Van H. Vu

activity

20232026

collaborators

8 papers

math.NA2026

Regional Stability and New Eigenvalue Perturbation Bounds

Phuc Tran, Van Vu

Let $A$ be an $n \times n$ symmetric matrix with eigenvalues $λ_{1} \geq \dots \geq λ_{n}$ . Let $A ~ := A + E$ , where $E$ is a symmetric noise matrix, and denote the eigenvalues of $\tild…

math.ST2026

Estimating eigenvectors and eigenspaces of covariance matrices: Optimal Bounds and Conditions for Consistency

Phuc Tran, Van Vu

Let $X = [ξ_{1}, ξ_{2}, ..., ξ_{d}]^{⊤}$ be a zero-mean random vector of large dimension $d$ ( $d \to \infty$ ) with (hidden) covariance matrix $M = (m_{ij})_{1 \leq i, j…

stat.ML2026

Improved Guarantees for Heterogeneous Treatment-Effect Estimation via Matrix Completion

Anay Mehrotra, Phuc Tran, Van H. Vu +1

A central goal of modern causal inference is estimating heterogeneous treatment effects to answer questions like "how does an intervention affect each unit," rather than only on av…

cs.LG2025

Spectral Perturbation Bounds for Low-Rank Approximation with Applications to Privacy

Phuc Tran, Nisheeth K. Vishnoi, Van H. Vu

A central challenge in machine learning is to understand how noise or measurement errors affect low-rank approximations, particularly in the spectral norm. This question is especia…

math.NA2025

Davis-Kahan Theorem under a moderate gap condition

Phuc Tran, Van Vu

The classical Davis-Kahan theorem provides an efficient bound on the perturbation of eigenspaces of a matrix under a large (eigenvalue) gap condition. In this paper, we consider th…

math.SP2024

New matrix perturbation bounds with relative strength: Perturbation of eigenspaces

Phuc Tran, Van Vu

Matrix perturbation bounds (such as Weyl and Davis--Kahan) are used abundantly in many areas of mathematics and data science. Many bounds (such as the above two) involve the spectr…

math.NA2024

Matrix perturbation bounds via contour bootstrapping

Phuc Tran, Van Vu

Matrix perturbation bounds play an essential role in the design and analysis of spectral algorithms. In this paper, we use a "contour bootstrapping" argument to derive several new…

math.CO2023

A short proof of Kahn-Kalai conjecture

P. Tran, V. Vu

In a recent paper, Park and Pham famously proved Kahn-Kalai conjecture. In this note, we simplify their proof, using an induction to replace the original analysis. This reduces the…