6 papers
Estimating eigenvectors and eigenspaces of covariance matrices: Optimal Bounds and Conditions for Consistency
Phuc Tran, Van Vu
Let be a zero-mean random vector of large dimension () with (hidden) covariance matrix $M = (m_{ij})_{1 \leq i…
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…
New matrix perturbation bounds with relative norm: 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 spectra…
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…
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…
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…