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Related papers: Spectral Guarantees for Adversarial Streaming PCA

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A streaming algorithm is said to be adversarially robust if its accuracy guarantees are maintained even when the data stream is chosen maliciously, by an adaptive adversary. We establish a connection between adversarial robustness of…

Data Structures and Algorithms · Computer Science 2020-04-14 Avinatan Hassidim , Haim Kaplan , Yishay Mansour , Yossi Matias , Uri Stemmer

We consider online packing problems where we get a stream of axis-parallel rectangles. The rectangles have to be placed in the plane without overlapping, and each rectangle must be placed without knowing the subsequent rectangles. The goal…

Computational Geometry · Computer Science 2021-01-27 Mikkel Abrahamsen , Lorenzo Beretta

We study streaming algorithms in the white-box adversarial model, where the stream is chosen adaptively by an adversary who observes the entire internal state of the algorithm at each time step. We show that nontrivial algorithms are still…

Data Structures and Algorithms · Computer Science 2022-07-26 Miklos Ajtai , Vladimir Braverman , T. S. Jayram , Sandeep Silwal , Alec Sun , David P. Woodruff , Samson Zhou

Spectral estimators are fundamental in lowrank matrix models and arise throughout machine learning and statistics, with applications including network analysis, matrix completion and PCA. These estimators aim to recover the leading…

Statistics Theory · Mathematics 2025-02-17 Hao Yan , Keith Levin

Kernel principal component analysis (KPCA) provides a concise set of basis vectors which capture non-linear structures within large data sets, and is a central tool in data analysis and learning. To allow for non-linear relations, typically…

Data Structures and Algorithms · Computer Science 2015-12-17 Mina Ghashami , Daniel Perry , Jeff M. Phillips

We provide a deterministic space-efficient algorithm for estimating ridge regression. For $n$ data points with $d$ features and a large enough regularization parameter, we provide a solution within $\varepsilon$ L$_2$ error using only…

Machine Learning · Computer Science 2021-06-29 Benwei Shi , Jeff M. Phillips

We consider the \textsf{Unit Interval Selection} problem in the one-pass random order streaming model. Here, an algorithm is presented a sequence of $n$ unit-length intervals on the line that arrive in uniform random order, and the…

Data Structures and Algorithms · Computer Science 2026-03-11 Cezar-Mihail Alexandru , Adithya Diddapur , Magnús M. Halldórsson , Christian Konrad , Kheeran K. Naidu

We initiate the investigation of the parameterized complexity of Diameter and Connectivity in the streaming paradigm. On the positive end, we show that knowing a vertex cover of size $k$ allows for algorithms in the Adjacency List (AL)…

Data Structures and Algorithms · Computer Science 2024-07-19 Jelle J. Oostveen , Erik Jan van Leeuwen

We present a novel view on principal component analysis (PCA) as a competitive game in which each approximate eigenvector is controlled by a player whose goal is to maximize their own utility function. We analyze the properties of this PCA…

Machine Learning · Computer Science 2021-03-18 Ian Gemp , Brian McWilliams , Claire Vernade , Thore Graepel

Oja's algorithm of principal component analysis (PCA) has been one of the methods utilized in practice to reduce dimension. In this paper, we focus on the convergence property of the discrete algorithm. To realize that, we view the…

Numerical Analysis · Mathematics 2023-01-05 Jian-Guo Liu , Zibu Liu

In this paper, we study streaming algorithms that minimize the number of changes made to their internal state (i.e., memory contents). While the design of streaming algorithms typically focuses on minimizing space and update time, these…

Data Structures and Algorithms · Computer Science 2024-06-12 Rajesh Jayaram , David P. Woodruff , Samson Zhou

Principal component analysis (PCA) has been a prominent tool for high-dimensional data analysis. Online algorithms that estimate the principal component by processing streaming data are of tremendous practical and theoretical interests.…

Optimization and Control · Mathematics 2017-10-09 Chris Junchi Li , Mengdi Wang , Han Liu , Tong Zhang

A graph spanner is a fundamental graph structure that faithfully preserves the pairwise distances in the input graph up to a small multiplicative stretch. The common objective in the computation of spanners is to achieve the best-known…

Data Structures and Algorithms · Computer Science 2019-02-25 Merav Parter , Ronitt Rubinfeld , Ali Vakilian , Anak Yodpinyanee

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…

Information Theory · Computer Science 2016-09-09 Chuang Wang , Yue M. Lu

In the online metric matching problem, $n$ servers and $n$ requests lie in a metric space. Servers are available upfront, and requests arrive sequentially. An arriving request must be matched immediately and irrevocably to an available…

Data Structures and Algorithms · Computer Science 2026-04-22 Yingxi Li , Ellen Vitercik , Mingwei Yang

We show a dichotomy result for $p$-pass streaming algorithms for all CSPs and for up to polynomially many passes. More precisely, we prove that for any arity parameter $k$, finite alphabet $\Sigma$, collection $\mathcal{F}$ of $k$-ary…

Computational Complexity · Computer Science 2026-04-03 Yumou Fei , Dor Minzer , Shuo Wang

Recently, the question of adversarially robust streaming, where the stream is allowed to depend on the randomness of the streaming algorithm, has gained a lot of attention. In this work, we consider a strong white-box adversarial model…

Data Structures and Algorithms · Computer Science 2024-06-12 Ying Feng , Aayush Jain , David P. Woodruff

We study the maximum matching problem in the random-order semi-streaming setting. In this problem, the edges of an arbitrary $n$-vertex graph $G=(V, E)$ arrive in a stream one by one and in a random order. The goal is to have a single pass…

Data Structures and Algorithms · Computer Science 2021-03-02 Sepehr Assadi , Soheil Behnezhad

We provide $\widetilde{O}(\epsilon^{-1})$-pass semi-streaming algorithms for computing $(1-\epsilon)$-approximate maximum cardinality matchings in bipartite graphs. Our most efficient methods are deterministic and use optimal, $O(n)$,…

Data Structures and Algorithms · Computer Science 2021-08-04 Sepehr Assadi , Arun Jambulapati , Yujia Jin , Aaron Sidford , Kevin Tian

We consider the problem of finding a minimum cut of a weighted graph presented as a single-pass stream. While graph sparsification in streams has been intensively studied, the specific application of finding minimum cuts in streams is less…

Data Structures and Algorithms · Computer Science 2024-12-09 Matthew Ding , Alexandro Garces , Jason Li , Honghao Lin , Jelani Nelson , Vihan Shah , David P. Woodruff