Phuc Tran

collaborators

6 papers

math.ST2026

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

Phuc Tran, Van Vu

Let $X = [I^¾_{1}, I^¾_{2}, ..., I^¾_{d}]^{⊤}$ be a zero-mean random vector of large dimension $d$ ( $d \to \infty$ ) with (hidden) covariance matrix $M = (m_{ij})_{1 \leq i…

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…

math.NA2026

Eigenvalue stability and new perturbation bounds for the extremal eigenvalues of a matrix

Phuc Tran, Van Vu

Let $A$ be a full ranked $n \times n$ matrix, with singular values $I ¨ _{1} (A) \geq \dots \geq I ¨ _{n} (A) > 0$ . The condition number $I^º (A) := I ¨ _{1} (A) / I ¨ _{n} (A) = ∥ A ∥ \cdot ∥ A ∥^{- 1}$ is a k…

math.NA2026

Matrices perturbed by random noise: The accuracy of low-rank approximation

Phuc Tran, Van Vu

Let $A$ be an $m \times n$ matrix with rank $r$ and singular value decomposition $A = \sum_{i = 1}^{r} σ_{i} u_{i} v_{i}^{⊤},$ where the $σ_{i}$ are its singular values, ordered decreasingl…

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…

cs.LG2025

Perturbation Bounds for Low-Rank Inverse Approximations under Noise

Phuc Tran, Nisheeth K. Vishnoi

Low-rank pseudoinverses are widely used to approximate matrix inverses in scalable machine learning, optimization, and scientific computing. However, real-world matrices are often…