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Автор: Grafiati

Опубліковано: 10 грудня 2022

Оновлено: 29 січня 2023

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1

Boloix-Tortosa, Rafael, Juan Jose Murillo-Fuentes, Francisco Javier Payan-Somet, and Fernando Perez-Cruz. "Complex Gaussian Processes for Regression." IEEE Transactions on Neural Networks and Learning Systems 29, no. 11 (November 2018): 5499–511. http://dx.doi.org/10.1109/tnnls.2018.2805019.

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2

Munoz-Gonzalez, Luis, Miguel Lazaro-Gredilla, and Anibal R. Figueiras-Vidal. "Divisive Gaussian Processes for Nonstationary Regression." IEEE Transactions on Neural Networks and Learning Systems 25, no. 11 (November 2014): 1991–2003. http://dx.doi.org/10.1109/tnnls.2014.2301951.

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3

Terry, Nick, and Youngjun Choe. "Splitting Gaussian processes for computationally-efficient regression." PLOS ONE 16, no. 8 (August 24, 2021): e0256470. http://dx.doi.org/10.1371/journal.pone.0256470.

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Анотація:

Gaussian processes offer a flexible kernel method for regression. While Gaussian processes have many useful theoretical properties and have proven practically useful, they suffer from poor scaling in the number of observations. In particular, the cubic time complexity of updating standard Gaussian process models can be a limiting factor in applications. We propose an algorithm for sequentially partitioning the input space and fitting a localized Gaussian process to each disjoint region. The algorithm is shown to have superior time and space complexity to existing methods, and its sequential nature allows the model to be updated efficiently. The algorithm constructs a model for which the time complexity of updating is tightly bounded above by a pre-specified parameter. To the best of our knowledge, the model is the first local Gaussian process regression model to achieve linear memory complexity. Theoretical continuity properties of the model are proven. We demonstrate the efficacy of the resulting model on several multi-dimensional regression tasks.

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4

Wu, Xing Hui, and Yu Ping Zhou. "Regression and Classification Method Based on Gaussian Processes." Advanced Materials Research 971-973 (June 2014): 1949–52. http://dx.doi.org/10.4028/www.scientific.net/amr.971-973.1949.

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Gaussian processes is a kind of machine learning method developed in recent years and also a promising technology that has been applied both in the regression problem and the classification problem. In this paper, the general principle of regression and classification based on Gaussian process and experimental verification was described. A comparison about accuracy between this method and Support Vector Machine (SVM) is made during the experiments.Finally, it was summarized of the regression and classification of Gaussian process application and future development direction.

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5

Gonçalves, Ítalo Gomes, Felipe Guadagnin, and Diogo Peixoto Cordova. "Learning spatial patterns with variational Gaussian processes: Regression." Computers & Geosciences 161 (April 2022): 105056. http://dx.doi.org/10.1016/j.cageo.2022.105056.

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6

Perez-Cruz, F., J. J. Murillo-Fuentes, and S. Caro. "Nonlinear Channel Equalization With Gaussian Processes for Regression." IEEE Transactions on Signal Processing 56, no. 10 (October 2008): 5283–86. http://dx.doi.org/10.1109/tsp.2008.928512.

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7

Zhang, Tong. "Approximation Bounds for Some Sparse Kernel Regression Algorithms." Neural Computation 14, no. 12 (December 1, 2002): 3013–42. http://dx.doi.org/10.1162/089976602760805395.

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Gaussian processes have been widely applied to regression problems with good performance. However, they can be computationally expensive. In order to reduce the computational cost, there have been recent studies on using sparse approximations in gaussian processes. In this article, we investigate properties of certain sparse regression algorithms that approximately solve a gaussian process. We obtain approximation bounds and compare our results with related methods.

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8

Carvalho, Ruan M., Iago G. L. Rosa, Diego E. B. Gomes, Priscila V. Z. C. Goliatt, and Leonardo Goliatt. "Gaussian processes regression for cyclodextrin host-guest binding prediction." Journal of Inclusion Phenomena and Macrocyclic Chemistry 101, no. 1-2 (July 12, 2021): 149–59. http://dx.doi.org/10.1007/s10847-021-01092-4.

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9

Munoz-Gonzalez, Luis, Miguel Lazaro-Gredilla, and Anibal R. Figueiras-Vidal. "Laplace Approximation for Divisive Gaussian Processes for Nonstationary Regression." IEEE Transactions on Pattern Analysis and Machine Intelligence 38, no. 3 (March 1, 2016): 618–24. http://dx.doi.org/10.1109/tpami.2015.2452914.

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10

Leithead, W. E., Kian Seng Neo, and D. J. Leith. "GAUSSIAN REGRESSION BASED ON MODELS WITH TWO STOCHASTIC PROCESSES." IFAC Proceedings Volumes 38, no. 1 (2005): 142–47. http://dx.doi.org/10.3182/20050703-6-cz-1902.00024.

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11

Lin, Lizhen, Niu Mu, Pokman Cheung, and David Dunson. "Extrinsic Gaussian Processes for Regression and Classification on Manifolds." Bayesian Analysis 14, no. 3 (September 2019): 887–906. http://dx.doi.org/10.1214/18-ba1135.

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12

Zhu, Bin, and David B. Dunson. "Locally Adaptive Bayes Nonparametric Regression via Nested Gaussian Processes." Journal of the American Statistical Association 108, no. 504 (December 2013): 1445–56. http://dx.doi.org/10.1080/01621459.2013.838568.

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13

Shi, J. Q., R. Murray-Smith, and D. M. Titterington. "Bayesian regression and classification using mixtures of Gaussian processes." International Journal of Adaptive Control and Signal Processing 17, no. 2 (2003): 149–61. http://dx.doi.org/10.1002/acs.744.

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14

Xu, Bohan, Rayus Kuplicki, Sandip Sen, and Martin P. Paulus. "The pitfalls of using Gaussian Process Regression for normative modeling." PLOS ONE 16, no. 9 (September 15, 2021): e0252108. http://dx.doi.org/10.1371/journal.pone.0252108.

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Анотація:

Normative modeling, a group of methods used to quantify an individual’s deviation from some expected trajectory relative to observed variability around that trajectory, has been used to characterize subject heterogeneity. Gaussian Processes Regression includes an estimate of variable uncertainty across the input domain, which at face value makes it an attractive method to normalize the cohort heterogeneity where the deviation between predicted value and true observation is divided by the derived uncertainty directly from Gaussian Processes Regression. However, we show that the uncertainty directly from Gaussian Processes Regression is irrelevant to the cohort heterogeneity in general.

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15

Durrande, Nicolas, James Hensman, Magnus Rattray, and Neil D. Lawrence. "Detecting periodicities with Gaussian processes." PeerJ Computer Science 2 (April 13, 2016): e50. http://dx.doi.org/10.7717/peerj-cs.50.

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We consider the problem of detecting and quantifying the periodic component of a function given noise-corrupted observations of a limited number of input/output tuples. Our approach is based on Gaussian process regression, which provides a flexible non-parametric framework for modelling periodic data. We introduce a novel decomposition of the covariance function as the sum of periodic and aperiodic kernels. This decomposition allows for the creation of sub-models which capture the periodic nature of the signal and its complement. To quantify the periodicity of the signal, we derive a periodicity ratio which reflects the uncertainty in the fitted sub-models. Although the method can be applied to many kernels, we give a special emphasis to the Matérn family, from the expression of the reproducing kernel Hilbert space inner product to the implementation of the associated periodic kernels in a Gaussian process toolkit. The proposed method is illustrated by considering the detection of periodically expressed genes in thearabidopsisgenome.

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16

Wang, Xiangyu, and J. Q. Sun. "Multi-stage regression fatigue analysis of non-Gaussian stress processes." Journal of Sound and Vibration 280, no. 1-2 (February 2005): 455–65. http://dx.doi.org/10.1016/j.jsv.2004.02.036.

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17

Nguyen, Thi Nhat Anh, Abdesselam Bouzerdoum, and Son Lam Phung. "Stochastic variational hierarchical mixture of sparse Gaussian processes for regression." Machine Learning 107, no. 12 (July 6, 2018): 1947–86. http://dx.doi.org/10.1007/s10994-018-5721-5.

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18

Benavoli, Alessio, Dario Azzimonti, and Dario Piga. "Skew Gaussian processes for classification." Machine Learning 109, no. 9-10 (September 2020): 1877–902. http://dx.doi.org/10.1007/s10994-020-05906-3.

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Анотація:

Abstract Gaussian processes (GPs) are distributions over functions, which provide a Bayesian nonparametric approach to regression and classification. In spite of their success, GPs have limited use in some applications, for example, in some cases a symmetric distribution with respect to its mean is an unreasonable model. This implies, for instance, that the mean and the median coincide, while the mean and median in an asymmetric (skewed) distribution can be different numbers. In this paper, we propose skew-Gaussian processes (SkewGPs) as a non-parametric prior over functions. A SkewGP extends the multivariate unified skew-normal distribution over finite dimensional vectors to a stochastic processes. The SkewGP class of distributions includes GPs and, therefore, SkewGPs inherit all good properties of GPs and increase their flexibility by allowing asymmetry in the probabilistic model. By exploiting the fact that SkewGP and probit likelihood are conjugate model, we derive closed form expressions for the marginal likelihood and predictive distribution of this new nonparametric classifier. We verify empirically that the proposed SkewGP classifier provides a better performance than a GP classifier based on either Laplace’s method or expectation propagation.

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19

Zhu, Jinlin, Zhiqiang Ge, and Zhihuan Song. "Variational Bayesian Gaussian Mixture Regression for Soft Sensing Key Variables in Non-Gaussian Industrial Processes." IEEE Transactions on Control Systems Technology 25, no. 3 (May 2017): 1092–99. http://dx.doi.org/10.1109/tcst.2016.2576999.

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20

Liang, Junjie, Yanting Wu, Dongkuan Xu, and Vasant G. Honavar. "Longitudinal Deep Kernel Gaussian Process Regression." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 10 (May 18, 2021): 8556–64. http://dx.doi.org/10.1609/aaai.v35i10.17038.

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Gaussian processes offer an attractive framework for predictive modeling from longitudinal data, \ie irregularly sampled, sparse observations from a set of individuals over time. However, such methods have two key shortcomings: (i) They rely on ad hoc heuristics or expensive trial and error to choose the effective kernels, and (ii) They fail to handle multilevel correlation structure in the data. We introduce Longitudinal deep kernel Gaussian process regression (L-DKGPR) to overcome these limitations by fully automating the discovery of complex multilevel correlation structure from longitudinal data. Specifically, L-DKGPR eliminates the need for ad hoc heuristics or trial and error using a novel adaptation of deep kernel learning that combines the expressive power of deep neural networks with the flexibility of non-parametric kernel methods. L-DKGPR effectively learns the multilevel correlation with a novel additive kernel that simultaneously accommodates both time-varying and the time-invariant effects. We derive an efficient algorithm to train L-DKGPR using latent space inducing points and variational inference. Results of extensive experiments on several benchmark data sets demonstrate that L-DKGPR significantly outperforms the state-of-the-art longitudinal data analysis (LDA) methods.

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21

McClintock, Thomas, and Eduardo Rozo. "Reconstructing probability distributions with Gaussian processes." Monthly Notices of the Royal Astronomical Society 489, no. 3 (September 2, 2019): 4155–60. http://dx.doi.org/10.1093/mnras/stz2426.

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ABSTRACT Modern cosmological analyses constrain physical parameters using Markov Chain Monte Carlo (MCMC) or similar sampling techniques. Oftentimes, these techniques are computationally expensive to run and require up to thousands of CPU hours to complete. Here we present a method for reconstructing the log-probability distributions of completed experiments from an existing chain (or any set of posterior samples). The reconstruction is performed using Gaussian process regression for interpolating the log-probability. This allows for easy resampling, importance sampling, marginalization, testing different samplers, investigating chain convergence, and other operations. As an example use case, we reconstruct the posterior distribution of the most recent Planck 2018 analysis. We then resample the posterior, and generate a new chain with 40 times as many points in only 30 min. Our likelihood reconstruction tool is made publicly available online.

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22

Сушникова, Д. А. "Application of block low-rank matrices in Gaussian processes for regression." Numerical Methods and Programming (Vychislitel'nye Metody i Programmirovanie), no. 3 (August 31, 2017): 214–20. http://dx.doi.org/10.26089/nummet.v18r319.

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Рассматривается задача регрессии на основе гауссовских процессов. В ходе моделирования коррелированного шума при помощи гауссовского процесса основной проблемой является подсчет апостериорного среднего и дисперсии прогноза, для чего необходимо обращать плотную матрицу ковариации размера $n\times n$, где $n$ - размер выборки.Кроме того, для оценки правдоподобия требуется вычислять логарифм определителя плотной ковариационной матрицы, что тоже является трудоемкой задачей. Предложен метод быстрого вычисления логарифма определителя матрицы ковариации на основе идеи ее аппроксимации разреженной матрицей. При сравнении с методом HODLR (Hierarchically Off-Diagonal Low-Rank) и с традиционным плотным методом предложенный метод оказался более эффективным по времени. The Gaussian processes for regression are considered. During simulation of correlated noises using the Gaussian processes, the main difficulty is the computation of the posterior mean and dispersion of the prediction. This computation requires the inversion of the dense covariance matrix of order $n$, where $n$ is the sample size. In addition, for the likelihood evaluation we need to compute the logarithm of the determinant of the dense covariance matrix, which is also a time-consuming problem. A new method for the fast computation of the covariance matrix logarithm is proposed. This method is based on the approximation of this matrix by a sparse matrix. The proposed method appears to be time efficient compared to the HODLR (Hierarchically Off-Diagonal Low-Rank) method and the traditional dense method.

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23

Burnaev, E. V., M. E. Panov, and A. A. Zaytsev. "Regression on the basis of nonstationary Gaussian processes with Bayesian regularization." Journal of Communications Technology and Electronics 61, no. 6 (June 2016): 661–71. http://dx.doi.org/10.1134/s1064226916060061.

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24

Yuan, Jin, Cheng-Liang Liu, Xuemei Liu, Kesheng Wang, and Tao Yu. "Incorporating prior model into Gaussian processes regression for WEDM process modeling." Expert Systems with Applications 36, no. 4 (May 2009): 8084–92. http://dx.doi.org/10.1016/j.eswa.2008.10.048.

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25

Burnaev, E. V., A. A. Zaytsev, and V. G. Spokoiny. "The Bernstein-von Mises theorem for regression based on Gaussian Processes." Russian Mathematical Surveys 68, no. 5 (October 31, 2013): 954–56. http://dx.doi.org/10.1070/rm2013v068n05abeh004863.

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26

Verrelst, Jochem, Juan Pablo Rivera, Anatoly Gitelson, Jesus Delegido, José Moreno, and Gustau Camps-Valls. "Spectral band selection for vegetation properties retrieval using Gaussian processes regression." International Journal of Applied Earth Observation and Geoinformation 52 (October 2016): 554–67. http://dx.doi.org/10.1016/j.jag.2016.07.016.

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27

di Sciascio, Fernando, and Adriana N. Amicarelli. "Biomass estimation in batch biotechnological processes by Bayesian Gaussian process regression." Computers & Chemical Engineering 32, no. 12 (December 2008): 3264–73. http://dx.doi.org/10.1016/j.compchemeng.2008.05.015.

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28

Liu, Yiqi, Yarong Song, Jurg Keller, Philip Bond, and Guangming Jiang. "Prediction of concrete corrosion in sewers with hybrid Gaussian processes regression model." RSC Advances 7, no. 49 (2017): 30894–903. http://dx.doi.org/10.1039/c7ra03959j.

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29

Tsay, Wen-Jen. "SPURIOUS REGRESSION BETWEEN I(1) PROCESSES WITH INFINITE VARIANCE ERRORS." Econometric Theory 15, no. 4 (August 1999): 622–28. http://dx.doi.org/10.1017/s0266466699154069.

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This paper considers spurious regression between integrated processes with stable errors. Our results show that the t-ratios diverge at the rate of √T, which is identical to what Phillips (1986, Journal of Econometrics 33, 311–340) has obtained for the Gaussian case. Therefore, it is the long memory in the dependent variable and regressors, instead of the moment conditions of the error terms, that causes the spurious regression.

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30

Albert, Christopher G. "Gaussian Processes for Data Fulfilling Linear Differential Equations." Proceedings 33, no. 1 (November 21, 2019): 5. http://dx.doi.org/10.3390/proceedings2019033005.

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A method to reconstruct fields, source strengths and physical parameters based on Gaussian process regression is presented for the case where data are known to fulfill a given linear differential equation with localized sources. The approach is applicable to a wide range of data from physical measurements and numerical simulations. It is based on the well-known invariance of the Gaussian under linear operators, in particular differentiation. Instead of using a generic covariance function to represent data from an unknown field, the space of possible covariance functions is restricted to allow only Gaussian random fields that fulfill the homogeneous differential equation. The resulting tailored kernel functions lead to more reliable regression compared to using a generic kernel and makes some hyperparameters directly interpretable. For differential equations representing laws of physics such a choice limits realizations of random fields to physically possible solutions. Source terms are added by superposition and their strength estimated in a probabilistic fashion, together with possibly unknown hyperparameters with physical meaning in the differential operator.

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31

Wei, San Xi, and Zong Hai Sun. "A Multi-Classification Method Based on Gaussian Processes." Applied Mechanics and Materials 198-199 (September 2012): 1333–37. http://dx.doi.org/10.4028/www.scientific.net/amm.198-199.1333.

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Gaussian processes (GPs) is a very promising technology that has been applied both in the regression problem and the classification problem. In recent years, models based on Gaussian process priors have attracted much attention in the machine learning. Binary (or two-class, C=2) classification using Gaussian process is a very well-developed method. In this paper, a Multi-classification (C>2) method is illustrated, which is based on Binary GPs classification. A good accuracy can be obtained through this method. Meanwhile, a comparison about decision time and accuracy between this method and Support Vector Machine (SVM) is made during the experiments.

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32

Lu, Chi-Ken, and Patrick Shafto. "Conditional Deep Gaussian Processes: Multi-Fidelity Kernel Learning." Entropy 23, no. 11 (November 20, 2021): 1545. http://dx.doi.org/10.3390/e23111545.

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Deep Gaussian Processes (DGPs) were proposed as an expressive Bayesian model capable of a mathematically grounded estimation of uncertainty. The expressivity of DPGs results from not only the compositional character but the distribution propagation within the hierarchy. Recently, it was pointed out that the hierarchical structure of DGP well suited modeling the multi-fidelity regression, in which one is provided sparse observations with high precision and plenty of low fidelity observations. We propose the conditional DGP model in which the latent GPs are directly supported by the fixed lower fidelity data. Then the moment matching method is applied to approximate the marginal prior of conditional DGP with a GP. The obtained effective kernels are implicit functions of the lower-fidelity data, manifesting the expressivity contributed by distribution propagation within the hierarchy. The hyperparameters are learned via optimizing the approximate marginal likelihood. Experiments with synthetic and high dimensional data show comparable performance against other multi-fidelity regression methods, variational inference, and multi-output GP. We conclude that, with the low fidelity data and the hierarchical DGP structure, the effective kernel encodes the inductive bias for true function allowing the compositional freedom.

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33

Komaki, Fumiyasu. "Homogeneous Gaussian Markov processes on general lattices." Advances in Applied Probability 28, no. 1 (March 1996): 189–206. http://dx.doi.org/10.2307/1427917.

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A homogeneous Gaussian Markov lattice-process model has a regression coefficient that determines the extent to which a random variable of a vertex is dependent on those of the neighbors. In many studies, the absolute value of this parameter has been assumed to be less than the reciprocal of the number of neighbors. This condition is shown to be necessary and sufficient for the existence of the Gaussian process satisfying the model equations under some assumptions on lattices using the notion of dual processes. We also give examples of models that neither satisfy the condition imposed on the region for the parameter nor the assumptions on lattices. A formula for autocovariance functions of Gaussian Markov processes on general lattices is derived, and numerical procedures to calculate the autocovariance functions are proposed.

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34

Komaki, Fumiyasu. "Homogeneous Gaussian Markov processes on general lattices." Advances in Applied Probability 28, no. 01 (March 1996): 189–206. http://dx.doi.org/10.1017/s0001867800027324.

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Анотація:

A homogeneous Gaussian Markov lattice-process model has a regression coefficient that determines the extent to which a random variable of a vertex is dependent on those of the neighbors. In many studies, the absolute value of this parameter has been assumed to be less than the reciprocal of the number of neighbors. This condition is shown to be necessary and sufficient for the existence of the Gaussian process satisfying the model equations under some assumptions on lattices using the notion of dual processes. We also give examples of models that neither satisfy the condition imposed on the region for the parameter nor the assumptions on lattices. A formula for autocovariance functions of Gaussian Markov processes on general lattices is derived, and numerical procedures to calculate the autocovariance functions are proposed.

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35

Zhou, Le, Junghui Chen, and Zhihuan Song. "Recursive Gaussian Process Regression Model for Adaptive Quality Monitoring in Batch Processes." Mathematical Problems in Engineering 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/761280.

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Анотація:

In chemical batch processes with slow responses and a long duration, it is time-consuming and expensive to obtain sufficient normal data for statistical analysis. With the persistent accumulation of the newly evolving data, the modelling becomes adequate gradually and the subsequent batches will change slightly owing to the slow time-varying behavior. To efficiently make use of the small amount of initial data and the newly evolving data sets, an adaptive monitoring scheme based on the recursive Gaussian process (RGP) model is designed in this paper. Based on the initial data, a Gaussian process model and the corresponding SPE statistic are constructed at first. When the new batches of data are included, a strategy based on the RGP model is used to choose the proper data for model updating. The performance of the proposed method is finally demonstrated by a penicillin fermentation batch process and the result indicates that the proposed monitoring scheme is effective for adaptive modelling and online monitoring.

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36

Hong, Xiaodan, Biao Huang, Yongsheng Ding, Fan Guo, Lei Chen, and Lihong Ren. "Multivariate Gaussian process regression for nonlinear modelling with colored noise." Transactions of the Institute of Measurement and Control 41, no. 8 (November 21, 2018): 2268–79. http://dx.doi.org/10.1177/0142331218798429.

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Nonlinearity of process systems along with colored noises is common in chemical processes. A multivariate (multiple inputs and multiple outputs) Gaussian process regression (MGPR) modelling approach, which can model multivariate nonlinear processes, is developed in this paper. The developed GPR model considers the Gaussian colored noise, rather than the traditional Gaussian white noise. The colored noise is described by the moving average (MA) model and the autoregressive (AR) model, respectively, with unknown parameters so that a MA-GPR model and an AR-GPR model are developed. These two colored noise based models are further extended to the MGPR model to generate the MA-MGPR model and the AR-MGPR model. The covariance functions of the MA-MGPR model or the AR-MGPR model are formulated with consideration of the autocorrelation of noises. Moreover, all parameters are estimated by using a unidimensional updated particle swarm optimization (PSO) algorithm, simultaneously. Numerical examples as well as a three-level drawing model of Carbon fiber production process are used to demonstrate the effectiveness of the proposed modelling approaches.

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37

Samuelsson, Oscar, Anders Björk, Jesús Zambrano, and Bengt Carlsson. "Gaussian process regression for monitoring and fault detection of wastewater treatment processes." Water Science and Technology 75, no. 12 (March 25, 2017): 2952–63. http://dx.doi.org/10.2166/wst.2017.162.

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Monitoring and fault detection methods are increasingly important to achieve a robust and resource efficient operation of wastewater treatment plants (WWTPs). The purpose of this paper was to evaluate a promising machine learning method, Gaussian process regression (GPR), for WWTP monitoring applications. We evaluated GPR at two WWTP monitoring problems: estimate missing data in a flow rate signal (simulated data), and detect a drift in an ammonium sensor (real data). We showed that GPR with the standard estimation method, maximum likelihood estimation (GPR-MLE), suffered from local optima during estimation of kernel parameters, and did not give satisfactory results in a simulated case study. However, GPR with a state-of-the-art estimation method based on sequential Monte Carlo estimation (GPR-SMC) gave good predictions and did not suffer from local optima. Comparisons with simple standard methods revealed that GPR-SMC performed better than linear interpolation in estimating missing data in a noisy flow rate signal. We conclude that GPR-SMC is both a general and powerful method for monitoring full-scale WWTPs. However, this paper also shows that it does not always pay off to use more sophisticated methods. New methods should be critically compared against simpler methods, which might be good enough for some scenarios.

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38

Sofro, A’yunin, Jian Qing Shi, and Chunzheng Cao. "Regression analysis for multivariate process data of counts using convolved Gaussian processes." Journal of Statistical Planning and Inference 206 (May 2020): 57–74. http://dx.doi.org/10.1016/j.jspi.2019.09.005.

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39

Yuan, Xiaofeng, Zhiqiang Ge, Hongwei Zhang, Zhihuan Song, and Peiliang Wang. "Soft Sensor for Multiphase and Multimode Processes Based on Gaussian Mixture Regression." IFAC Proceedings Volumes 47, no. 3 (2014): 1067–72. http://dx.doi.org/10.3182/20140824-6-za-1003.01752.

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40

Tong, Chudong, Ting Lan, and Xuhua Shi. "Soft sensing of non-Gaussian processes using ensemble modified independent component regression." Chemometrics and Intelligent Laboratory Systems 157 (October 2016): 120–26. http://dx.doi.org/10.1016/j.chemolab.2016.07.006.

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41

Mei, Congli, Yong Su, Guohai Liu, Yuhan Ding, and Zhiling Liao. "Dynamic soft sensor development based on Gaussian mixture regression for fermentation processes." Chinese Journal of Chemical Engineering 25, no. 1 (January 2017): 116–22. http://dx.doi.org/10.1016/j.cjche.2016.07.005.

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42

Yin, Yuehong, Ming Jun Ren, and Lijian Sun. "Dependant Gaussian processes regression for intelligent sampling of freeform and structured surfaces." CIRP Annals 66, no. 1 (2017): 511–14. http://dx.doi.org/10.1016/j.cirp.2017.04.063.

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43

Phan, Anh Tuan, Thi Tuyet Hong Vu, Dinh Quang Nguyen, Eleonora Riva Sanseverino, Hang Thi-Thuy Le, and Van Cong Bui. "Data Compensation with Gaussian Processes Regression: Application in Smart Building’s Sensor Network." Energies 15, no. 23 (December 4, 2022): 9190. http://dx.doi.org/10.3390/en15239190.

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Data play an essential role in the optimal control of smart buildings’ operation, especially in building energy-management for the target of nearly zero buildings. The building monitoring system is in charge of collecting and managing building data. However, device imperfections and failures of the monitoring system are likely to produce low-quality data, such as data loss and inconsistent data, which then seriously affect the control quality of the buildings. This paper proposes a new approach based on Gaussian process regression for data-quality monitoring and sensor network data compensation in smart buildings. The proposed method is proven to effectively detect and compensate for low-quality data thanks to the application of data analysis to the energy management monitoring system of a building model in Viet Nam. The research results provide a good opportunity to improve the efficiency of building energy-management systems and support the development of low-cost smart buildings.

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44

Mao, Runjun, Chengdong Cao, James Jing Yue Qian, Jiufan Wang, and Yunpeng Liu. "Mixture of Gaussian Processes Based on Bayesian Optimization." Journal of Sensors 2022 (September 15, 2022): 1–10. http://dx.doi.org/10.1155/2022/7646554.

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This paper gives a detailed introduction of implementing mixture of Gaussian process (MGP) model and develops its application for Bayesian optimization (BayesOpt). The paper also develops techniques for MGP in finding its mixture components and introduced an alternative gating network based on the Dirichlet distributions. BayesOpt using the resultant MGP model significantly outperforms the one based on Gaussian process regression in terms of optimization efficiency in the test on tuning the hyperparameters in common machine learning algorithms. This indicates the success of the methods, implying a promising future of wider application for MGP model and the BayesOpt based on it.

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45

Sundararajan, S., and S. S. Keerthi. "Predictive Approaches for Choosing Hyperparameters in Gaussian Processes." Neural Computation 13, no. 5 (May 1, 2001): 1103–18. http://dx.doi.org/10.1162/08997660151134343.

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Gaussian processes are powerful regression models specified by parameterized mean and covariance functions. Standard approaches to choose these parameters (known by the name hyperparameters) are maximum likelihood and maximum a posteriori. In this article, we propose and investigate predictive approaches based on Geisser's predictive sample reuse (PSR) methodology and the related Stone's cross-validation (CV) methodology. More specifically, we derive results for Geisser's surrogate predictive probability (GPP), Geisser's predictive mean square error (GPE), and the standard CV error and make a comparative study. Within an approximation we arrive at the generalized cross-validation (GCV) and establish its relationship with the GPP and GPE approaches. These approaches are tested on a number of problems. Experimental results show that these approaches are strongly competitive with the existing approaches.

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46

Tian, Jinkai, Peifeng Yan, and Da Huang. "Kernel Analysis Based on Dirichlet Processes Mixture Models." Entropy 21, no. 9 (September 2, 2019): 857. http://dx.doi.org/10.3390/e21090857.

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Kernels play a crucial role in Gaussian process regression. Analyzing kernels from their spectral domain has attracted extensive attention in recent years. Gaussian mixture models (GMM) are used to model the spectrum of kernels. However, the number of components in a GMM is fixed. Thus, this model suffers from overfitting or underfitting. In this paper, we try to combine the spectral domain of kernels with nonparametric Bayesian models. Dirichlet processes mixture models are used to resolve this problem by changing the number of components according to the data size. Multiple experiments have been conducted on this model and it shows competitive performance.

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47

Sollich, Peter, and Anason Halees. "Learning Curves for Gaussian Process Regression: Approximations and Bounds." Neural Computation 14, no. 6 (June 1, 2002): 1393–428. http://dx.doi.org/10.1162/089976602753712990.

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We consider the problem of calculating learning curves (i.e., average generalization performance) of gaussian processes used for regression. On the basis of a simple expression for the generalization error, in terms of the eigenvalue decomposition of the covariance function, we derive a number of approximation schemes. We identify where these become exact and compare with existing bounds on learning curves; the new approximations, which can be used for any input space dimension, generally get substantially closer to the truth. We also study possible improvements to our approximations. Finally, we use a simple exactly solvable learning scenario to show that there are limits of principle on the quality of approximations and bounds expressible solely in terms of the eigenvalue spectrum of the covariance function.

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48

Agou, Vasiliki D., Andrew Pavlides, and Dionissios T. Hristopulos. "Spatial Modeling of Precipitation Based on Data-Driven Warping of Gaussian Processes." Entropy 24, no. 3 (February 23, 2022): 321. http://dx.doi.org/10.3390/e24030321.

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Modeling and forecasting spatiotemporal patterns of precipitation is crucial for managing water resources and mitigating water-related hazards. Globally valid spatiotemporal models of precipitation are not available. This is due to the intermittent nature, non-Gaussian distribution, and complex geographical dependence of precipitation processes. Herein we propose a data-driven model of precipitation amount which employs a novel, data-driven (non-parametric) implementation of warped Gaussian processes. We investigate the proposed warped Gaussian process regression (wGPR) using (i) a synthetic test function contaminated with non-Gaussian noise and (ii) a reanalysis dataset of monthly precipitation from the Mediterranean island of Crete. Cross-validation analysis is used to establish the advantages of non-parametric warping for the interpolation of incomplete data. We conclude that wGPR equipped with the proposed data-driven warping provides enhanced flexibility and—at least for the cases studied– improved predictive accuracy for non-Gaussian data.

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49

Li, Jin Hua, Shui Sheng Chen, and Wei Bing Sheng. "Conditional Simulation of No-Gaussian Stochastic Process Based on Neural Networks." Advanced Materials Research 479-481 (February 2012): 1959–62. http://dx.doi.org/10.4028/www.scientific.net/amr.479-481.1959.

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In many fields such as wind engineering, ocean engineering, soil engineering and so on, it is obvious that the development of effective methods to generate sample functions of non-Gaussian stochastic processes and fields is of paramount significance for many systems subjected to non-Gaussian excitations. In this paper, neural network technique is proposed for the conditional simulation of non-Gaussian stochastic processes and fields. In machine learning of neural network, interpolation is employed to train finite non-Gaussian samples. As numerical examples, the conditional simulation of non-Gaussian fluctuating wind pressures is carried out through using back propagation neural network and generalized regression neural network respectively.

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50

Fiedler, Christian, Carsten W. Scherer, and Sebastian Trimpe. "Practical and Rigorous Uncertainty Bounds for Gaussian Process Regression." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 8 (May 18, 2021): 7439–47. http://dx.doi.org/10.1609/aaai.v35i8.16912.

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Gaussian Process regression is a popular nonparametric regression method based on Bayesian principles that provides uncertainty estimates for its predictions. However, these estimates are of a Bayesian nature, whereas for some important applications, like learning-based control with safety guarantees, frequentist uncertainty bounds are required. Although such rigorous bounds are available for Gaussian Processes, they are too conservative to be useful in applications. This often leads practitioners to replacing these bounds by heuristics, thus breaking all theoretical guarantees. To address this problem, we introduce new uncertainty bounds that are rigorous, yet practically useful at the same time. In particular, the bounds can be explicitly evaluated and are much less conservative than state of the art results. Furthermore, we show that certain model misspecifications lead to only graceful degradation. We demonstrate these advantages and the usefulness of our results for learning-based control with numerical examples.

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