Research

Preprints

• Covariance operator estimation via adaptive thresholding. With O. Al-Ghattas, (2024). [arXiv].

• A First Course in Monte Carlo Methods. With O. Al-Ghattas, (2024). [arXiv].

• Data assimilation with machine learning surrogate models: a case-study with FourCastNet. With M. Adrian and R. Willett, (2024). [arXiv].

• Enhancing Gaussian processes for optimization and posterior approximation via random exploration. With H. Kim, (2024). [arXiv].

• Hierarchical Bayesian inverse problems: a high-dimensional statistics viewpoint. With N. Waniorek, (2024). [arXiv].

• Gaussian process regression under computational and epistemic misspecification. With R. Yang, (2023). [arXiv].

• Covariance operator estimation: sparsity, lengthscale, and ensemble Kalman filters. With O. Al-Ghattas, J. Chen, and N. Waniorek, (2023). [arXiv].

Publications

• Ensemble Kalman filters with resampling. With O. Al-Ghattas and J. Bao. 

SIAM/ASA Journal on Uncertainty Quantification, 12(2), 411-441, (2024). [arXiv].

• Optimization on manifolds via graph Gaussian processes. With H. Kim and R. Yang. 

SIAM Journal on Mathematics of Data Science, 6(1), 1-25, (2024). [arXiv].

• Analysis of a computational framework for Bayesian inverse problems: ensemble Kalman updates and MAP estimators under mesh refinement. With N. Waniorek. 

SIAM/ASA Journal on Uncertainty Quantification, 12(1), 30-68, (2024). [arXiv].

• Non-asymptotic analysis of ensemble Kalman updates: effective dimension and localization. With O. Al-Ghattas.

Information and Inference: A Journal of the IMA, 13(1), 1-66, (2024). [arXiv].

• Reduced-order autodifferentiable ensemble Kalman filters. With Y. Chen and R. Willett.

Inverse Problems, 39, 124001, 36pp, (2023). [arXiv].

• From optimization to sampling through gradient flows. With N. Garcia Trillos and B. Hosseini.

Notices of the American Mathematical Society, 70(6), 905-917, (2023).  [arXiv].

• Hierarchical ensemble Kalman methods with sparsity-promoting generalized gamma hyperpriors. With H. Kim and A. Strang.

Foundations of Data Science, 5, 366-388, (2023). [arXiv].

• Inverse Problems and Data Assimilation. With A. Stuart and A. Taeb. 

Cambridge University Press, Vol. 107, 228pp, (2023). [CUP, Amazon, Barnes and Noble]. Older version: [arXiv]. 

• Mathematical foundations of graph-based Bayesian semi-supervised learning. With N. Garcia Trillos and R. Yang.

Notices of the American Mathematical Society, 69(10), 1717-1729, (2022). [arXiv].

• A variational inference approach to inverse problems with gamma hyperpriors.  With S. Agarwal, H. Kim, and A. Strang.

SIAM/ASA J. Uncertainty Quantification, 10(4), 1533-1559, (2022). [arXiv].

• The SPDE approach to Matern fields: graph representations. With R. Yang.

Statistical Science, Vol 37, No. 4, 519-540, (2022). [arXiv].

• Finite element representations of Gaussian processes: Balancing numerical and statistical accuracy. With R. Yang.  

SIAM/ASA J. Uncertainty Quantification, 10(4), 1323-1349, (2022). [arXiv].

• Autodifferentiable ensemble Kalman filters. With Y. Chen and R. Willett. 

SIAM Journal on Mathematics of Data Science, 4(2), 801-833, (2022). [arXiv].

• Unlabeled data help in graph-based semi-supervised learning: a Bayesian nonparametrics perspective. With R. Yang.  

Journal of Machine Learning Research, 23, 1-28, (2022). [arXiv].

• Graph-based prior and forward models for inverse problems on manifolds with boundaries. With J. Harlim, S. Jiang, and H. Kim. 

Inverse Problems, 38, 035006, 31pp,  (2022).  [arXiv].

• Iterative ensemble Kalman methods: a unified perspective with some new variants. With N. Chada and Y. Chen.

Foundations of Data Science, 3, 331-369, (2021). [arXiv].

• HMC: avoiding rejections by not using leapfrog and some results on the acceptance rate. With M. P. Calvo and J. M. Sanz Serna. 

Journal of Computational Physics, 110333, (2021). [arXiv] [Journal].

• Bayesian update with importance sampling: required sample size. With Z. Wang. 

Entropy, 23(1), 22, 21pp, (2021). [arXiv].

• Kernel methods for Bayesian elliptic inverse problems on manifolds. With J. Harlim and R. Yang.

SIAM/ASA J. Uncertainty Quantification, 8(4), 1414-1445, (2020). [arXiv].

• Data-driven forward discretizations for Bayesian inversion. With D. Bigoni, Y. Chen, N. Garcia Trillos, and Y. Marzouk. 

Inverse Problems, 36, 105008, 27pp, (2020). [Journal].

• On the consistency of graph based Bayesian learning and the scalability of sampling algorithms. With N. García Trillos, Z. Kaplan, and T. Samakhoana.

Journal of Machine Learning Research, 21, 1-47, (2020). [arXiv]. 

• The Bayesian update: variational formulations and gradient flows. With N. García Trillos.

Bayesian Analysis, 15, 1, 29-56, (2020). [arXiv]. 

• Local regularization of noisy point clouds: improved global geometric estimates and data analysis. With N. García Trillos and R. Yang.

Journal of Machine Learning Research, 20, 1-37, (2019). [arXiv].

• Variational characterizations of local entropy and heat regularization in deep learning. With N. García Trillos and Z. Kaplan.

Entropy, 21(5), 511, 19pp, (2019). [Journal].

• Importance sampling and necessary sample size: an information theory approach. 

SIAM/ASA J. Uncertainty Quantification, 6(2), 867 (2018). [arXiv].

• Continuum limit of posteriors in graph Bayesian inverse problems. With N. García Trillos.

SIAM Journal on Mathematical Analysis, 50(4), 4020-4040 (2018). [arXiv].

• The Bayesian formulation and well-posedness of fractional elliptic inverse problems. With N. García Trillos.

Inverse Problems, 33, 6, 23pp, (2017). [arXiv].

• Importance sampling: intrinsic dimension and computational cost. With S. Agapiou, O. Papaspiliopoulos, and A. Stuart.

Statistical Science, Vol. 32, No. 3, 405-431, (2017). [arXiv]. 

• Gaussian approximations of small noise diffusions in Kullback-Leibler divergence. With A. Stuart.

Communications in Mathematical Sciences, Vol. 15, No. 7, 2087-2097, (2017). [arXiv]. 

• Filter accuracy for the Lorenz 96 model: Fixed versus adaptive observation operators. With K. Law, A. Shukla, and A. Stuart. 

Physica D: Nonlinear Phenomena, 325, 1-13, (2016). [Journal].

• Long-time asymptotics of the filtering distribution for partially observed chaotic dynamical systems. With A. Stuart. 

SIAM/ASA J. Uncertainty Quantification, 3(1), 1200-1220, (2015). [Journal].