Research

I have a broad interest in a range of statistics and machine learning topics, largely motivated by neuroscience, medical imaging analysis, and biomedical applications including Alzheimer's disease, diabetes, and Parkinson's disease.

Imaging tensor analysis

• Tensor predictor regression:
  We study a class of regression models where the predictor is a multi-dimensional array, aka, tensor. We aim to answer questions like using MRI images to predict the clinical outcome, and to identify brain regions that are most predictive of the outcome.

  • Zhou, H., Li, L., and Zhu, H. (2013). Tensor regression with applications in neuroimaging data analysis. Journal of the American Statistical Association, 108, 540-552.

  • Zhou, H., and Li, L. (2014). Regularized matrix regression. Journal of the Royal Statistical Society, Series B., 76, 463-483.

  • Li, Z., Suk, H-I., Shen, D., and Li, L. (2016). Sparse multi-response tensor regression for Alzheimer's disease study with multivariate clinical assessments. IEEE Transactions on Medical Imaging, 35, 1927-1936.

  • Zhang, X. and Li, L. (2017). Tensor envelope partial least squares regression. Technometrics, 59, 426-436.

  • Li, X., Xu, D., Li, L., and Zhou, H. (2018). Tucker tensor regression and neuroimaging analysis. Statistics in Biosciences, 10, 520-545.

  • Zhang, X., Li, L., Zhou, H., Zhou, Y., and Shen, D. (2019). Tensor generalized estimating equations for longitudinal imaging analysis. Statistica Sinica, 29, 1977-2005.

• Tensor response regression:
  We study a class of regression models where the response is a tensor. We aim to answer questions like finding “differentially-expressed” brain regions between the group of disorder patients and healthy controls while accounting for other covariates.

  • Sun, W.W. and Li, L. (2017). Sparse tensor response regression and neuroimaging analysis. Journal of Machine Learning Research, 18, 4908-4944.

  • Li, L. and Zhang, X. (2017). Parsimonious tensor response regression. Journal of the American Statistical Association, 112, 1131-1146.

  • Zhou, J., Sun, W.W., Zhang, J., and Li, L. (2023). Partially observed dynamic tensor response regression. Journal of the American Statistical Association, 118, 424-439.

  • Zhang, D., Li, L., Sripada, C., and Kang, J. (2023). Image response regression via deep neural networks. Journal of the Royal Statistical Society, Series B., 85, 1589-1614.

• Tensor decomposition and tensor clustering:
  We study tensor clustering, and decomposition of a tensor where all entries are binary-valued.

  • Sun, W.W., and Li, L. (2019). Dynamic tensor clustering. Journal of the American Statistical Association, 114, 1894-1907.

  • Wang, M., and Li, L. (2020). Learning from binary multiway data: probabilistic tensor decomposition and its statistical optimality. Journal of Machine Learning Research, 21, 1-38.

• Review of statistical tensor analysis:
  We survey tensor analysis in modern statistical learning, and cover four main topics, including tensor supervised learning, tensor unsupervised learning, tensor reinforcement learning, and tensor deep learning.

  • Sun, W.W., Hao, B., and Li, L. (2021). Tensor data analysis. Wiley StatsRef: Statistics Reference Online, 1-26.

Brain connectivity analysis

• Functional connectivity network estimation:
  We estimate brain functional connectivity networks, and aim to understand the differences of connectivity networks across different groups of subjects.

  • Zhu, Y. and Li, L. (2018). Multiple matrix Gaussian graphs estimation. Journal of the Royal Statistical Society, Series B., 80, 927-950.

  • Wang, W., Zhang, X., and Li, L. (2019). Common reducing subspace model and network alternation analysis. Biometrics, 75, 1109-1120.

  • Lee, K.Y., Li, L., Li, B., and Zhao, H. (2023). Nonparametric functional graphical modeling through functional additive regression operator. Journal of the American Statistical Association, 118, 1718-1732.

• Functional connectivity network inference:
  We perform formal statistical inference and compute the p-values for the individual edges of brain functional connectivity networks, in the one-sample setting, two-sample setting, and paired (before and after the treatment) setting.

  • Xia, Y. and Li, L. (2017). Hypothesis testing of matrix graph model with application to brain connectivity analysis. Biometrics, 73, 780-791.

  • Xia, Y. and Li, L. (2019). Matrix graph hypothesis testing and application in brain connectivity alternation detection. Statistica Sinica, 29, 303-328.

  • Ye, Y., Xia, Y., and Li, L. (2021). Paired test of matrix graphs and brain connectivity analysis. Biostatistics, 22, 402-420.

  • Xia, Y., and Li, L. (2022). Hypothesis testing for network data with power enhancement. Statistica Sinica, 32, 293-321.

• Functional connectivity network association modeling:
  We build a class of regression models where the response is a functional connectivity network, and aim to identify both the brain regions whose connectivity is significantly altered and the important driving factors that alter the connectivity.

  • Zhang, J., Sun, W.W., and Li, L. (2023). Generalized connectivity matrix response regression with applications in brain connectivity studies. Journal of Computational and Graphical Statistics, 32, 252-262.

• Dynamic functional connectivity network modeling:
  We model brain functional connectivity networks that change over time or some conditioning phenotypic variables.

  • Sun, W.W., and Li, L. (2019). Dynamic tensor clustering. Journal of the American Statistical Association, 114, 1894-1907.

  • Zhang, J., Sun, W.W., and Li, L. (2020). Mixed-effect time-varying stochastic blockmodel and application in brain connectivity analysis. Journal of the American Statistical Association, 115, 2022-2036.

  • Lee, K.Y., Ji, D., Li, L., Constable, T., and Zhao, H. (2023). Conditional functional graphical models. Journal of the American Statistical Association/, 118, 257-271.

• Effective connectivity network estimation:
  We estimate brain effective connectivity networks where the edges have directions.

  • Lyu, X., Kang, J., and Li, L. (2023). Statistical inference for high-dimensional vector autoregression with measurement error. Statistica Sinica, 33, 1435-1459.

  • Dai, X., and Li, L. (2022). Kernel ordinary differential equations. Journal of the American Statistical Association, 117, 1711-1725.

• Review of statistical modeling of brain networks:
  We review statistical and computational methods for two types of biological networks, gene networks and brain connectivity networks.

  • Wang, Y.R., Li, L., Li, J.J. and Huang, H. (2021). Network modeling in biology: statistical methods for gene and brain networks. Statistical Science, 36, 89-108.

Multimodal neuroimaging analysis

• Multimodal association analysis:
  We aim to identify brain regions where two imaging modalities are significantly correlated, or change the most as the third imaging modality changes.

  • Li, L., Kang, J., Lockhart, S.N., Adams, J., and Jagust, W. (2019). Spatially adaptive varying correlation analysis for multimodal neuroimaging data. IEEE Transactions on Medical Imaging, 38, 113-123.

  • Xia, Y., Li, L., Lockhart, S.N., and Jagust, W.J. (2020). Simultaneous covariance inference for multimodal integrative analysis. Journal of the American Statistical Association, 115, 1279-1291.

  • Li, L., Zeng, J., and Zhang, X. (2023). Generalized liquid association analysis for multimodal neuroimaging. Journal of the American Statistical Association, 118, 1984-1996.

• Multimodal joint regression analysis:
  We study a joint classification or regression model with multiple imaging modalities as the predictors. We aim to quantify the contribution of each individual modality given the other modalities, and to rigorously infer the effect of primary imaging modality after controlling the auxiliary modalities.

  • Adams J.N., Lockhart, S.N., Li, L., and Jagust, W.J. (2018). Relationships between tau and glucose metabolism reflect Alzheimer’s disease pathology in cognitively normal older adults. Cerebral Cortex, 29, 1997-2009.

  • Li, Q., and Li, L. (2018). Integrative linear discriminant analysis with guaranteed error rate improvement. Biometrika, 105, 917-930.

  • Li, Q., and Li, L. (2022). Integrative factor regression and its inference for multimodal data analysis. Journal of the American Statistical Association, 117, 2207-2221.

  • Dai, X. and Li, L. (2023). Orthogonalized kernel debiased machine learning for multimodal data analysis. Journal of the American Statistical Association, 118, 1796-1810.

Neuroimaging causal inference and mediation analysis

• Dynamic causal modeling and directed acyclic graph modeling:
  We study estimation and inference of directed acyclic graphs and dynamic causal modeling, and can handle nonlinear interactions and tens to hundreds of nodes.

  • Dai, X., and Li, L. (2022). Kernel ordinary differential equations. Journal of the American Statistical Association, 117, 1711-1725.

  • Lee, K.Y., and Li, L. (2022). Functional structural equation model. Journal of the Royal Statistical Society, Series B., 84, 600-629.

  • Lee, K.Y., Li, L., and Li, B. (2024+). Functional directed acyclic graphs. Journal of Machine Learning Research, accepted.

  • Shi, C., Zhou, Y., and Li, L. (2024+). Testing directed acyclic graph via structural, supervised and generative adversarial learning. Journal of the American Statistical Association, accepted.

• Mediation analysis:
  We develop formal hypothesis testing procedures to quantify the significance of individual mediators while allowing interactions among the mediators. We also study the sparse estimation and inference when there are a sequence sets of mediators or when there are high-dimensional exposure variables.

  • Zhao, Y., Li, L., and Caffo, B.S. (2021). Multimodal neuroimaging data integration and pathway analysis. Biometrics, 77, 879-889.

  • Zhao, Y., and Li, L. (2022). Multimodal data integration via mediation analysis with high-dimensional exposures and mediators. Human Brain Mapping, 43, 2519–2533.

  • Shi, C., and Li, L. (2022). Testing mediation effects using logic of Boolean matrices. Journal of the American Statistical Association, 117, 2014-2027.

  • Li, L., Shi, C., Guo, T., and Jagust, W.J. (2022). Sequential pathway inference for multimodal neuroimaging analysis. Stat, 11:e433.

Ordinary differential equations, point process, and functional data analysis

• Ordinary differential equations modeling:
  We use reproducing kernels and deep neural networks to model nonparametric associations in a system of ordinary differential equations.

  • Dai, X., and Li, L. (2022). Kernel ordinary differential equations. Journal of the American Statistical Association, 117, 1711-1725.

  • Liu, Y., Li, L., and Wang, X. (2022). A nonlinear sparse neural ordinary differential equation model for multiple functional processes. The Canadian Journal of Statistics, 50, 59-85.

  • Dai, X. and Li, L. (2024). Post-regularization confidence bands for ordinary differential equations. Journal of Machine Learning Research, 25, 1-51.

• Point process modeling:
  We model the event times data arising from neural spike trains and electronic health records.

  • Tang, X. and Li, L. (2023). Multivariate temporal point process regression. Journal of the American Statistical Association, 118, 830-845.

• Functional data modeling:
  We develop a series of linear operator-based methods to estimate graphical models of multivariate functions, and to study parametric and nonparametric, static and dynamic connectivity networks.

  • Lee, K.Y., Li, L., Li, B., and Zhao, H. (2023). Nonparametric functional graphical modeling through functional additive regression operator. Journal of the American Statistical Association, 118, 1718-1732.

  • Lee, K.Y., Ji, D., Li, L., Constable, T., and Zhao, H. (2023). Conditional functional graphical models. Journal of the American Statistical Association, 118, 257-271.

  • Lee, K.Y., Li, L., and Li, B. (2024+). Functional directed acyclic graphs. Journal of Machine Learning Research, accepted.

Machine learning, deep learning, and reinforcement learning

• Machine learning:
  We develop various new methods extending modern machine learning methods such as knockoffs and online learning.

  • Luo, L. and Li, L. (2022). Online two-way estimation and inference via linear mixed-effects models. Statistics in Medicine, 41, 5113–5133.

  • Dai, X., Lyu, X., and Li, L. (2023). Kernel knockoffs selection for nonparametric additive models. Journal of the American Statistical Association, 118, 2158-2170.

  • Jiang, F., Tian, L., Kang, J., and Li, L. (2024+). High-dimensional subgroup regression analysis. Statistica Sinica, accepted.

• Deep learning:
  We incorporate deep learning tools to enhance classical statistical inference.

  • Shi, C., Xu, T., Bergsma, W., and Li, L. (2021). Double generative adversarial networks for conditional independence testing. Journal of Machine Learning Research, 22, 1-32.

  • Zhang, D., Li, L., Sripada, C., and Kang, J. (2023). Image response regression via deep neural networks. Journal of the Royal Statistical Society, Series B., 85, 1589-1614.

  • Zhou, Y., Shi, C., Li, L., and Yao, Q. (2023). Testing for the Markov property in time series via deep conditional generative learning. Journal of the Royal Statistical Society, Series B., 85, 1204-1222.

  • Shi, C., Zhou, Y., and Li, L. (2024+). Testing directed acyclic graph via structural, supervised and generative adversarial learning. Journal of the American Statistical Association, accepted.

• Reinforcement learning:
  We are developing a series of reinforcement learning methods to study deep brain stimulations, brain-computer-interface, and human cognition.

  • Zhou, Y., Shi, C., Qi, Z., and Li, L. (2023). Optimizing pessimism in dynamic treatment regimes: a Bayesian learning approach. Proceedings of Machine Learning Research, 206, 1-18.