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Research

My research focuses on scalable inference in high-dimensional random models. I am particularly interested in message-passing algorithms, spectral methods, and related optimization techniques, with an emphasis on precise asymptotic characterization and algorithmic optimality. My work is motivated by fundamental problems in statistical inference, signal processing, and communication systems.

Keywords: high-dimensional inference, message passing, spectral methods, precise asymptotics, random matrix models, statistical recovery, communication systems.

Foundations of High-Dimensional Inference

A central theme of my research is the design and analysis of scalable inference algorithms for high-dimensional random models. I am especially interested in AMP-type methods and their precise asymptotic characterization beyond the classical i.i.d. Gaussian setting. My recent work develops unified perspectives for message-passing algorithms under rotationally invariant models, clarifies the role of Onsager corrections, and studies principled algorithm design in structured inference problems.

  1. Unifying AMP Algorithms for Rotationally-Invariant Models, Songbin Liu and Junjie Ma, arXiv:2412.01574, 2024.

  2. Orthogonal AMP, Junjie Ma and Li Ping, IEEE Access, vol. 5, pp. 2020--2033, 2017.

Structured Random Models and Statistical Recovery

Another main direction of my work concerns statistical recovery in structured high-dimensional models. I study the interplay between information-theoretic limits, efficient algorithms, and sharp asymptotic analysis in problems such as spiked matrix estimation and phase retrieval. A recurring goal is to understand when simple scalable algorithms, including message-passing and spectral methods, achieve optimal statistical performance.

An overview of the spiked-model line of work was recently featured in the newsletter of the IEEE Information Theory Society, Guangzhou Chapter. Newsletter Article

  1. Optimality of Approximate Message Passing for Spiked Matrix Models with Rotationally Invariant Noise, Rishabh Dudeja, Songbin Liu, and Junjie Ma, Annals of Statistics, 54(1): 466--489, 2026.

  2. Orthogonal Approximate Message Passing with Optimal Spectral Initializations for Rectangular Spiked Matrix Models, Haohua Chen, Songbin Liu, and Junjie Ma, arXiv:2502.05524, 2025.

  3. Towards Designing Optimal Sensing Matrices for Generalized Linear Inverse Problems, Junjie Ma, Ji Xu, and Arian Maleki, IEEE Transactions on Information Theory, vol. 70, no. 1, pp. 482--508, 2024.

  4. Optimization-Based AMP for Phase Retrieval: The Impact of Initialization and ℓ2-Regularization, Junjie Ma, Ji Xu, and Arian Maleki, IEEE Transactions on Information Theory, vol. 65, no. 6, June 2019.

  5. Spectral Method for Phase Retrieval: an Expectation Propagation Perspective, Junjie Ma, Rishabh Dudeja, Ji Xu, Arian Maleki, and Xiaodong Wang, IEEE Transactions on Information Theory, vol. 67, no. 2, pp. 1332--1355, 2021.

  6. Information-Theoretic Limits for Phase Retrieval with Subsampled Haar Sensing Matrices, Rishabh Dudeja, Junjie Ma, and Arian Maleki, IEEE Transactions on Information Theory, vol. 66, no. 12, pp. 8002--8045, 2020.

  7. Improved Turbo Message Passing for Compressive Robust Principal Component Analysis: Algorithm Design and Asymptotic Analysis, Zhuohang He, Junjie Ma, and Xiaojun Yuan, IEEE Transactions on Information Theory, vol. 71, no. 2, pp. 1323--1361, 2025.

Inference and Optimization in Large-Scale Information Systems

I am also interested in mathematically grounded problems arising from communication and sensing systems. In this line of work, communication models serve not only as application domains but also as testbeds for scalable inference and optimization methods in high dimensions. Current topics include discrete precoding for massive MIMO systems and covariance-based activity detection in grant-free random access.

  1. Asymptotic SEP Analysis and Optimization of Linear-Quantized Precoding in Massive MIMO Systems, Zheyu Wu, Junjie Ma, Ya-Feng Liu, and A. Lee Swindlehurst, IEEE Transactions on Information Theory, 70(4): 2566--2589, 2024.

  2. Asymptotic Analysis of Nonlinear One-Bit Precoding in Massive MIMO Systems via Approximate Message Passing, Zheyu Wu, Junjie Ma, Ya-Feng Liu, and Bruno Clerckx, IEEE Transactions on Information Theory, 2026+.

  3. Precise Analysis of Covariance Identifiability for Activity Detection in Grant-Free Random Access, Shengsong Luo, Junjie Ma, Chongbin Xu, and Xin Wang, arXiv:2406.01138, 2024.

  4. Energy-Spreading-Transform-Based MIMO Systems: Iterative Equalization, Evolution Analysis, and Precoder Optimization, Xiaojun Yuan, Junjie Ma, and Li Ping, IEEE Transactions on Wireless Communications, vol. 13, no. 9, pp. 5237--5250, 2014.

Collaboration

I am interested in collaborations on high-dimensional inference, message-passing algorithms, spectral methods, and mathematically grounded problems arising from communication and sensing systems.