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.
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
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
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.