4,800 research outputs found
A Distributed Frank-Wolfe Algorithm for Communication-Efficient Sparse Learning
Learning sparse combinations is a frequent theme in machine learning. In this
paper, we study its associated optimization problem in the distributed setting
where the elements to be combined are not centrally located but spread over a
network. We address the key challenges of balancing communication costs and
optimization errors. To this end, we propose a distributed Frank-Wolfe (dFW)
algorithm. We obtain theoretical guarantees on the optimization error
and communication cost that do not depend on the total number of
combining elements. We further show that the communication cost of dFW is
optimal by deriving a lower-bound on the communication cost required to
construct an -approximate solution. We validate our theoretical
analysis with empirical studies on synthetic and real-world data, which
demonstrate that dFW outperforms both baselines and competing methods. We also
study the performance of dFW when the conditions of our analysis are relaxed,
and show that dFW is fairly robust.Comment: Extended version of the SIAM Data Mining 2015 pape
Reconciling modern machine learning practice and the bias-variance trade-off
Breakthroughs in machine learning are rapidly changing science and society,
yet our fundamental understanding of this technology has lagged far behind.
Indeed, one of the central tenets of the field, the bias-variance trade-off,
appears to be at odds with the observed behavior of methods used in the modern
machine learning practice. The bias-variance trade-off implies that a model
should balance under-fitting and over-fitting: rich enough to express
underlying structure in data, simple enough to avoid fitting spurious patterns.
However, in the modern practice, very rich models such as neural networks are
trained to exactly fit (i.e., interpolate) the data. Classically, such models
would be considered over-fit, and yet they often obtain high accuracy on test
data. This apparent contradiction has raised questions about the mathematical
foundations of machine learning and their relevance to practitioners.
In this paper, we reconcile the classical understanding and the modern
practice within a unified performance curve. This "double descent" curve
subsumes the textbook U-shaped bias-variance trade-off curve by showing how
increasing model capacity beyond the point of interpolation results in improved
performance. We provide evidence for the existence and ubiquity of double
descent for a wide spectrum of models and datasets, and we posit a mechanism
for its emergence. This connection between the performance and the structure of
machine learning models delineates the limits of classical analyses, and has
implications for both the theory and practice of machine learning
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