相关论文: Co-Occuring Directions Sketching for Approximate M…
In this work, we propose a (linearized) Alternating Direction Method-of-Multipliers (ADMM) algorithm for minimizing a convex function subject to a nonconvex constraint. We focus on the special case where such constraint arises from the…
We give the first L_1-sketching algorithm for integer vectors which produces nearly optimal sized sketches in nearly linear time. This answers the first open problem in the list of open problems from the 2006 IITK Workshop on Algorithms for…
The increasing demand for larger and higher fidelity simulations has made Adaptive Mesh Refinement (AMR) and unstructured mesh techniques essential to focus compute effort and memory cost on just the areas of interest in the simulation…
Sketching and stochastic gradient methods are arguably the most common techniques to derive efficient large scale learning algorithms. In this paper, we investigate their application in the context of nonparametric statistical learning.…
In this note we illustrate how common matrix approximation methods, such as random projection and random sampling, yield projection-cost-preserving sketches, as introduced in [FSS13, CEM+15]. A projection-cost-preserving sketch is a matrix…
We study the problem of constructing a linear sketch of minimum dimension that allows approximation of a given real-valued function $f \colon \mathbb{F}_2^n \rightarrow \mathbb R$ with small expected squared error. We develop a general…
Count-sketch is a popular matrix sketching algorithm that can produce a sketch of an input data matrix X in O(nnz(X))time where nnz(X) denotes the number of non-zero entries in X. The sketched matrix will be much smaller than X while…
We consider distributed optimization methods for problems where forming the Hessian is computationally challenging and communication is a significant bottleneck. We leverage randomized sketches for reducing the problem dimensions as well as…
Recently, Pagh presented a randomized approximation algorithm for the multiplication of real-valued matrices building upon work for detecting the most frequent items in data streams. We continue this line of research and present new {\em…
Accounting for the uncertainty in the predictions of modern neural networks is a challenging and important task in many domains. Existing algorithms for uncertainty estimation require modifying the model architecture and training procedure…
Matching pursuit algorithms are an important class of algorithms in signal processing and machine learning. We present a blended matching pursuit algorithm, combining coordinate descent-like steps with stronger gradient descent steps, for…
Stochastic computing is a paradigm in which logical operations are performed on randomly generated bit streams. Complex arithmetic operations can be executed by simple logic circuits, resulting in a much smaller area footprint compared to…
While traditional data-management systems focus on evaluating single, ad-hoc queries over static data sets in a centralized setting, several emerging applications require (possibly, continuous) answers to queries on dynamic data that is…
Efficient estimation of high-dimensional matrices-including covariance and precision matrices-is a cornerstone of modern multivariate statistics. Most existing studies have focused primarily on the theoretical properties of the estimators…
We study the problem of solving semidefinite programs (SDP) in the streaming model. Specifically, $m$ constraint matrices and a target matrix $C$, all of size $n\times n$ together with a vector $b\in \mathbb{R}^m$ are streamed to us…
We analyze the performance of the alternating direction method of multipliers (ADMM) to track, in a decentralized manner, a solution of a stochastic sequence of optimization problems parametrized by a discrete time Markov process. The main…
Decision-making, motion planning, and trajectory prediction are crucial in autonomous driving systems. By accurately forecasting the movements of other road users, the decision-making capabilities of the autonomous system can be enhanced,…
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…
Matrix sketching is aimed at finding close approximations of a matrix by factors of much smaller dimensions, which has important applications in optimization and machine learning. Given a matrix A of size m by n, state-of-the-art randomized…
Alternating Direction Method of Multipliers (ADMM) is a popular method for solving large-scale Machine Learning problems. Stochastic ADMM was proposed to reduce the per iteration computational complexity, which is more suitable for big data…