9 accepted papers
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 $\\mathbf{\Sigma}$, whose top eigenvector $\\mathbf{v} \in \\mathbb{R}^d$ is $s$-sparse. Existing sparse PCA algorithms can be broadly categor…
We propose a novel statistical inference framework for streaming principal component analysis (PCA) using Oja’s algorithm, enabling the construction of confidence intervals for individual entries of the estimated eigenvector. Most existing works on streaming PCA focus on providing sharp sin-squared
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 distribution, progressively adding noise. Previous sample complexity bounds have a polynomial dependence on the dimension $d…
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 quantization resolution required to achieve a target accuracy for the leading eigenvector. We study Oja's algorithm for streamin…
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 $(\epsilon, \delta)$-differentially private algorithm obtaining an $\alpha$-multiplicative approximation to the geometric median…
Independent Component Analysis (ICA) was introduced in the 1980's as a model for Blind Source Separation (BSS), which refers to the process of recovering the sources underlying a mixture of signals, with little knowledge about the source signals or the mixing process. While there are many sophistica…
Oja's algorithm for Streaming Principal Component Analysis (PCA) for $n$ data-points in a $d$ dimensional space achieves the same sin-squared error $O(r_{\mathsf{eff}}/n)$ as the offline algorithm in $O(d)$ space and $O(nd)$ time and a single pass through the datapoints. Here $r_{\mathsf{eff}}$ is t…
Since its inception in 1982, Oja's algorithm has become an established method for streaming principle component analysis (PCA). We study the problem of streaming PCA, where the data-points are sampled from an irreducible, aperiodic, and reversible Markov chain starting in stationarity. Our goal is t…
Generating code-switched text is a problem of growing interest, especially given the scarcity of corpora containing large volumes of real code-switched text. In this work, we adapt a state-of-the-art neural machine translation model to generate Hindi-English code-switched sentences starting from mon…