985,434 research outputs found
Generalization Properties and Implicit Regularization for Multiple Passes SGM
We study the generalization properties of stochastic gradient methods for
learning with convex loss functions and linearly parameterized functions. We
show that, in the absence of penalizations or constraints, the stability and
approximation properties of the algorithm can be controlled by tuning either
the step-size or the number of passes over the data. In this view, these
parameters can be seen to control a form of implicit regularization. Numerical
results complement the theoretical findings.Comment: 26 pages, 4 figures. To appear in ICML 201
Gradual Generalization of Nautical Chart Contours with a Cube B-Spline Snake Model
—B-spline snake methods have been used in cartographic generalization in the past decade, particularly in the generalization of navigational charts where this method yields good results with respect to the shoal-bias rules for generalization of chart contours. However, previous studies only show generalization results at particular generalization (or scale) levels, and the user can only see two conditions: before the generalization and after generalization, but nothing in between. This paper presents an improved method of using B-spline snakes for generalization in the context of nautical charts, where the generalization process is done gradually, and the user can see the complete process of the generalization
Robustness and Generalization
We derive generalization bounds for learning algorithms based on their
robustness: the property that if a testing sample is "similar" to a training
sample, then the testing error is close to the training error. This provides a
novel approach, different from the complexity or stability arguments, to study
generalization of learning algorithms. We further show that a weak notion of
robustness is both sufficient and necessary for generalizability, which implies
that robustness is a fundamental property for learning algorithms to work
E-Generalization Using Grammars
We extend the notion of anti-unification to cover equational theories and
present a method based on regular tree grammars to compute a finite
representation of E-generalization sets. We present a framework to combine
Inductive Logic Programming and E-generalization that includes an extension of
Plotkin's lgg theorem to the equational case. We demonstrate the potential
power of E-generalization by three example applications: computation of
suggestions for auxiliary lemmas in equational inductive proofs, computation of
construction laws for given term sequences, and learning of screen editor
command sequences.Comment: 49 pages, 16 figures, author address given in header is meanwhile
outdated, full version of an article in the "Artificial Intelligence
Journal", appeared as technical report in 2003. An open-source C
implementation and some examples are found at the Ancillary file
Projective simulation with generalization
The ability to generalize is an important feature of any intelligent agent.
Not only because it may allow the agent to cope with large amounts of data, but
also because in some environments, an agent with no generalization capabilities
cannot learn. In this work we outline several criteria for generalization, and
present a dynamic and autonomous machinery that enables projective simulation
agents to meaningfully generalize. Projective simulation, a novel, physical
approach to artificial intelligence, was recently shown to perform well in
standard reinforcement learning problems, with applications in advanced
robotics as well as quantum experiments. Both the basic projective simulation
model and the presented generalization machinery are based on very simple
principles. This allows us to provide a full analytical analysis of the agent's
performance and to illustrate the benefit the agent gains by generalizing.
Specifically, we show that already in basic (but extreme) environments,
learning without generalization may be impossible, and demonstrate how the
presented generalization machinery enables the projective simulation agent to
learn.Comment: 14 pages, 9 figure
Generalization of Gutzwiller Approximation
We derive expressions required in generalizing the Gutzwiller approximation
to models comprising arbitrarily degenerate localized orbitals.Comment: 6 pages, 1 figure, to appear in J.Phys.Soc.Jpn. vol.6
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