Research

My PhD research focused on statistical learning and information theory. Specifically, I was interested in applying tools from information theory and coding theory to high-dimensional statistical estimation problems, such as changepoints detection and random access in large user networks. I study the tradeoff between sample complexity and estimation error from both a fundamental theoretical perspective and an algorithmic perspective.

I’ve been particularly interested in studying message passing algorithms for the estimation problems mentioned above, which is a class of iterative algorithms that are fast to implement and achieve statistical optimality in various problems. I studied both belief propagation and approximate message passing (AMP) as two types of message passing algorithms.

I review papers for the Conference on Neural Information Processing Systems (NeurIPS), International Symposium on Information Theory (ISIT) and International Symposium on Topics in Coding (ISTC).

Interests:

• High-dimensional statistical learning
• Information theory and communication systems
• General first-order methods e.g. gradient descent, approximate message passing
• Finite-sample analysis and asymptotic analysis

Preprints:

X. Liu, P. Pascual Cobo and R. Venkataramanan, “Many-user multiple access with random user activity: achievability bounds and efficient schemes”, in submission, 2024.

G. Arpino, X. Liu, J. Gontarek and R. Venkataramanan, “Inferring Change Points in High-Dimensional Regression via Approximate Message Passing”, in submission, 2024.

Publications:

X. Liu, P. Pascual Cobo and R. Venkataramanan, “Many-user multiple access with random user activity”, IEEE International Symposium on Information Theory, Athens, Greece, 2024. (poster, talk)

X. Liu, K. Hsieh and R. Venkataramanan, “Coded many-user multiple access via Approximate Messsage Passing”, IEEE International Symposium on Information Theory, Athens, Greece, 2024. (arXiv, talk)

G. Arpino, X. Liu and R. Venkataramanan, “Inferring Change Points in High-Dimensional Linear Regression via Approximate Message Passing”, Proceedings of the 41st International Conference on Machine Learning, PMLR 235:1841-1864, 2024. (poster, code)

X. Liu and R. Venkataramanan, “Sketching Sparse Low-Rank Matrices With Near-Optimal Sample- and Time-Complexity Using Message Passing”, in IEEE Transactions on Information Theory, vol. 69, no. 9, pp. 6071-6097, Sept. 2023, doi: 10.1109/TIT.2023.3273181.

X. Liu and R. Venkataramanan, “Sketching sparse low-rank matrices with near-optimal sample- and time-complexity”, IEEE International Symposium on Information Theory, Espoo, Finland, 2022, pp. 3138-3143, doi: 10.1109/ISIT50566.2022.9834693. (talk)

PhD thesis:

X. Liu, “Message Passing Algorithms for Statistical Estimation and Communication”, Apollo-University of Cambridge Repository.