5 papers
Low-Precision Streaming PCA
Sanjoy Dasgupta, Syamantak Kumar, Shourya Pandey +1
Low-precision streaming PCA estimates the top principal component in a streaming setting under limited precision. We establish an information-theoretic lower bound on the quantizat…
Beyond Sin-Squared Error: Linear-Time Entrywise Uncertainty Quantification for Streaming PCA
Syamantak Kumar, Shourya Pandey, Purnamrita Sarkar
We propose a novel statistical inference framework for streaming principal component analysis (PCA) using Oja's algorithm, enabling the construction of confidence intervals for ind…
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…
Dimension-free Score Matching and Time Bootstrapping for Diffusion Models
Syamantak Kumar, Dheeraj Nagaraj, Purnamrita Sarkar
Diffusion models generate samples by estimating the score function of the target distribution at various noise levels. The model is trained using samples drawn from the target dist…