts of traditional machine learning (supervised learning and unsupervised learning). This method ignores part of the information generated by agents exploring the environment contained in the updating of the reinforcement learning value function, which will affect the performance of the convergence and cumulative return of reinforcement learning. The reinforcement learning algorithm based on dynamic parameter adjustment is a new method for setting learning rate parameters of deep reinforcement learning. Based on the traditional method of setting parameters for reinforcement learning, this method analyzes the advantages of different learning rates at different stages of reinforcement learning and dynamically adjusts the learning rates in combination with the temporal-difference (TD) error values to achieve the advantages of different learning rates in different stages to improve the rationality of the algorithm in practical application. At the same time, by combining the Robbins–Monro approximation algorithm and deep reinforcement learning algorithm, it is proved that the algorithm of dynamic regulation learning rate can theoretically meet the convergence requirements of the intelligent control algorithm. In the experiment, the effect of this method is analyzed through the continuous control scenario in the standard experimental environment of ”Car-on-The-Hill” of reinforcement learning, and it is verified that the new method can achieve better results than the traditional reinforcement learning in practical application. According to the model characteristics of the deep reinforcement learning, a more suitable setting method for the learning rate of the deep reinforcement learning network proposed. At the same time, the feasibility of the method has been proved both in theory and in the application. Therefore, the method of setting the learning rate parameter is worthy of further development and research.

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30

Arouna, Bouhari. "Robbins–Monro algorithms and variance reduction in finance." Journal of Computational Finance 7, no. 2 (2003): 35–61. http://dx.doi.org/10.21314/jcf.2003.111.

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31

Garthwaite, P. H., Y. Fan, and S. A. Sisson. "Adaptive optimal scaling of Metropolis–Hastings algorithms using the Robbins–Monro process." Communications in Statistics - Theory and Methods 45, no. 17 (July 5, 2016): 5098–111. http://dx.doi.org/10.1080/03610926.2014.936562.

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32

Qian-Yu Tang, Han-Fu Chen, and Zeng-Jin Han. "Convergence rates of perturbation-analysis-Robbins-Monro-single-run algorithms for single server queues." IEEE Transactions on Automatic Control 42, no. 10 (1997): 1442–47. http://dx.doi.org/10.1109/9.633835.

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33

Dereich, Steffen, and Thomas Müller-Gronbach. "General multilevel adaptations for stochastic approximation algorithms of Robbins–Monro and Polyak–Ruppert type." Numerische Mathematik 142, no. 2 (February 6, 2019): 279–328. http://dx.doi.org/10.1007/s00211-019-01024-y.

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34

Lambrou, George I., Kyriaki Hatziagapiou, Petros Toumpaniaris, Penelope Ioannidou, and Dimitrios Koutsouris. "Computational Modelling in Epidemiological Dispersion Using Diffusion and Epidemiological Equations." International Journal of Reliable and Quality E-Healthcare 8, no. 4 (October 2019): 1–37. http://dx.doi.org/10.4018/ijrqeh.2019100101.

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Although a considerable amount of knowledge is gathered concerning diseases and their transmission, still more is to learn on their mathematical modelling. The present work reviews the existent knowledge on models of epidemiological dispersion, the creation of a new form of an epidemiological diffusion equation, and the subsequent application of this equation to the investigation of epidemiological phenomena. Towards that scope, the authors have used mathematical models which have been previously reported, as well as algorithmic approaches of stochastic nature for the solution of complex functions. In particular, they have used dynamic programming algorithms, Robbins-Monro and Kiefer-Wolfowitz stochastic optimization algorithms, Markov chains and cellular automata. The modified diffusion equation could potentially provide a useful tool to the investigation of epidemiological phenomena. More research is required in order to explore the extent of its possibilities and uses.

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35

Liu, Chen-Wei. "Efficient Metropolis-Hastings Robbins-Monro Algorithm for High-Dimensional Diagnostic Classification Models." Applied Psychological Measurement, September 8, 2022, 014662162211239. http://dx.doi.org/10.1177/01466216221123981.

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The expectation-maximization (EM) algorithm is a commonly used technique for the parameter estimation of the diagnostic classification models (DCMs) with a prespecified Q-matrix; however, it requires O(2 K) calculations in its expectation-step, which significantly slows down the computation when the number of attributes, K, is large. This study proposes an efficient Metropolis-Hastings Robbins-Monro (eMHRM) algorithm, needing only O( K + 1) calculations in the Monte Carlo expectation step. Furthermore, the item parameters and structural parameters are approximated via the Robbins-Monro algorithm, which does not require time-consuming nonlinear optimization procedures. A series of simulation studies were conducted to compare the eMHRM with the EM and a Metropolis-Hastings (MH) algorithm regarding the parameter recovery and execution time. The outcomes presented in this article reveal that the eMHRM is much more computationally efficient than the EM and MH, and it tends to produce better estimates than the EM when K is large, suggesting that the eMHRM is a promising parameter estimation method for high-dimensional DCMs.

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36

Lin, Xiaofan, Siliang Zhang, Yincai Tang, and Xuan Li. "A Gibbs‐INLA algorithm for multidimensional graded response model analysis." British Journal of Mathematical and Statistical Psychology, September 29, 2023. http://dx.doi.org/10.1111/bmsp.12321.

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AbstractIn this paper, we propose a novel Gibbs‐INLA algorithm for the Bayesian inference of graded response models with ordinal response based on multidimensional item response theory. With the combination of the Gibbs sampling and the integrated nested Laplace approximation (INLA), the new framework avoids the cumbersome tuning which is inevitable in classical Markov chain Monte Carlo (MCMC) algorithm, and has low computing memory, high computational efficiency with much fewer iterations, and still achieve higher estimation accuracy. Therefore, it has the ability to handle large amount of multidimensional response data with different item responses. Simulation studies are conducted to compare with the Metroplis‐Hastings Robbins‐Monro (MH‐RM) algorithm and an application to the study of the IPIP‐NEO personality inventory data is given to assess the performance of the new algorithm. Extensions of the proposed algorithm for application on more complicated models and different data types are also discussed.

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37

Liu, Chen-Wei, Björn Andersson, and Anders Skrondal. "Erratum: A Constrained Metropolis–Hastings Robbins–Monro Algorithm for Q Matrix Estimation in DINA Models." Psychometrika, May 16, 2024. http://dx.doi.org/10.1007/s11336-024-09974-5.

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38

Godichon-Baggioni, Antoine, Nicklas Werge, and Olivier Wintenberger. "Non-asymptotic analysis of stochastic approximation algorithms for streaming data." ESAIM: Probability and Statistics, March 6, 2023. http://dx.doi.org/10.1051/ps/2023006.

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We introduce a streaming framework for analyzing stochastic approximation/optimization problems. This streaming framework is analogous to solving optimization problems using time-varying mini-batches that arrive sequentially. We provide non-asymptotic convergence rates of various gradient-based algorithms; this includes the famous Stochastic Gradient (SG) descent (a.k.a. Robbins-Monro algorithm), mini-batch SG and time-varying mini-batch SG algorithms, as well as their iterated averages (a.k.a. Polyak-Ruppert averaging). We show i) how to accelerate convergence by choosing the learning rate according to the time-varying mini-batches, ii) that Polyak-Ruppert averaging achieves optimal convergence in terms of attaining the Cramer-Rao lower bound, and iii) how time-varying mini-batches together with Polyak-Ruppert averaging can provide variance reduction and accelerate convergence simultaneously, which is advantageous for many learning problems, such as online, sequential, and large-scale learning. We further demonstrate these favorable effects for various time-varying mini-batches.

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39

Liu, Tianci, Chun Wang, and Gongjun Xu. "Estimating three- and four-parameter MIRT models with importance-weighted sampling enhanced variational auto-encoder." Frontiers in Psychology 13 (August 15, 2022). http://dx.doi.org/10.3389/fpsyg.2022.935419.

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Multidimensional Item Response Theory (MIRT) is widely used in educational and psychological assessment and evaluation. With the increasing size of modern assessment data, many existing estimation methods become computationally demanding and hence they are not scalable to big data, especially for the multidimensional three-parameter and four-parameter logistic models (i.e., M3PL and M4PL). To address this issue, we propose an importance-weighted sampling enhanced Variational Autoencoder (VAE) approach for the estimation of M3PL and M4PL. The key idea is to adopt a variational inference procedure in machine learning literature to approximate the intractable marginal likelihood, and further use importance-weighted samples to boost the trained VAE with a better log-likelihood approximation. Simulation studies are conducted to demonstrate the computational efficiency and scalability of the new algorithm in comparison to the popular alternative algorithms, i.e., Monte Carlo EM and Metropolis-Hastings Robbins-Monro methods. The good performance of the proposed method is also illustrated by a NAEP multistage testing data set.

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40

Huang, Sijia, Jinwen (Jevan) Luo, and Li Cai. "An Explanatory Multidimensional Random Item Effects Rating Scale Model." Educational and Psychological Measurement, December 13, 2022, 001316442211409. http://dx.doi.org/10.1177/00131644221140906.

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Random item effects item response theory (IRT) models, which treat both person and item effects as random, have received much attention for more than a decade. The random item effects approach has several advantages in many practical settings. The present study introduced an explanatory multidimensional random item effects rating scale model. The proposed model was formulated under a novel parameterization of the nominal response model (NRM), and allows for flexible inclusion of person-related and item-related covariates (e.g., person characteristics and item features) to study their impacts on the person and item latent variables. A new variant of the Metropolis-Hastings Robbins-Monro (MH-RM) algorithm designed for latent variable models with crossed random effects was applied to obtain parameter estimates for the proposed model. A preliminary simulation study was conducted to evaluate the performance of the MH-RM algorithm for estimating the proposed model. Results indicated that the model parameters were well recovered. An empirical data set was analyzed to further illustrate the usage of the proposed model.

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41

Huang, Sijia, and Li Cai. "Cross-Classified Item Response Theory Modeling With an Application to Student Evaluation of Teaching." Journal of Educational and Behavioral Statistics, August 24, 2023. http://dx.doi.org/10.3102/10769986231193351.

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The cross-classified data structure is ubiquitous in education, psychology, and health outcome sciences. In these areas, assessment instruments that are made up of multiple items are frequently used to measure latent constructs. The presence of both the cross-classified structure and multivariate categorical outcomes leads to the so-called item-level data with cross-classified structure. An example of such data structure is the routinely collected student evaluation of teaching (SET) data. Motivated by the lack of research on multilevel IRT modeling with crossed random effects and the need of an approach that can properly handle SET data, this study proposed a cross-classified IRT model, which takes into account both the cross-classified data structure and properties of multiple items in an assessment instrument. A new variant of the Metropolis–Hastings Robbins–Monro (MH-RM) algorithm was introduced to address the computational complexities in estimating the proposed model. A preliminary simulation study was conducted to evaluate the performance of the algorithm for fitting the proposed model to data. The results indicated that model parameters were well recovered. The proposed model was also applied to SET data collected at a large public university to answer empirical research questions. Limitations and future research directions were discussed.

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42

Amini Tehrani, Hamed, Ali Bakhshi, and Tony T. Y. Yang. "Online jointly estimation of hysteretic structures using the combination of central difference Kalman filter and Robbins–Monro technique." Journal of Vibration and Control, May 12, 2020, 107754632092560. http://dx.doi.org/10.1177/1077546320925604.

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Rapid assessment of structural safety and performance right after the occurrence of significant earthquake shaking is crucial for building owners and decision-makers to make informed risk management decisions. Hence, it is vital to develop online and pseudo-online health monitoring methods to quantify the health of the building right after significant earthquake shaking. Many Bayesian inference–based methods have been developed in the past which allow the users to estimate the unknown states and parameters. However, one of the most challenging part of the Bayesian inference–based methods is the determination of the parameter noise covariance matrix. It is especially difficult when the number of unknown states and parameters is large. In this study, an effective online joint estimation method for nonlinear hysteretic structures, with consideration of degradation and pinching phenomena, is proposed. Simultaneous estimation of states and parameters is conducted using the combination of a central difference Kalman filter as an effective estimator and the Robbins–Monro stochastic approximation technique as the parameters noise covariance matrix regulator. The proposed algorithm is implemented on three shear buildings with 36, 54, and 90 unknown states and parameters. To verify the performance of the system identification method, robust simulations with synthetic measurement noises and modeling errors were generated using the Monte Carlo random simulation method. The result shows the proposed method can be used to estimate the unknown parameters and states of highly nonlinear systems efficiently and effectively.

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Huang, Sijia, and Dubravka Svetina Valdivia. "Wald χ² Test for Differential Item Functioning Detection with Polytomous Items in Multilevel Data." Educational and Psychological Measurement, July 11, 2023. http://dx.doi.org/10.1177/00131644231181688.

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Identifying items with differential item functioning (DIF) in an assessment is a crucial step for achieving equitable measurement. One critical issue that has not been fully addressed with existing studies is how DIF items can be detected when data are multilevel. In the present study, we introduced a Lord’s Wald [Formula: see text] test-based procedure for detecting both uniform and non-uniform DIF with polytomous items in the presence of the ubiquitous multilevel data structure. The proposed approach is a multilevel extension of a two-stage procedure, which identifies anchor items in its first stage and formally evaluates candidate items in the second stage. We applied the Metropolis–Hastings Robbins–Monro (MH-RM) algorithm to estimate multilevel polytomous item response theory (IRT) models and to obtain accurate covariance matrices. To evaluate the performance of the proposed approach, we conducted a preliminary simulation study that considered various conditions to mimic real-world scenarios. The simulation results indicated that the proposed approach has great power for identifying DIF items and well controls the Type I error rate. Limitations and future research directions were also discussed.

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Huang, Sijia, Seungwon Chung, and Carl F. Falk. "Modeling Response Styles in Cross‐Classified Data Using a Cross‐Classified Multidimensional Nominal Response Model." Journal of Educational Measurement, May 31, 2024. http://dx.doi.org/10.1111/jedm.12401.

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AbstractIn this study, we introduced a cross‐classified multidimensional nominal response model (CC‐MNRM) to account for various response styles (RS) in the presence of cross‐classified data. The proposed model allows slopes to vary across items and can explore impacts of observed covariates on latent constructs. We applied a recently developed variant of the Metropolis‐Hastings Robbins‐Monro (MH‐RM) algorithm to address the computational challenge of estimating the proposed model. To demonstrate our new approach, we analyzed empirical student evaluation of teaching (SET) data collected from a large public university with three models: a CC‐MNRM with RS, a CC‐MNRM with no RS, and a multilevel MNRM with RS. Results indicated that the three models led to different inferences regarding the observed covariates. Additionally, in the example, ignoring/incorporating RS led to changes in student substantive scores, while the instructor substantive scores were less impacted. Misspecifying the cross‐classified data structure resulted in apparent changes on instructor scores. To further evaluate the proposed modeling approach, we conducted a preliminary simulation study and observed good parameter and score recovery. We concluded this study with discussions of limitations and future research directions.

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Chung, Seungwon, and Li Cai. "Cross-Classified Random Effects Modeling for Moderated Item Calibration." Journal of Educational and Behavioral Statistics, January 12, 2021, 107699862098390. http://dx.doi.org/10.3102/1076998620983908.

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In the research reported here, we propose a new method for scale alignment and test scoring in the context of supporting students with disabilities. In educational assessment, students from these special populations take modified tests because of a demonstrated disability that requires more assistance than standard testing accommodation. Updated federal education legislation and guidance require that these students be assessed and included in state education accountability systems, and their achievement reported with respect to the same rigorous content and achievement standards that the state adopted. Routine item calibration and linking methods are not feasible because the size of these special populations tends to be small. We develop a unified cross-classified random effects model that utilizes item response data from the general population as well as judge-provided data from subject matter experts in order to obtain revised item parameter estimates for use in scoring modified tests. We extend the Metropolis–Hastings Robbins–Monro algorithm to estimate the parameters of this model. The proposed method is applied to Braille test forms in a large operational multistate English language proficiency assessment program. Our work not only allows a broader range of modifications that is routinely considered in large-scale educational assessments but also directly incorporates the input from subject matter experts who work directly with the students needing support. Their structured and informed feedback deserves more attention from the psychometric community.

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Wang, Xue, Jing Lu, and Jiwei Zhang. "A Metropolis–Hastings Robbins–Monro algorithm via variational inference for estimating the multidimensional graded response model: a calculationally efficient estimation scheme to deal with complex test structures." Computational Statistics, July 29, 2024. http://dx.doi.org/10.1007/s00180-024-01533-x.

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