Related papers: New Subset Selection Algorithms for Low Rank Appro…
We study web and mobile applications that are used to schedule advance service, from medical appointments to restaurant reservations. We model them as online weighted bipartite matching problems with non-stationary arrivals. We propose new…
How to efficiently perform network tomography is a fundamental problem in network management and monitoring. A network tomography task usually consists of applying multiple probing experiments, e.g., across different paths or via different…
Low-distortional metric embeddings are a crucial component in the modern algorithmic toolkit. In an online metric embedding, points arrive sequentially and the goal is to embed them into a simple space irrevocably, while minimizing the…
We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…
Many machine learning frameworks, such as resource-allocating networks, kernel-based methods, Gaussian processes, and radial-basis-function networks, require a sparsification scheme in order to address the online learning paradigm. For this…
In the Sparse Linear Regression (SLR) problem, given a $d \times n$ matrix $M$ and a $d$-dimensional query $q$, the goal is to compute a $k$-sparse $n$-dimensional vector $\tau$ such that the error $||M \tau-q||$ is minimized. This problem…
Learning-based low rank approximation algorithms can significantly improve the performance of randomized low rank approximation with sketch matrix. With the learned value and fixed non-zero positions for sketch matrices from learning-based…
Online sparse linear regression is an online problem where an algorithm repeatedly chooses a subset of coordinates to observe in an adversarially chosen feature vector, makes a real-valued prediction, receives the true label, and incurs the…
We give the first input-sparsity time algorithms for the rank-$k$ low rank approximation problem in every Schatten norm. Specifically, for a given $n\times n$ matrix $A$, our algorithm computes $Y,Z\in \mathbb{R}^{n\times k}$, which, with…
We study online convex optimization under stochastic sub-gradient observation faults, where we introduce adaptive algorithms with minimax optimal regret guarantees. We specifically study scenarios where our sub-gradient observations can be…
Low Rank Approximation is among most fundamental subjects of numerical linear algebra having important applications to various areas of modern computing and %they range from machine learning theory and %neural networks to data mining and…
In this paper, we derive entrywise error bounds for low-rank approximations of kernel matrices obtained using the truncated eigen-decomposition (or singular value decomposition). While this approximation is well-known to be optimal with…
We study distributed low rank approximation in which the matrix to be approximated is only implicitly represented across the different servers. For example, each of $s$ servers may have an $n \times d$ matrix $A^t$, and we may be interested…
The best algorithm for a computational problem generally depends on the "relevant inputs," a concept that depends on the application domain and often defies formal articulation. While there is a large literature on empirical approaches to…
Feature selection removes redundant features to enhanc performance and computational efficiency in downstream tasks. Existing works often struggle to capture complex feature interactions and adapt to diverse scenarios. Recent advances in…
Deep neural networks are commonly trained using stochastic non-convex optimization procedures, which are driven by gradient information estimated on fractions (batches) of the dataset. While it is commonly accepted that batch size is an…
We present statistical methods for big data arising from online analytical processing, where large amounts of data arrive in streams and require fast analysis without storage/access to the historical data. In particular, we develop…
In many problems in machine learning and operations research, we need to optimize a function whose input is a random variable or a probability density function, i.e. to solve optimization problems in an infinite dimensional space. On the…
Structured Low-Rank Approximation is a problem arising in a wide range of applications in Numerical Analysis and Engineering Sciences. Given an input matrix $M$, the goal is to compute a matrix $M'$ of given rank $r$ in a linear or affine…
We consider processing an n x d matrix A in a stream with row-wise updates according to a recent algorithm called Frequent Directions (Liberty, KDD 2013). This algorithm maintains an l x d matrix Q deterministically, processing each row in…