26,385 research outputs found
Learning by stochastic serializations
Complex structures are typical in machine learning. Tailoring learning
algorithms for every structure requires an effort that may be saved by defining
a generic learning procedure adaptive to any complex structure. In this paper,
we propose to map any complex structure onto a generic form, called
serialization, over which we can apply any sequence-based density estimator. We
then show how to transfer the learned density back onto the space of original
structures. To expose the learning procedure to the structural particularities
of the original structures, we take care that the serializations reflect
accurately the structures' properties. Enumerating all serializations is
infeasible. We propose an effective way to sample representative serializations
from the complete set of serializations which preserves the statistics of the
complete set. Our method is competitive or better than state of the art
learning algorithms that have been specifically designed for given structures.
In addition, since the serialization involves sampling from a combinatorial
process it provides considerable protection from overfitting, which we clearly
demonstrate on a number of experiments.Comment: Submission to NeurIPS 201
Exotic trees
We discuss the scaling properties of free branched polymers. The scaling
behaviour of the model is classified by the Hausdorff dimensions for the
internal geometry: d_L and d_H, and for the external one: D_L and D_H. The
dimensions d_H and D_H characterize the behaviour for long distances while d_L
and D_L for short distances. We show that the internal Hausdorff dimension is
d_L=2 for generic and scale-free trees, contrary to d_H which is known be equal
two for generic trees and to vary between two and infinity for scale-free
trees. We show that the external Hausdorff dimension D_H is directly related to
the internal one as D_H = \alpha d_H, where \alpha is the stability index of
the embedding weights for the nearest-vertex interactions. The index is
\alpha=2 for weights from the gaussian domain of attraction and 0<\alpha <2 for
those from the L\'evy domain of attraction. If the dimension D of the target
space is larger than D_H one finds D_L=D_H, or otherwise D_L=D. The latter
result means that the fractal structure cannot develop in a target space which
has too low dimension.Comment: 33 pages, 6 eps figure
The Grow-Shrink strategy for learning Markov network structures constrained by context-specific independences
Markov networks are models for compactly representing complex probability
distributions. They are composed by a structure and a set of numerical weights.
The structure qualitatively describes independences in the distribution, which
can be exploited to factorize the distribution into a set of compact functions.
A key application for learning structures from data is to automatically
discover knowledge. In practice, structure learning algorithms focused on
"knowledge discovery" present a limitation: they use a coarse-grained
representation of the structure. As a result, this representation cannot
describe context-specific independences. Very recently, an algorithm called
CSPC was designed to overcome this limitation, but it has a high computational
complexity. This work tries to mitigate this downside presenting CSGS, an
algorithm that uses the Grow-Shrink strategy for reducing unnecessary
computations. On an empirical evaluation, the structures learned by CSGS
achieve competitive accuracies and lower computational complexity with respect
to those obtained by CSPC.Comment: 12 pages, and 8 figures. This works was presented in IBERAMIA 201
Elimination of Spurious Ambiguity in Transition-Based Dependency Parsing
We present a novel technique to remove spurious ambiguity from transition
systems for dependency parsing. Our technique chooses a canonical sequence of
transition operations (computation) for a given dependency tree. Our technique
can be applied to a large class of bottom-up transition systems, including for
instance Nivre (2004) and Attardi (2006)
Causal and homogeneous networks
Growing networks have a causal structure. We show that the causality strongly
influences the scaling and geometrical properties of the network. In particular
the average distance between nodes is smaller for causal networks than for
corresponding homogeneous networks. We explain the origin of this effect and
illustrate it using as an example a solvable model of random trees. We also
discuss the issue of stability of the scale-free node degree distribution. We
show that a surplus of links may lead to the emergence of a singular node with
the degree proportional to the total number of links. This effect is closely
related to the backgammon condensation known from the balls-in-boxes model.Comment: short review submitted to AIP proceedings, CNET2004 conference;
changes in the discussion of the distance distribution for growing trees,
Fig. 6-right change
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