Research


My research interests lie in Bayesian statistics, uncertainty quantification, machine learning, and statistical computing. My work focuses on the development of both Bayesian models to address UQ and machine learning problems, as well as computational algorithms to facilitate inference in complex statistical models.


RESEARCH INTERESTS
  • Bayesian methods
Model Selection ● Big Data analysis ● High Dimensionality ● Variable Selection
  • Statistical machine learning, & Uncertainty quantification
Computer model calibration ● inverse problems ● Gaussian process regression ● generalized polynomial chaos
  • Monte Carlo methods
Markov chain Monte Carlo (MCMC) ● reversible jump MCMC ●  pseudo-marginal MCMC
stochastic approximation Monte Carlo
● simulated annealing algorithms ● Approximate Bayesian Computations ● stochastic gradient MCMC
  • Applications:  Climate,  and Engineering,
 Storm Surge ● Ice Sheet Weather precipitation models & calibration
Carbon Capture models & calibration ● Smart Devices ● Smart Power Systems


SOME RESEARCH DIRECTIONS

Design of emulators for predictive modeling and uncertainty quantification

Description: Uncertainty quantification (UQ) provides a quantitative characterization of uncertainties in complex systems and the efficient propagation of them for model prediction given available data. Computer experiments are used to study such problems. When the actual system is expensive to `run', it is often required the construction of a cheap, tractable but approximated mathematical model able to emulate its output as a function of the input. Such models are called emulators, or surrogate-models and are based on Gaussian process regression, and generalized polynomial chaos expansions. Nowadays, the growing complexity of systems requires the design of improved emulators to address new challenges.

Results:
We have developed Bayesian models providing nonstationarity/discontinuity modeling in UQ problems. Based on these models, we have proposed a sequential design of experiments technique to `wisely' select training-data, that allow the accurate evaluation of the emulator in an adaptive manner. We have designed Bayesian variable selection procedures able to address the `curse of dimensionality' challenge often encountered, for example in the context of generalized polynomial chaos surrogate models.

References:

  • Ma, P., Karagiannis, G., Konomi, B.A., Asher, T.G., Toro, G.R. & Cox, A.T. (2022) Multifidelity computer model emulation with high-dimensional output: An application to storm surge. Journal of the Royal Statistical Society: Series C, 1–23
  • Karagiannis, G., Konomi, B. A., and Lin, G. (2015). A Bayesian mixed shrinkage prior procedure for spatial-stochastic basis selection and evaluation of gPC expansions: Applications to elliptic SPDEs. Journal of Computational Physics, 284:528 - 546.
  • Konomi, B. A., Karagiannis, G., and Lin, G. (2015). On the Bayesian treed multivariate Gaussian process with linear model of coregionalization. Journal of Statistical Planning and Inference, 157-158:1 - 15.
  • Zhang, B., Konomi, B. A., Sang, H., Karagiannis, G., and Lin, G. (2015). Full scale multi-output Gaussian process emulator with nonseparable auto-covariance functions. Journal of Computational Physics, 300:623 - 642.
  • Karagiannis, G. and Lin, G. (2014). Selection of polynomial chaos bases via Bayesian model uncertainty methods with applications to sparse approximation of PDEs with stochastic inputs. Journal of Computational Physics, 259:114 - 134.
  • Konomi, B. A., Karagiannis, G., Sarkar, A., Sun, X., and Lin, G. (2014). Bayesian treed multivariate Gaussian process with adaptive design: Application to a carbon capture unit. Technometrics, 56(2):145- 158.

Bayesian inverse, and model calibration problems

Description:
Computer experiments often use computer models (simulators) to simulate the behavior of a complex real system under consideration. Simulators often include additional calibration parameters that regulate their behavior. It is important to find optimal values for these parameters, as well as to quantify their uncertainty through probabilities, in order to improve the predictive ability of the simulator, or in order to better understand a physical phenomenon associated with a specific parametrization.

Results:  We have proposed procedures that lead to more accurately calibrated the simulators in challenging problems.  We have developed Bayesian model calibration method that accounts for non-stationarity, discontinuity, or localized features in the output of the simulator or the real system. Moreover, we have worked on the development of a new Bayesian method that recovers these optimal values of the calibration parameters as functions of the inputs.

References:
  • Chang, W., Konomi, B. A., Karagiannis, G., Guan, Y., & Haran, M. (2022). Ice Model Calibration Using Semi-continuous Spatial Data. Annals of Applied Statistics.
  • Cheng, S., Konomi, B. A., Matthews, J. L., Karagiannis, G., & Kang, E. L. (2021). Hierarchical Bayesian nearest neighbor co-kriging Gaussian process models; an application to intersatellite calibration. Spatial Statistics, 100516.
  • Karagiannis, G., Konomi, B. A., and Lin, G. (2019). On the Bayesian calibration of expensive computer models with input dependent parameters, Spatial Statistics
  • Konomi, B. A., Karagiannis, G., Lai, K., and Lin, G. (2017). Bayesian treed calibration: An application to carbon capture with AX sorbent. Journal of the American Statistical Association, 112(517):37-53.


Selection, and combination of  computer models


Description: For many real systems, several computer models (simulators) may exist with different physics and predictive abilities. To achieve more accurate simulations/predictions, it is desirable for these models to be properly combined and calibrated. In the same context, are the problems that involve fast & slow simulators that is, when one simulator is slow to run but very accurate while the other is slow to run but less accurate. In other cases, the simulator may require the selection of a sub-model (from a set of available ones) in order to run, and hence it is desirable to select the `best' one.


Results: The development of Bayesian procedures able to combine the different simulators, such that the contribution of each simulator is different at different input values. Moreover, we have worked on the development of procedures able to select the `best' sub-model, which may be different at different inputs, from a set of available ones in the Bayesian framework.


References:

  • Ma, P., Karagiannis, G., Konomi, B.A., Asher, T.G., Toro, G.R. & Cox, A.T. (2022) Multifidelity computer model emulation with high-dimensional output: An application to storm surge. Journal of the Royal Statistical Society: Series C, 1–23
  • Konomi, B. A., & Karagiannis, G. (2020). Bayesian analysis of multifidelity computer models with local features and non-nested experimental designs: Application to the WRF model. Technometrics., 1-31.
  • Karagiannis, G., Konomi, B. A., and Lin, G. (2019). On the Bayesian calibration of expensive computer models with input dependent parameters, Spatial Statistics
  • Karagiannis, G. and Lin, G. (2017). On the Bayesian calibration of computer model mixtures through experimental data, and the design of predictive models. Journal of Computational Physics, 342:139 - 160.


Monte Carlo methods 

Details: Monte Carlo methods are simulation algorithms aiming at computing probabilities and expectations in complex stochastic models. They are important computational methods used to facilitate inference in complex statistical models. The growing complexity of statistical models requires the construction of new more powerful Monte Carlo algorithms.

Results: We have worked on the construction of a trans-dimensional MCMC algorithm that aims at mitigating the sensitivity of reversible jump algorithms to the poor design of their proposals, and can be used for Bayesian model selection inference. Also, we have constructed a stochastic optimization algorithm that aims at overcoming the local trapping problem, and can be implemented in parallel computational environments.

References:
  • Deng, W., Feng, Q., Karagiannis, G., Lin, G., & Liang, F. (2021). Accelerating Convergence of Replica Exchange Stochastic Gradient MCMC via Variance Reduction. International Conference on Learning Representations (ICLR'21).
  • Karagiannis, G., Konomi, B. A., Lin, G., and Liang, F. (2017). Parallel and interacting stochastic approximation annealing algorithms for global optimisation. Statistics and Computing, 27(4):927–945.  [arXiv] [Supplementary material]
  • Karagiannis, G. and Andrieu, C. (2013). Annealed importance sampling reversible jump MCMC algorithms. Journal of Computational and Graphical Statistics, 22(3):623-648.


Interdisciplinary Research


Results: We have worked on interdisciplinary research on areas such as engineering, climatology, renewable energy, biology, etc... where we used modern statistical techniques and data analytics.

References:
  • Karagiannis, G., Hou, Z., Huang, M., & Lin, G. (2022). Inverse modeling of hydrologic parameters in CLM4 via generalized polynomial chaos in the Bayesian framework. Computation, 10(5), 72.
  • Alamaniotis, M., Martinez-Molina, A., & Karagiannis, G. (2021, June). Data Driven Update of Load Forecasts in Smart Power Systems using Fuzzy Fusion of Learning GPs. In 2021 IEEE Madrid PowerTech (pp. 1-6). IEEE.
  • Karagiannis, G., Hao, W., & Lin, G. (2020) Calibrations and validations of biological models with an application on the renal fibrosis. International Journal for Numerical Methods in Biomedical Engineering, e3329.
  • Alamaniotis, M., and Karagiannis, G. (2017). Integration of Gaussian Processes and Particle Swarm Optimization for Very-Short Term Wind Speed Forecasting in Smart Power. International Journal of Monitoring and Surveillance Technologies Research (IJMSTR), 5(3), 1-14.
  • Alamaniotis, M., & Karagiannis, G. (2018), Genetic Driven Multi-Relevance Vector Regression Forecasting of Hourly Wind Speed in Smart Power Systems, IEEE PES Innovative Smart Grid Technologies – North America, pp. 1-5.
  • Nasiakou, A., Alamaniotis, M., Toukalas, L.H. & Karagiannis, G. (2017), A Three-Stage Scheme for Consumers' Partitioning Using Hierarchical Clustering Algorithm, 8th International Conference on Information, Systems and Applications (IISA). Larnaca, Cyprus, 6.