Related papers: Spectral Guarantees for Adversarial Streaming PCA
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…
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…
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…
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…
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…
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…
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…
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)…
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…
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…
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…
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.…
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…
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…
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…
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…
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…
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…
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, $O(n)$,…
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…