Related papers: Streaming Kernel PCA with $\tilde{O}(\sqrt{n})$ Ra…
The efficient estimation of frequency moments of a data stream in one-pass using limited space and time per item is one of the most fundamental problem in data stream processing. An especially important estimation is to find the number of…
Online principal component analysis (PCA) has been an efficient tool in practice to reduce dimension. However, convergence properties of the corresponding ODE are still unknown, including global convergence, stable manifolds, and…
Recent works have derived neural networks with online correlation-based learning rules to perform \textit{kernel similarity matching}. These works applied existing linear similarity matching algorithms to nonlinear features generated with…
Random Fourier features is a widely used, simple, and effective technique for scaling up kernel methods. The existing theoretical analysis of the approach, however, remains focused on specific learning tasks and typically gives pessimistic…
We study the distributed computing setting in which there are multiple servers, each holding a set of points, who wish to compute functions on the union of their point sets. A key task in this setting is Principal Component Analysis (PCA),…
We study streaming algorithms for the fundamental geometric problem of computing the cost of the Euclidean Minimum Spanning Tree (MST) on an $n$-point set $X \subset \mathbb{R}^d$. In the streaming model, the points in $X$ can be added and…
We introduce a new computational model for data streams: asymptotically exact streaming algorithms. These algorithms have an approximation ratio that tends to one as the length of the stream goes to infinity while the memory used by the…
Kernel methods provide a principled way to perform non linear, nonparametric learning. They rely on solid functional analytic foundations and enjoy optimal statistical properties. However, at least in their basic form, they have limited…
We propose an algorithm for quickly evaluating polynomials. It pre-conditions a complex polynomial $P$ of degree $d$ in time $O(d\log d)$, with a low multiplicative constant independent of the precision. Subsequent evaluations of $P$…
We study the classic NP-Hard problem of finding the maximum $k$-set coverage in the data stream model: given a set system of $m$ sets that are subsets of a universe $\{1,\ldots,n \}$, find the $k$ sets that cover the most number of distinct…
We consider maximizing a monotone submodular function under a cardinality constraint or a knapsack constraint in the streaming setting. In particular, the elements arrive sequentially and at any point of time, the algorithm has access to…
We explore the use of Optical Processing Units (OPU) to compute random Fourier features for sketching, and adapt the overall compressive clustering pipeline to this setting. We also propose some tools to help tuning a critical…
We introduce a novel algorithm to perform graph clustering in the edge streaming setting. In this model, the graph is presented as a sequence of edges that can be processed strictly once. Our streaming algorithm has an extremely low memory…
We overcome two major bottlenecks in the study of low rank approximation by assuming the low rank factors themselves are sparse. Specifically, (1) for low rank approximation with spectral norm error, we show how to improve the best known…
Many real-world applications pose challenges in incorporating fairness constraints into the $k$-center clustering problem, where the dataset consists of $m$ demographic groups, each with a specified upper bound on the number of centers to…
This paper resolves one of the longest standing basic problems in the streaming computational model. Namely, optimal construction of quantile sketches. An $\varepsilon$ approximate quantile sketch receives a stream of items $x_1,\ldots,x_n$…
In recent years, kernel density estimation has been exploited by computer scientists to model machine learning problems. The kernel density estimation based approaches are of interest due to the low time complexity of either O(n) or…
We study the problem of distributed distinct element estimation, where $\alpha$ servers each receive a subset of a universe $[n]$ and aim to compute a $(1+\varepsilon)$-approximation to the number of distinct elements using minimal…
Principal component analysis has been widely adopted to reduce the dimension of data while preserving the information. The quantum version of PCA (qPCA) can be used to analyze an unknown low-rank density matrix by rapidly revealing the…
In the context of sparse principal component detection, we bring evidence towards the existence of a statistical price to pay for computational efficiency. We measure the performance of a test by the smallest signal strength that it can…