Research

Large models and enormous data are essential driven forces of the unprecedented successes achieved by modern algorithms, especially in scientific computing and machine learning. Nevertheless, the growing dimensionality and model complexity, as well as the non-negligible workload of data pre-processing, also bring formidable costs to such successes in both computation and data aggregation. As the deceleration of Moore's Law slackens the cost reduction of computation from the hardware level, fast heuristics for expensive classical routines and efficient algorithms for exploiting limited data are becoming increasingly indispensable for pushing the limit of algorithm potency.

My research focuses on such efficient algorithms for fast execution and effective data utilization.

• From the computational efficiency perspective, I work on designing and analyzing randomized low-rank decomposition algorithms that can be executed fast on large matrices.

  • Randomized pivoting-based CUR decompositions

  • Canonical angles in randomized subspace approximations

• From the sample efficiency perspective, I am interested in studying and improving the generalization and distributional robustness of learning algorithms in data-limited settings.

  • Sample efficiency of data augmentation consistency regularization

  • Distributionally robust optimization under concept shift

Preprints

1. Robust Blockwise Random Pivoting: Fast and Accurate Adaptive Interpolative Decomposition
   Yijun Dong, Chao Chen, Per-Gunnar Martinsson, Katherine Pearce. 2023. [GitHub]
   

2. Efficient Bounds and Estimates for Canonical Angles in Randomized Subspace Approximations.
   Yijun Dong, Per-Gunnar Martinsson, Yuji Nakatsukasa. 2022. [GitHub]
   

3. Adaptive Parallelizable Algorithms for Interpolative Decompositions via Partially Pivoted LU.
   Katherine J. Pearce, Chao Chen, Yijun Dong, Per-Gunnar Martinsson. 2023. [GitHub]
   

Publications

1. Cluster-aware Semi-supervised Learning: Relational Knowledge Distillation Provably Learns Clustering.
   Yijun Dong*, Kevin Miller*, Qi Lei, Rachel Ward.
   Thirty-seventh Conference on Neural Information Processing Systems (NeurIPS) 2023. [GitHub]
   

2. Adaptively Weighted Data Augmentation Consistency Regularization for Robust Optimization under Concept Shift.
   Yijun Dong*, Yuege Xie*, Rachel Ward.
   International Conference on Machine Learning (ICML) 2023. [GitHub, poster]
   

3. Sample Efficiency of Data Augmentation Consistency Regularization.
   Shuo Yang*, Yijun Dong*, Rachel Ward, Inderjit Dhillon, Sujay Sanghavi, Qi Lei.
   International Conference on Artificial Intelligence and Statistics (AISTATS) 2023. [pmlr]
   

4. Simpler is better: A comparative study of randomized algorithms for computing the CUR decomposition.
   Yijun Dong, Per-Gunnar Martinsson.
   Advances in Computational Mathematics 2023. [GitHub]
   

5. Quantifying Biofilm Formation of Sinorhizobium meliloti Bacterial Strains in Microfluidic Platforms by Measuring the Diffusion Coefficient of Polystyrene Beads.
   Chen Cheng*, Yijun Dong*, Matthew Dorian*, Farhan Kamili*, Effrosyni Seitaridou.
   Open Journal of Biophysics 2017.
   

Selected Presentations

• Talk at SIAM PP24, Minisymposium on Randomized Methods in Linear Solvers and Matrix Decompositions: Robust Blockwise Random Pivoting: Fast and Accurate Adaptive Interpolative Decomposition. [slides]

• Talk at ICIAM 2023, Minisymposium on Randomized Numerical Linear Algebra: Efficient Bounds and Estimates for Canonical Angles in Randomized Subspace Approximations. [slides]

• Dissertation defense at Oden Institute, UT Austin (Austin, TX, 2023/03/29): ‘‘Randomized Dimension Reduction with Statistical Guarantees’’. [dissertation, slides]

Service

• Journal reviewer

  • Journal of Computational Mathematics and Data Science (2024)

  • Annals of Applied Probability (2023)

  • Calcolo (2023)

  • BIT Numerical Mathematics (2022)

  • IMA Journal of Numerical Analysis (2022)

  • SIAM Journal on Matrix Analysis and Applications (2020)

• Conference reviewer

  • AISTATS (2023)