48,581 research outputs found
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
L1-Regularized Distributed Optimization: A Communication-Efficient Primal-Dual Framework
Despite the importance of sparsity in many large-scale applications, there
are few methods for distributed optimization of sparsity-inducing objectives.
In this paper, we present a communication-efficient framework for
L1-regularized optimization in the distributed environment. By viewing
classical objectives in a more general primal-dual setting, we develop a new
class of methods that can be efficiently distributed and applied to common
sparsity-inducing models, such as Lasso, sparse logistic regression, and
elastic net-regularized problems. We provide theoretical convergence guarantees
for our framework, and demonstrate its efficiency and flexibility with a
thorough experimental comparison on Amazon EC2. Our proposed framework yields
speedups of up to 50x as compared to current state-of-the-art methods for
distributed L1-regularized optimization
High-performance Kernel Machines with Implicit Distributed Optimization and Randomization
In order to fully utilize "big data", it is often required to use "big
models". Such models tend to grow with the complexity and size of the training
data, and do not make strong parametric assumptions upfront on the nature of
the underlying statistical dependencies. Kernel methods fit this need well, as
they constitute a versatile and principled statistical methodology for solving
a wide range of non-parametric modelling problems. However, their high
computational costs (in storage and time) pose a significant barrier to their
widespread adoption in big data applications.
We propose an algorithmic framework and high-performance implementation for
massive-scale training of kernel-based statistical models, based on combining
two key technical ingredients: (i) distributed general purpose convex
optimization, and (ii) the use of randomization to improve the scalability of
kernel methods. Our approach is based on a block-splitting variant of the
Alternating Directions Method of Multipliers, carefully reconfigured to handle
very large random feature matrices, while exploiting hybrid parallelism
typically found in modern clusters of multicore machines. Our implementation
supports a variety of statistical learning tasks by enabling several loss
functions, regularization schemes, kernels, and layers of randomized
approximations for both dense and sparse datasets, in a highly extensible
framework. We evaluate the ability of our framework to learn models on data
from applications, and provide a comparison against existing sequential and
parallel libraries.Comment: Work presented at MMDS 2014 (June 2014) and JSM 201
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