Overview

My research centers around methodological aspects of Bayesian statistics and its application to large scale complex data. I am particularly focused on developing methodology in a broad range of areas including semi-parametric density regression, shrinkage priors for anisotropic function estimation, variable selection with non-Gaussian errors, massive covariance matrix estimation, surface reconstruction and imaging and modeling shapes of non-Euclidean objects. I enjoy developing methodology that has an immediate motivation and impact to a particular application area, while being broadly applicable and leading to foundational questions. In the Bayes paradigm this often involves developing new classes of flexible prior distributions for densities, conditional densities, functions, sparse vectors, matrices or tensors. It is fascinating to explore the structure of the spaces on which the priors are supported while studying how the posterior concentrates as increasing amounts of data are collected. Studying these spaces becomes more challenging outside of unconstrained Euclidean spaces, such as in studying closed surfaces and other shapes, and when the dimension explodes. While Bayesian hierarchical models offer an unified and coherent framework for structured modeling and inference, two key challenges persist. First, as one moves away from simple parametric models, understanding properties of a posterior distribution poses a stiff challenge. Second, even if the true posterior has desirable properties, sampling from the posterior distribution in large scale problems commonly face scalability issues. This is relevant both for high-dimensional and big data problems. My research aims at addressing these challenges simultaneously, developing new theory to evaluate the associated procedures and developing scalable and highly efficient algorithms for Bayesian computation.


Grant support
  1. Office of Naval Research, 2014-2017, PI
  2. NSF DMS-1613156, 2016-2019, PI

Preprints and submitted papers
  1. Vo G., Pati D. Sparse additive Gaussian process with soft interactions. [link]
  2. Pati D., Bhattacharya A. Optimal Bayesian estimation in stochastic block models. [link]
  3. Wang L., Tang Y., Sinha D., Pati D., Lipsitz S.R. Bayesian Variable Selection for Skewed Heteroscedastic Response. [link] [code]
  4. Bhattacharya A., Pati D., Yang Y. Bayesian fractional posteriors. [link]
  5. Karwa V., Pati D., Petrovic S., Solus L. et al. Exact tests for stochastic block models. [link]
  6. Yang Y., Pati D. Bayesian model selection consistency and oracle inequality with intractable marginal likelihood. [link]
  7. Dasgupta S., Pati D., Srivastava A. A geometric framework For density modeling. [link] [Density-estimation-code] [Density-regression-code]
  8. Kumar P., Mukherjee T., Pati D., Xu L. Large scale FM signal strength map estimation for passive approximate localization. [link]
  9. Sabnis G., Pati D., Engelhardt B., Pillai N.S. A divide and conquer strategy for high dimensional Bayesian factor models. [link] [code]
  10. Zhou S., Pati D., Bhattacharya A., Dunson D.B. Adaptive posterior convergence rates in non-linear latent variable models. [link]
  11. Bhingare A., Sinha D., Pati D., Bandyopadhyay, D., Lipsitz S.R. Multivariate skewed responses: new semiparametric regression model and a Bayesian recourse. [link]
  12. Yang Y., Bhattacharya A., Pati D. Frequentist coverage and sup-norm convergence rate in Gaussian process regression. [link]

Published or accepted papers
  1. Pati, D., Reich, B.J., Dunson, D.B. (2011). Biometrika, 98 (1): 35-48.
    Bayesian geostatistical modeling with informative sampling locations.
    [link]
  2. Pati, D., Dunson, D.B., Tokdar, S.T. (2013). Journal of Multivariate Analysis, 116: 456-472.
    Posterior consistency in conditional distribution estimation.
    [link]
  3. Pati, D., & Dunson, D.B. (2014). Annals of the Institute for Statistical Mathematics, 66 (1): 1-31.
    Bayesian nonparametric regression with varying residual density.
    [link]
  4. Bhattacharya, A., Pati, D., & Dunson, D.B. (2014). Annals of Statistics, 32 (1): 352-381.
    Anisotropic function estimation with multi-bandwidth Gaussian process.
    [link]
  5. Pati, D., Bhattacharya, A., Pillai, N.S. & Dunson, D.B. (2014). Annals of Statistics, 42 (3): 1102-1130.
    Posterior contraction in sparse Bayesian factor models for massive covariance matrices.
    [link]
  6. Sarkar, A., Mallick, B.K., Staudenmayer, J., Pati, D. & Carroll, R.J. (2014) Journal of Computational and Graphical Statistics , 24 (3): 1101-1125.
    Bayesian Semiparametric Density Deconvolution in the Presence of Conditionally Heteroscedastic Measurement Errors.
    [link]
  7. Cervone, D., Pillai, N.S., Pati, D., Berbecko, R., & Lewis, J.H. (2014). Annals of Applied Statistics, 8 (3): 1341-1371.
    A location-mixture autoregressive model for online forecasting of lung-tumor motion.
    [link]
  8. Gu, K., Pati, D. & Dunson, D.B. (2014). Journal of the American Statistical Association, 109 (508): 1481-1494.
    Bayesian Multiscale Modeling of Closed Curves in Point Clouds.
    [link]
  9. Bhattacharya, A., Pati, D., Pillai, N.S. & Dunson, D.B. (2015). Journal of the American Statistical Association, 110 (512): 1479-1489.
    Dirichlet Laplace priors for optimal shrinkage.
    [link]
  10. Tang, Y., Sinha, D., Pati, D., Lipsitz, S. & Lipshultz, S. (2015). Biostatistics, 16 (3): 441-453.
    Bayesian Partial Linear Model for Skewed Longitudinal Data.
    [link]
  11. Zhang, Z., Pati, D. & Srivastava, A. (2015). Journal of Statistical Planning and Inference, 166: 171-186.
    Bayesian Clustering of Shapes of Curves.
    [link]
  12. Pati, D. & Bhattacharya, A. (2015). Statistics and Probability Letters, 103: 100-104.
    Adaptive Bayesian inference in the Gaussian sequence model using exponential-variance priors.
    [link]
  13. Pati, D., Bhattacharya, A. & Cheng G. (2015). Journal of Machine Learning Research, 16: 2837-2851.
    Optimal Bayesian estimation in random covariate design with a rescaled Gaussian process prior.
    [link]
  14. Bhattacharya, A., Pati, D., Pillai, N.S. & Dunson, D.B. (2016). Stochastic Processes and their Applications, 26 (12): 3828-3842.
    Sub-optimality of some continuous shrinkage priors.
    [link]
  15. Norets, A. & Pati, D. (2017). Econometric Theory, 33 (4): 980-1012.
    Adaptive Bayesian estimation of conditional densities.
    [link]
  16. Hanning, L. & Pati, D. (2017). Computational Statistics & Data Analysis, 107: 107-119.
    Variable selection using shrinkage priors.
    [link] [code]
  17. Sarkar, A., Pati, D., Chakrabarty, A., Mallick, B., Carroll, R.J. (2017). Journal of the American Statistical Association, to appear.
    Bayesian semiparametric multivariate density deconvolution.
    [link]
  18. Bhattacharya A., Pati D. (2017). Information and Inference. 6: 416-440. Posterior contraction in Gaussian process regression using Wasserstein approximations.
    [link]
  19. Vo, G., Pati, D. (2017) Open Journal of Statistics 7: 567-588.
    Sparse additive Gaussian process with soft interactions.
    [link]
  20. Pati, D., Bhattacharya, A., Yang, Y. (2018). Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics (AISTATS).
    On the Statistical optimality of variational Bayes.
    [link]
  21. Geng, J., Bhattacharya, A., Pati, D. (2018). Journal of the American Statistical Association, to appear.
    Probabilistic community detection with unknown number of communities.
    [link]
  22. Bhattacharya A., Pati D., Yang Y (2018) The Annals of Statistics, to appear.
    Bayesian fractional posteriors.
    [link]
  23. Dasgupta S., Pati D., Jermyn I, Srivastava S. (2018) 2018 IEEE Statistical Signal Processing Workshop (SSP).
    Shape-Constrained and Unconstrained Density Estimation Using Geometric Exploration.
  24. Bayesian fitting of closed surfaces through tensor products.
    Debdeep Pati, David B. Dunson. Journal of Machine Learning Research, accepted pending minor revisions.
    [link]

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