Research

Research Overview

The research of our lab focuses on advancing theory, model and algorithms for general statistical and optimization problems arising in data science. One of the central theme of our research is to employ mathematical tools and insights from Algebraic Geometry, Algebraic Topology,  Differential Geometry/Riemannian geometry for statistics and optimization. Our main areas of research include (1) Geometry and Statistics; (2) Network Analysis; (2) Optimizations; and (4) Big Data Analysis. 

Publications 

Books

Bhattacharya, R., Lin, L.,  and Patrangenaru, V (2016).   A Course in Mathematical Statistics and Large Sample Theory. Springer Series in Statistics.  Link.

Research Articles

2020

Kolaczyk, E., Lin, L.,  Rosenberg, S., Xu, J. and Jackson, W. (2020). Averages of unlabeled networks: geometric characterization and asymptotic behavior .pdf
      Annals of Statistics (2020), Vol. 48, No. 1, 514-538.

Lee, K. and Lin, L. (2020). Bayesian Bandwidth Test and Selection for High-dimensional Banded Precision Matrices .pdf  
    Bayesian Analysis (2020), to appear.

 

2019

Niu, M., Cheung, P., Lin, L.,  Dai, Z., Lawrence, N. and Dunson, D. B. (2019). Intrinsic Gaussian processes on complex constrained domains .pdf.

 Journal of the Royal Statistical Society, Ser. B. (2019). vol. 81, 603--627

 Lee, K.,  Lee, J., and Lin, L (2019). Minimax posterior convergence rates and model selection consistency in high-dimensional DAG models based on sparse Cholesky factors .pdf 
      Annals of Statistics (2019), volume 47, Number 6, 3413--3437.

Lin, L., Niu, M., Pokman, C. and Dunson. D.B. (2019). Extrinsic Gaussian process models for regression and classification on manifolds .pdf
      Bayesian Analysis (2019), vol. 14, 907--926.

Bhattacharya, R. and Lin, L.(2019). Differential geometry for model independent analysis of images and other non-Euclidean data: recent development.pdf
      In: Sidoravicius V. (eds) Sojourns in Probability Theory and Statistical Physics - II. Springer Proceedings in Mathematics & Statistics, vol 299. Springer.

 Chae, M., Lin, L. and Dunson, D.B. (2019)  Bayesian sparse linear regression with unknown symmetric error. 
      Information and Inference (2019), vol 8 (3), 621--653. 

 Li, C., Lin, L. and Dunson, D.B. (2019).   On posterior consistency of tail index for Bayesian kernel mixture models. 
      Bernoulli (2019), vol. 25(3), 1999–2028. . Link.

Larsen, M. and Nguyen, D. Q (2019).
 Waring's problem for unipotent algebraic groupspdf
Annales de L'Institut Fourier, Tome 69, n.4 (2019), 1857-1877

Nguyen, D. Q (2019). Representation of units in cyclotomic function fields. pdf                                                International Journal of Number Theory, Vol. 15 (7), 1385-1401. 

 

 

2018

Sarpavayeva, B., Zhang, M. and Lin, L. (2018). Communication efficient parallel algorithms for optimization on manifold. Neural Information Processing Systems 2018.

Zhang, M., Lam, H. and Lin, L. (2018).  Robust and scalable Bayesian model selection. Computational Statistics & Data Analysis, Vol. 127, 229--247. Link.

Nguyen, D. Q. (2018). The Distribution of the Carlitz Binomial Coefficients Modulo a Prime. Annals of Combinatorics1-17. Link.

2017

Minsker, S., Srivastava, S., Lin, L. and Dunson, D.B. (2017). Robust and scalable Bayes via a median of subset posterior measure.  Journal of Machine Learning Research, 18(124):1--40. Link.

Mukherjee, S. S.,  Sarkar, P., and  Lin, L (2017). On clustering network-valued data. Neural Information Processing Systems 2017. Link.

Lin, L., Thomas, B., Zhu, H. and Dunson, D.B (2017).   Extrinsic local regression on manifold-valued data. Journal of the American Statistical Association-Theory and Methods. 112(519), 1261-1273. Link.

Bhattacharya, R. and Lin, L., (2017).  Omnibus CLTs for Fr\'echet means and nonparametric inference on non-Euclidean spaces.  Proceedings of American Mathematical Society, Vol. 145, 413-428 . Link.

Lazar, D. and Lin, L. (2017). Scale and curvature effects in principal geodesic analysis.  Journal of the Multivariate Analysis 153, 64--82. Link.

Lin, L., Rao, V.,  and Dunson, D.B (2017).  Bayesian nonparametric inference on Stiefel manifold.   Statistics Sinica, 27,  535--553.  Link.

Borg, J.S., Lin, L. et al. (2017) Rat intersubjective decisions are encoded by frequency-specific oscillatory contexts.  Brain and Behavior 7: e00710. DOI: 10.1002/brb3.710. Link.

Nguyen, D. Q.(2017) Certain sets over function fields are polynomial families. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, Volume XVII, 205–230. Link.

Nguyen, D. Q.(2017) The Brauer-Manin obstruction for certain quartic curves with negative discriminant. Communications in Algebra, 45 (2017), no. 2, 455–468. Link.

Nguyen, D.Q. (2017) Certain K3 surfaces parametrized by the Fibonacci sequence violate the Hasse principle Rocky Mountain Journal of Mathematics, Volume 47, Number 5, 1693–1710. Link.

Nguyen, D.Q. (2017) Certain forms violate the Hasse principle. Tokyo Journal of Mathematics, Volume 40 (2017), No. 1, 277–299. Link.  

Nguyen, D. Q.(2017). The classical umbral calculus, and the flow of a Drinfeld module. Transactions of the American Mathematical Society, Volume 369, no. 2, 1265–1289. Link.  

2016

Hultman, R., Mague, S.D., Li, Q., Katz, B.M., Michel, N., Lin, L., et.al (2016). Dysregulation of cortical-mediated slow evolving limbic dynamics drives stress-induced emotional pathology. Neuron 91(2),439–452. Link.

Rao, V., Lin, L., and Dunson, D.B (2016). Data augmentation for models based on rejection sampling. Biometrika 103 (2): 319–335 Arxiv:1406.6652. Link.

Li, D. , Wang, X., Lin, L. and Dey (2016). Flexible link functions in nonparametric binary regression with Gaussian process priors. Biometrics 72, 707–719. Link.

Nguyen, D.Q. (2016). Non-vanishing of Carlitz-Fermat quotients modulo primes. Rocky Mountain Journal of Mathematics, Volume 46, Number 1, 125–130. Link.

Nguyen, D.Q. (2016). Certain generalized Mordell curves over the rationals are pointless. Journal of the Australian Mathematical Society, 100, Issue 1, 42–64. Link.

Nguyen, D.Q. (2016). Function field analogues of Bang-Zsigmondy’s theorem and Feit’s theorem. Indiana University Mathematics Journal, Volume 65, Issue 6, 2081–2124. Link.

Nguyen, D.Q. (2016). Some basic results in elementary number theory in function fields. Journal of Number Theory, 159, 295–306. Link. 

2015

Lin, L, Piegorsch, W., and Bhattacharya, R. (2015). Nonparametric benchmark dose estimation with continuous dose-response data. Scandinavian Journal of Statistics 42, 713–731. Link.

Nguyen, D.Q. (2015). Algebraic families of hyperelliptic curves violating the Hasse principle. Pacific Journal of Mathematics, 274 (2015), no. 1, 141–182.  Link. 

2014

Lin, L. and Dunson, D. B. (2014). Bayesian monotone regression using Gaussian process projection. Biometrika, 101 (2): 303–317. Link.

Piegorsch, W., Xiong, H, Bhattacharya, R., and Lin, L. (2014). Benchmark dose analysis via nonparametric regression modeling. Risk Analysis 34(1), 135–151. Link.

Minsker, S., Srivastava, S., Lin, L., and Dunson, D.B. (2014) Scalable and robust Bayesian inference via the median posterior. Journal of Machine Learning Research, W&CP. Link.

Nguyen, D.Q. (2014) From separable polynomials to nonexistence of rational points on certain hyperelliptic curves. Journal of the Australian Mathematical Society, 96, Issue 3, 354–385. Link. 

Nguyen, D.Q. (2014) Carlitz module analogues of Mersenne primes, Wieferich primes, and certain prime elements in cyclotomic function fieldsJournal of Number Theory, 145, 181–193. Link.

 2013

Bhattacharya, R. and Lin, L. (2013). Recent progress in the nonparametric estimation of monotone curves -with applications to bioassay and environmental risk assessment.Computational Statistics & Data Analysis, 63, 63–80. Link.

Bhattacharya, R., Majumdar, M., and Lin, L. (2013). Problem of ruin and survival in economics: application of limit theorems in probability. Sankhyā, Ser.B 75(2), 145–180. Link.

Nguyen, D.Q. (2013). The Hasse principle for certain hyperelliptic curves and forms. The Quarterly Journal of Mathematics (Oxford), 64, no.1, 253–268. Link.

 

2012

 

Piegorsch, W., Xiong, H., Bhattacharya, R., and Lin, L.(2012). Nonparametric estimation of benchmark doses in environmental risk assessment. Environmetrics 23 (8), 717–728. Link.

Nguyen, D.Q. (2012). The arithmetic of certain del Pezzo surfaces and K3 surfaces
Journal de Th ́eorie des Nombres de Bordeaux, 24, no.2, pp. 447–460. Link. 

Nguyen, D.Q. (2012). The arithmetic of certain quartic curves. Monatshefte fu ̈r Mathematik, 168, no. 2, 191–214. Link. 

 

2011

Bhattacharya, R. and Lin, L. (2011). Nonparametric benchmark analysis in risk assessment: a comparative study by simulation and data analysis. Sankhyā, Ser.B 73(1), 144-163. Link.

Nguyen, D.Q. (2011). On the Hasse principle for certain quartic hypersurfaces. Proceedings of The American Mathematical Society, 139 (2011), no.12, pp. 4293–4305. Link. 

2010

Bhattacharya, R. and Lin, L. (2010). An adaptive nonparametric method in benchmark analysis for bioassay and environmental Studies. Stat & Probab. Lett 80, 1947-1953. Link.