50,223 research outputs found
Fast Conical Hull Algorithms for Near-separable Non-negative Matrix Factorization
The separability assumption (Donoho & Stodden, 2003; Arora et al., 2012)
turns non-negative matrix factorization (NMF) into a tractable problem.
Recently, a new class of provably-correct NMF algorithms have emerged under
this assumption. In this paper, we reformulate the separable NMF problem as
that of finding the extreme rays of the conical hull of a finite set of
vectors. From this geometric perspective, we derive new separable NMF
algorithms that are highly scalable and empirically noise robust, and have
several other favorable properties in relation to existing methods. A parallel
implementation of our algorithm demonstrates high scalability on shared- and
distributed-memory machines.Comment: 15 pages, 6 figure
CoCoA: A General Framework for Communication-Efficient Distributed Optimization
The scale of modern datasets necessitates the development of efficient
distributed optimization methods for machine learning. We present a
general-purpose framework for distributed computing environments, CoCoA, that
has an efficient communication scheme and is applicable to a wide variety of
problems in machine learning and signal processing. We extend the framework to
cover general non-strongly-convex regularizers, including L1-regularized
problems like lasso, sparse logistic regression, and elastic net
regularization, and show how earlier work can be derived as a special case. We
provide convergence guarantees for the class of convex regularized loss
minimization objectives, leveraging a novel approach in handling
non-strongly-convex regularizers and non-smooth loss functions. The resulting
framework has markedly improved performance over state-of-the-art methods, as
we illustrate with an extensive set of experiments on real distributed
datasets
A hybrid swarm-based algorithm for single-objective optimization problems involving high-cost analyses
In many technical fields, single-objective optimization procedures in
continuous domains involve expensive numerical simulations. In this context, an
improvement of the Artificial Bee Colony (ABC) algorithm, called the Artificial
super-Bee enhanced Colony (AsBeC), is presented. AsBeC is designed to provide
fast convergence speed, high solution accuracy and robust performance over a
wide range of problems. It implements enhancements of the ABC structure and
hybridizations with interpolation strategies. The latter are inspired by the
quadratic trust region approach for local investigation and by an efficient
global optimizer for separable problems. Each modification and their combined
effects are studied with appropriate metrics on a numerical benchmark, which is
also used for comparing AsBeC with some effective ABC variants and other
derivative-free algorithms. In addition, the presented algorithm is validated
on two recent benchmarks adopted for competitions in international conferences.
Results show remarkable competitiveness and robustness for AsBeC.Comment: 19 pages, 4 figures, Springer Swarm Intelligenc
Linearized Alternating Direction Method with Parallel Splitting and Adaptive Penalty for Separable Convex Programs in Machine Learning
Many problems in machine learning and other fields can be (re)for-mulated as
linearly constrained separable convex programs. In most of the cases, there are
multiple blocks of variables. However, the traditional alternating direction
method (ADM) and its linearized version (LADM, obtained by linearizing the
quadratic penalty term) are for the two-block case and cannot be naively
generalized to solve the multi-block case. So there is great demand on
extending the ADM based methods for the multi-block case. In this paper, we
propose LADM with parallel splitting and adaptive penalty (LADMPSAP) to solve
multi-block separable convex programs efficiently. When all the component
objective functions have bounded subgradients, we obtain convergence results
that are stronger than those of ADM and LADM, e.g., allowing the penalty
parameter to be unbounded and proving the sufficient and necessary conditions}
for global convergence. We further propose a simple optimality measure and
reveal the convergence rate of LADMPSAP in an ergodic sense. For programs with
extra convex set constraints, with refined parameter estimation we devise a
practical version of LADMPSAP for faster convergence. Finally, we generalize
LADMPSAP to handle programs with more difficult objective functions by
linearizing part of the objective function as well. LADMPSAP is particularly
suitable for sparse representation and low-rank recovery problems because its
subproblems have closed form solutions and the sparsity and low-rankness of the
iterates can be preserved during the iteration. It is also highly
parallelizable and hence fits for parallel or distributed computing. Numerical
experiments testify to the advantages of LADMPSAP in speed and numerical
accuracy.Comment: Preliminary version published on Asian Conference on Machine Learning
201
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