Research

My research is partially supported by the National Science Foundation and the Simons Foundation.
My Google Scholar page.

My research focuses on developing statistical theory and methodology for high-dimensional data, complex dependence structures, and modern scientific applications. I am particularly interested in problems where classical assumptions break down due to dimensionality, heterogeneity, or nonstationarity.

High-dimensional Statistics and Quadratic Models

I work on statistical learning problems in high dimensions, with an emphasis on variable screening, interaction detection, and classification under complex dependence structures. My research develops theory-driven methods that are computationally scalable while retaining rigorous statistical guarantees.

Representative publications:

• Wu, R., and Hao, N. (2022)
  Quadratic Discriminant Analysis by Projection.
  Journal of Multivariate Analysis, 190, 104987.
  [PDF] [arXiv]; R package QDAP

• Hao, N., Feng, Y., and Zhang, H.H. (2018)
  Model Selection for High Dimensional Quadratic Regressions via Regularization.
  Journal of the American Statistical Association, 113, 615–625.
  [PDF] [arXiv]; R package RAMP

• Hao, N., and Zhang, H.H. (2014)
  Interaction Screening for Ultra-High Dimensional Data.
  Journal of the American Statistical Association, 109, 1285–1301.
  [PDF]; Matlab codes

• Fan, J., Guo, S., and Hao, N. (2012)
  Variance Estimation Using Refitted Cross-Validation in Ultrahigh Dimensional Regression.
  Journal of the Royal Statistical Society: Series B, 74, 37–65.
  [PDF]

Change-point Detection and Inference for Time Series

A central theme of my research is change-point detection and inference for time series and high-throughput sequencing data, particularly in high-dimensional settings and under frequent or complex distributional changes. I develop scalable algorithms and provide useful inference tools and theoretical guarantees for detecting short segments, epidemic changes, and multiple change-points.

Representative publications:

• Liu, Z., Hao, N., Niu, Y.S., Xiao, H., and Ding, H. (2025)
  Autocorrelation Test under Frequent Mean Shifts.
  [arXiv]; R package SIP

• Hao, N., Niu, Y.S., and Xiao, H. (2023)
  Equivariant Variance Estimation for Multiple Change-point Model.
  Electronic Journal of Statistics, 17, 3811–3853.
  [PDF] [arXiv]; R package EVE

• Niu, Y.S., Hao, N., and Zhang, H. (2016)
  Multiple Change-Point Detection, a Selective Overview.
  Statistical Science, 31, 611–623.
  [PDF] [arXiv]

• Hao, N., Niu, Y.S., and Zhang, H. (2013)
  Multiple Change-Point Detection via a Screening and Ranking Algorithm.
  Statistica Sinica, 23, 1553–1572.
  [PDF]; R package SaRa

Dimension Reduction and Supervised PCA

I work on dimension reduction methods for high-dimensional data, with a focus on supervised and task-driven settings where classical unsupervised techniques such as PCA are insufficient. My research develops theory and methodology for extracting low-dimensional representations that are directly relevant for prediction, classification, and inference, including dynamic and multi-task scenarios. These methods aim to balance interpretability, statistical efficiency, and computational scalability.

Representative publications:

• Ouyang, W., Wu, R., Hao, N., and Zhang, H.H. (2025)
  Dynamic Supervised Principal Component Analysis for Classification.
  Journal of Computational and Graphical Statistics, 34, 1446–1455.
  [PDF] [arXiv]; R package DSPCA

• Niu, Y.S., Hao, N., and Dong, B. (2018)
  A New Reduced-Rank Linear Discriminant Analysis Method and Its Applications.
  Statistica Sinica, 28, 189–202.
  [PDF] [arXiv]; R package SPCALDA

• Hao, N., Dong, B., and Fan, J. (2015)
  Sparsifying the Fisher Linear Discriminant by Rotation.
  Journal of the Royal Statistical Society: Series B, 77, 827–851.
  [PDF] [arXiv]; Matlab codes

Network Models and Graphical Inference

Another line of my research focuses on statistical inference for networks and graph-structured data, including stochastic block models, degree correction, and heterogeneous covariance structures.

Representative publications:

• Li, X., Zhao, Y., Pan, Q., and Hao, N. (2025+)
  Community Detection with Heterogeneous Block Covariance Model.
  Journal of Computational and Graphical Statistics, to appear.
  [PDF] [arXiv]; R package hbcm

• Park, J., Zhao, Y., and Hao, N. (2025)
  A Note on the Identifiability of Degree-Corrected Stochastic Block Model.
  STAT, 14, e70067.
  [PDF] [arXiv]

• Zhao, Y., Hao, N., and Zhu, J. (2024)
  Variational Estimators of the Degree-corrected Latent Block Model for Bipartite Networks.
  Journal of Machine Learning Research, 25, 150, 1–42.
  [PDF] [arXiv]

Applications

I also collaborate on applied statistical methodology motivated by biomedical and genomic data, particularly nanopore sequencing and copy number variation analysis. These projects integrate statistical modeling, algorithmic development, and real data applications.

Representative publications:

• Wang, Z., Liu, Z., Fang, Y., Zhang, H.H., Sun, X., Hao, N., Que, J., and Ding, H. (2025)
  Training Data Diversity Enhances the Basecalling of Novel RNA Modification-Induced Nanopore Sequencing Readouts.
  Nature Communications, 16, 679.
  [PDF] [bioRxiv]; Code

• Wang, Z., Fang, Y., Liu, Z., Hao, N., Zhang, H.H., Sun, X., Que, J., and Ding, H. (2024)
  Adapting Nanopore Sequencing Basecalling Models for Modification Detection via Incremental Learning and Anomaly Detection.
  Nature Communications, 15, 7148.
  [PDF] [bioRxiv]; Code

• Xiao, F., Luo, X., Hao, N., Niu, Y.S., Xiao, X., Cai, G., Amos, C.I., and Zhang, H. (2019)
  An Accurate and Powerful Method for Copy Number Variation Detection.
  Bioinformatics, 35, 2891–2898.
  [PDF]; R package modSaRa2