4 papers
On the Curse of Dimensionality in Private Sparse Covariance Estimation and PCA
Syamantak Kumar, Shourya Pandey, Purnamrita Sarkar +1
We study high-dimensional differentially private (DP) covariance estimation in the operator norm, and principal component analysis (PCA), under -row-column sparsity (-RCS) of…
Combinatorial Sparse PCA Beyond the Spiked Identity Model
Syamantak Kumar, Purnamrita Sarkar, Kevin Tian +1
Sparse PCA is one of the most well-studied problems in high-dimensional statistics. In this problem, we are given samples from a distribution with covariance , whose top eigenv…
Private Geometric Median in Nearly-Linear Time
Syamantak Kumar, Daogao Liu, Kevin Tian +1
Estimating the geometric median of a dataset is a robust counterpart to mean estimation, and is a fundamental problem in computational geometry. Recently, [HSU24] gave an $(\vareps…
Spike-and-Slab Posterior Sampling in High Dimensions
Syamantak Kumar, Purnamrita Sarkar, Kevin Tian +1
Posterior sampling with the spike-and-slab prior [MB88], a popular multimodal distribution used to model uncertainty in variable selection, is considered the theoretical gold stand…