Related papers: Subspace Estimation from Incomplete Observations: …
Many real world data sets exhibit an embedding of low-dimensional structure in a high-dimensional manifold. Examples include images, videos and internet traffic data. It is of great significance to reduce the storage requirements and…
In this paper, we design sub-linear space streaming algorithms for estimating three fundamental parameters -- maximum independent set, minimum dominating set and maximum matching -- on sparse graph classes, i.e., graphs which satisfy…
This work presents GROUSE (Grassmanian Rank-One Update Subspace Estimation), an efficient online algorithm for tracking subspaces from highly incomplete observations. GROUSE requires only basic linear algebraic manipulations at each…
We present a framework for analyzing the exact dynamics of a class of online learning algorithms in the high-dimensional scaling limit. Our results are applied to two concrete examples: online regularized linear regression and principal…
This paper addresses the challenge of efficient principal component analysis (PCA) in high-dimensional spaces by analyzing a compressively sampled variant of Oja's algorithm with adaptive sensing. Traditional PCA methods incur substantial…
In this paper we analyze the behavior of the Oja's algorithm for online/streaming principal component subspace estimation. It is proved that with high probability it performs an efficient, gap-free, global convergence rate to approximate an…
The turnstile continual release model of differential privacy captures scenarios where a privacy-preserving real-time analysis is sought for a dataset evolving through additions and deletions. In typical applications of real-time data…
We study the space complexity of estimating the diameter of a subset of points in an arbitrary metric space in the dynamic (turnstile) streaming model. The input is given as a stream of updates to a frequency vector $x \in \mathbb{Z}_{\geq…
We study the dynamics of an online algorithm for learning a sparse leading eigenvector from samples generated from a spiked covariance model. This algorithm combines the classical Oja's method for online PCA with an element-wise…
Spatial frequency estimation from a mixture of noisy sinusoids finds applications in various fields. While subspace-based methods offer cost-effective super-resolution parameter estimation, they demand precise array calibration, posing…
In this paper, we propose to adopt the diffusion approximation tools to study the dynamics of Oja's iteration which is an online stochastic gradient descent method for the principal component analysis. Oja's iteration maintains a running…
We analyze the dynamics of an online algorithm for independent component analysis in the high-dimensional scaling limit. As the ambient dimension tends to infinity, and with proper time scaling, we show that the time-varying joint empirical…
Direction of arrival (DoA) estimation is a fundamental task in array processing. A popular family of DoA estimation algorithms are subspace methods, which operate by dividing the measurements into distinct signal and noise subspaces.…
Extracting the underlying low-dimensional space where high-dimensional signals often reside has long been at the center of numerous algorithms in the signal processing and machine learning literature during the past few decades. At the same…
Big data problems frequently require processing datasets in a streaming fashion, either because all data are available at once but collectively are larger than available memory or because the data intrinsically arrive one data point at a…
Estimating the quantiles of a large dataset is a fundamental problem in both the streaming algorithms literature and the differential privacy literature. However, all existing private mechanisms for distribution-independent quantile…
We present a framework for supervised subspace tracking, when there are two time series $x_t$ and $y_t$, one being the high-dimensional predictors and the other being the response variables and the subspace tracking needs to take into…
Out-of-distribution (OOD) detection is essential for deploying deep learning models in open-world environments. Existing approaches, such as energy-based scoring and gradient-projection methods, typically rely on high-dimensional…
GROUSE (Grassmannian Rank-One Update Subspace Estimation) is an iterative algorithm for identifying a linear subspace of R^n from data consisting of partial observations of random vectors from that subspace. This paper examines local…
Estimating the size of the maximum matching is a canonical problem in graph algorithms, and one that has attracted extensive study over a range of different computational models. We present improved streaming algorithms for approximating…