Gaussian Process Controlled B-Spline Surface

References

• Akaike H (1998) Information theory and an extension of the maximum likelihood principle. Selected Papers of Hirotugu Akaike (Springer, New York), 199–213.Google Scholar
• Akritas AG, Akritas EK, Malaschonok GI (1996) Various proofs of Sylvester’s (determinant) identity. Math. Comput. Simulations 42(4):585–593.Google Scholar
• Atkinson PM, Lloyd CD (1998) Mapping precipitation in Switzerland with ordinary and indicator kriging. Special issue: Spatial interpolation comparison 97. J. Geographic Inform. Decision Anal. (Oxford) 2(1–2):72–86.Google Scholar
• Austin R (2011) Unmanned Aircraft Systems: UAVS Design, Development and Deployment (John Wiley & Sons, Hoboken, NJ).Google Scholar
• Besag J (1975) Statistical analysis of non-lattice data. Statistician 24(3):179–195.Google Scholar
• Bilionis I, Zabaras N (2012) Multi-output local Gaussian process regression: Applications to uncertainty quantification. J. Comput. Phys. 231(17):5718–5746.Google Scholar
• Blevins TL (2012) PID advances in industrial control. IFAC Proc. Volumes 45(3):23–28.Google Scholar
• Boer EP, de Beurs KM, Hartkamp AD (2001) Kriging and thin plate splines for mapping climate variables. Internat. J. Appl. Earth Observation Geoinformation 3(2):146–154.Google Scholar
• Cao J, Genton MG, Keyes DE, Turkiyyah GM (2021) Sum of Kronecker products representation and its Cholesky factorization for spatial covariance matrices from large grids. Comput. Statist. Data Anal. 157(1):107165.Google Scholar
• Caragea PC, Smith RL (2007) Asymptotic properties of computationally efficient alternative estimators for a class of multivariate normal models. J. Multivariance Anal. 98(7):1417–1440.Google Scholar
• Cetin M, Iplikci S (2015) A novel auto-tuning pid control mechanism for nonlinear systems. ISA Trans. 58(September):292–308.Google Scholar
• Che Y, Ma Y, Li Y, Ouyang L (2024) A novel active-learning kriging reliability analysis method based on parallelized sampling considering budget allocation. IEEE Trans. Reliability 73(1):589–601.Google Scholar
• Chen Z, Fan J, Wang K (2023) Multivariate Gaussian processes: Definitions, examples and applications. Metron 81(2):145–180.Google Scholar
• Cressie N (1993) Statistics for Spatial Data (John Wiley & Sons, Hoboken, NJ).Google Scholar
• Cressie N, Johannesson G (2008) Fixed rank kriging for very large spatial data sets. J. Roy. Statist. Soc. Ser. B 70(1):209–226.Google Scholar
• Eidsvik J, Shaby BA, Reich BJ, Wheeler M, Niemi J (2014) Estimation and prediction in spatial models with block composite likelihoods. J. Comput. Graphical Statist. 23(2):295–315.Google Scholar
• Finley AO, Datta A, Banerjee S (2022) spNNGP R package for nearest neighbor Gaussian process models. J. Statist. Software 103(5):1–40.Google Scholar
• Finney MA (1998) FARSITE: Fire Area Simulator-model development and evaluation, U.S. Department of Agriculture, Forest Service, Rocky Mountain Research Station, Ogden, UT.Google Scholar
• Fricker TE, Oakley JE, Urban NM (2013) Multivariate Gaussian process emulators with nonseparable covariance structures. Technometrics 55(1):47–56.Google Scholar
• Friedman JH (1991) Multivariate adaptive regression splines. Ann. Statist. 19(1):1–67.Google Scholar
• Fuhg JN, Fau A, Nackenhorst U (2021) State-of-the-art and comparative review of adaptive sampling methods for kriging. Arch. Computational Methods Engrg. 28:2689–2747.Google Scholar
• Furrer R, Genton MG, Nychka D (2006) Covariance tapering for interpolation of large spatial data sets. J. Comput. Graph. Statist. 15(3):502–523.Google Scholar
• Ghosh M, Li Y, Zeng L, Zhang Z, Zhou Q (2021) Modeling multivariate profiles using Gaussian process-controlled B-splines. IISE Trans. 53(7):787–798.Google Scholar
• Gu C (2013) Smoothing Spline ANOVA Models, vol. 297 (Springer, Berlin).Google Scholar
• Guinness J (2018) Permutation and grouping methods for sharpening Gaussian process approximations. Technometrics 60(4):415–429.Google Scholar
• He X, Shen L, Shen Z (2001) A data-adaptive knot selection scheme for fitting splines. IEEE Signal Processing Lett. 8(5):137–139.Google Scholar
• Heagerty PJ, Lele SR (1998) A composite likelihood approach to binary spatial data. J. Amer. Statist. Assoc. 93(443):1099–1111.Google Scholar
• Hensman J, Fusi N, Lawrence ND (2013) Gaussian processes for big data. Nicholson AE, Smyth P, ed. Proc. Twenty-Ninth Conf. Uncertainty Artificial Intelligence (UAI’13) (AUAI Press, Arlington, TX), 282–290.Google Scholar
• Hristopulos DT (2024) Non-separable covariance kernels for spatiotemporal Gaussian processes based on a hybrid spectral method and the harmonic oscillator. IEEE Trans. Inform. Theory 70(2):1268–1283.Google Scholar
• Hurtt GC, Dubayah R, Drake J, Moorcroft PR, Pacala SW, Blair JB, Fearon MG (2004) Beyond potential vegetation: Combining lidar data and a height-structured model for carbon studies. Ecological Appl. 14(3):873–883.Google Scholar
• Jones DR, Schonlau M, Welch WJ (1998) Efficient global optimization of expensive black-box functions. J. Global Optim. 13:455–492.Google Scholar
• Katzfuss M (2017) A multi-resolution approximation for massive spatial data sets. J. Amer. Statist. Assoc. 112(517):201–214.Google Scholar
• Katzfuss M, Guinness J (2021) A general framework for Vecchia approximations of Gaussian processes. Statist. Sci. 36(1):124–141.Google Scholar
• Katzfuss M, Guinness J, Gong W, Zilber D (2020) Vecchia approximations of Gaussian-process predictions. J. Agricultural Biological Environment. Statist. 25(3):383–414.Google Scholar
• Kaufman CG, Schervish MJ, Nychka DW (2008) Covariance tapering for likelihood-based estimation in large spatial data sets. J. Amer. Statist. Assoc. 103(484):1545–1555.Google Scholar
• Kleijnen JPC (2009) Kriging metamodeling in simulation: A review. Eur. J. Oper. Res. 192(3):707–716.Google Scholar
• Klein T, Randin C, Körner C (2015) Water availability predicts forest canopy height at the global scale. Ecology Lett. 18(12):1311–1320.Google Scholar
• Lee JH, Song JY, Kim DW, Kim JW, Kim YJ, Jung SY (2018) Particle swarm optimization algorithm with intelligent particle number control for optimal design of electric machines. IEEE Trans. Industry Electronics 65(2):1791–1798.Google Scholar
• Li Y, Li Y, Wang D (2025) Periodic Gaussian process controlled B-spline for scalable modeling of irregularly spaced signals. IEEE Trans. Inform. Theory 71(10):7842–7855.Google Scholar
• Li Y, Zhou Q, Jiang W, Tsui KL (2024a) Optimal composite likelihood estimation and prediction for distributed Gaussian process modeling. IEEE Trans. Pattern Anal. Machine Intelligence 46(2):1134–1147.Google Scholar
• Li Y, Zhang Y, Wu J, Xie M (2024b) Regularized periodic Gaussian process for nonparametric sparse feature extraction from noisy periodic signals. IEEE Trans. Automation Sci. Engrg. 22:3011–3020.Google Scholar
• Lindsay BG (1988) Composite likelihood methods. Contemporary Math. 80(1):221–239.Google Scholar
• Lindsay BG, Yi GY, Sun J (2011) Issues and strategies in the selection of composite likelihoods. Statist. Sinica 21(1):71–105.Google Scholar
• Liu H, Ong YS, Shen X, Cai J (2020) When Gaussian process meets big data: A review of scalable GPS. IEEE Trans. Neural Networks Learn. Systems 31(11):4405–4423.Google Scholar
• Ma P, Huang JZ, Zhang N (2015) Efficient computation of smoothing splines via adaptive basis sampling. Biometrika 102(3):631–645.Google Scholar
• Mallasto A, Feragen A (2017) Learning from uncertain curves: The 2-Wasserstein metric for Gaussian processes. Guyon I, von Luxburg UV, Bengio S, Wallach H, Fergus R, Vishwanathan S, Garnett R, eds. Advances in Neural Information Processing Systems, vol. 30 (Curran Associates, Red Hook, NY), 5660–5670.Google Scholar
• Matheron G (1963) Principles of geostatistics. Econom. Geology 58(8):1246–1266.Google Scholar
• Morris MD, Mitchell TJ, Ylvisaker D (1993) Bayesian design and analysis of computer experiments: Use of derivatives in surface prediction. Technometrics 35(3):243–255.Google Scholar
• Mühlenbein H, Schomisch M, Born J (1991) The parallel genetic algorithm as function optimizer. Parallel Comput. 17(6–7):619–632.Google Scholar
• Park JS (1994) Optimal latin-hypercube designs for computer experiments. J. Statist. Planning Inference 39(1):95–111.Google Scholar
• Powell JL (1994) Estimation of semiparametric models. Handbook Econom. 4:2443–2521.Google Scholar
• Prautzsch H, Boehm W, Paluszny M (2002) Bézier and B-Spline Techniques (Springer Science & Business Media, Boston).Google Scholar
• Rasmussen CE, Williams CKI (2006) Gaussian Processes for Machine Learning (MIT Press, Cambridge, MA).Google Scholar
• Redivo-Zaglia M, Rodriguez G (2012) SMT: A matlab toolbox for structured matrices. Numerical Algorithms 59(4):639–659.Google Scholar
• Ruppert D, Wand MP, Carroll RJ (2003) Semiparametric Regression (Cambridge University Press, New York).Google Scholar
• Sacks J, Schiller SB, Welch WJ (1989) Designs for computer experiments. Technometrics 31(1):41–47.Google Scholar
• Salimi-Khorshidi G, Nichols T, Smith S, Woolrich M (2011) Using Gaussian-process regression for meta-analytic neuroimaging inference based on sparse observations. IEEE Trans. Medical Imaging 30(7):1401–1416.Google Scholar
• Sang H, Huang JZ (2012) A full scale approximation of covariance functions for large spatial data sets. J. Roy. Statist. Soc. Ser. B Statist. Methodology 74(1):111–132.Google Scholar
• Santner TJ, Williams BJ, Notz WI (2003) The design and analysis of computer experiments. Series in Statistcs (Springer, New York):1–13.Google Scholar
• Schulz E, Speekenbrink M, Krause A (2018) A tutorial on Gaussian process regression: Modelling, exploring, and exploiting functions. J. Math. Psych. 85(August):1–16.Google Scholar
• Sherman J, Morrison WJ (1950) Adjustment of an Inverse matrix corresponding to a change in one element of a given matrix. Ann. Math. Statist. 21(1):124–127.Google Scholar
• Snelson E, Ghahramani Z (2006) Sparse Gausian processes using pseudo-inputs. Adv. Neural Inform. Processing Systems 18:1257–1264.Google Scholar
• Snoek J, Larochelle H, Adams RP (2012) Practical Bayesian optimization of machine learning algorithms. Pereira F, Burges CJ, Bottou L, Weinberger KQ, ed. Advances in Neural Information Processing Systems (Curran Associates, Red Hook, NY), 2951–2959.Google Scholar
• Son PW, Rhee JH, Hwang J, Seo J (2019) Universal kriging for Loran ASF map generation. IEEE Trans. Aerospace Electronic Systems 55(4):1828–1842.Google Scholar
• Srinivas N, Krause A, Kakade SM, Seeger M (2010) Gaussian process optimization in the bandit setting: No regret and experimental design. Fürnkranz J, Joachims T, ed. Proc. 27th Internat. Conf. Machine Learn. (Omnipress, Madison, WI), 1015–1022.Google Scholar
• Stein ML (2008) A modeling approach for large spatial data sets. J. Korean Statist. Soc. 37(1):3–10.Google Scholar
• Stein ML, Chi Z, Welty LJ (2004) Approximating likelihoods for large spatial data sets. J. Roy. Statist. Soc. Ser. B 66(2):275–296.Google Scholar
• Su G, Peng L, Hu L (2017) A Gaussian process-based dynamic surrogate model for complex engineering structural reliability analysis. Structural Safety 68(September):97–109.Google Scholar
• Sun L, Hong L, Hu Z (2014) Balancing exploitation and exploration in discrete optimization via simulation through a Gaussian process-based search. Oper. Res. 62(6):1416–1438.Link, Google Scholar
• Sun J, Zhou S, Veeramani D, Liu K (2024) Prediction of condition monitoring signals using scalable pairwise Gaussian processes and Bayesian model averaging. IEEE Trans. Automation Sci. Engrg. 22:2746–2757.Google Scholar
• Titsias M (2009) Variational learning of inducing variables in sparse Gaussian processes. Proc. 12th Internat. Conf. Artificial Intelligence Statist., vol. 5 (PMLR, New York), 567–574. Google Scholar
• Valavanis KP, Vachtsevanos GJ (2014) Handbook of Unmanned Aerial Vehicles (Springer, Berlin).Google Scholar
• Varin C, Reid N, Firth D (2011) An overview of composite likelihood methods. Statist. Sinica 21(1):5–42.Google Scholar
• Vaserstein LN (1969) Markov processes over denumerable products of spaces describing large systems of automata. Problemy Peredachi Informatsii 5(3):47–52.Google Scholar
• Vecchia AV (1988) Estimation and model identification for continuous spatial processes. J. Roy. Statist. Soc. Ser. B (Methodological) 50(2):297–312.Google Scholar
• Villani C (2009) Optimal Transport: Old and New (Springer, Berlin).Google Scholar
• Wahba G (1990) Spline Models for Observational Data (SIAM, Philadelphia).Google Scholar
• Wang X, Hong LJ, Jiang Z, Shen H (2023) Gaussian process-based random search for continuous optimization via simulation. Oper. Res. 73(1):1–23.Google Scholar
• Wilson A, Nickisch H (2015) Kernel interpolation for scalable structured Gaussian processes (KISS-GP). Bach F, Blei DM, ed. Proc. 32nd Internat. Conf. Machine Learn. (PMLR, Bethesda, MD), 1775–1784.Google Scholar
• Xiong S (2021) The reconstruction approach: From interpolation to regression. Technometrics 63(2):225–235.Google Scholar
• Xu R, Huang S, Song Z, Gao Y, Wu J (2024) A deep mixed-effects modeling approach for real-time monitoring of metal additive manufacturing process. IISE Trans. 56(9):945–959.Google Scholar
• Yasarla R, Sindagi VA, Patel VM (2021) Semi-supervised image deraining using Gaussian processes. IEEE Trans. Image Processing 30:6570–6582.Google Scholar
• Yuan Y, Chen N, Zhou S (2013) Adaptive B-spline knot selection using multi-resolution basis set. IIE Trans. 45(12):1263–1277.Google Scholar
• Zhang Y, Apley DW, Chen W (2020) Bayesian optimization for materials design with mixed quantitative and qualitative variables. Sci. Rep. 10(1):4924.Google Scholar