29,032 research outputs found
S2: An Efficient Graph Based Active Learning Algorithm with Application to Nonparametric Classification
This paper investigates the problem of active learning for binary label
prediction on a graph. We introduce a simple and label-efficient algorithm
called S2 for this task. At each step, S2 selects the vertex to be labeled
based on the structure of the graph and all previously gathered labels.
Specifically, S2 queries for the label of the vertex that bisects the *shortest
shortest* path between any pair of oppositely labeled vertices. We present a
theoretical estimate of the number of queries S2 needs in terms of a novel
parametrization of the complexity of binary functions on graphs. We also
present experimental results demonstrating the performance of S2 on both real
and synthetic data. While other graph-based active learning algorithms have
shown promise in practice, our algorithm is the first with both good
performance and theoretical guarantees. Finally, we demonstrate the
implications of the S2 algorithm to the theory of nonparametric active
learning. In particular, we show that S2 achieves near minimax optimal excess
risk for an important class of nonparametric classification problems.Comment: A version of this paper appears in the Conference on Learning Theory
(COLT) 201
Automated Termination Analysis for Logic Programs with Cut
Termination is an important and well-studied property for logic programs.
However, almost all approaches for automated termination analysis focus on
definite logic programs, whereas real-world Prolog programs typically use the
cut operator. We introduce a novel pre-processing method which automatically
transforms Prolog programs into logic programs without cuts, where termination
of the cut-free program implies termination of the original program. Hence
after this pre-processing, any technique for proving termination of definite
logic programs can be applied. We implemented this pre-processing in our
termination prover AProVE and evaluated it successfully with extensive
experiments
Multiclass Data Segmentation using Diffuse Interface Methods on Graphs
We present two graph-based algorithms for multiclass segmentation of
high-dimensional data. The algorithms use a diffuse interface model based on
the Ginzburg-Landau functional, related to total variation compressed sensing
and image processing. A multiclass extension is introduced using the Gibbs
simplex, with the functional's double-well potential modified to handle the
multiclass case. The first algorithm minimizes the functional using a convex
splitting numerical scheme. The second algorithm is a uses a graph adaptation
of the classical numerical Merriman-Bence-Osher (MBO) scheme, which alternates
between diffusion and thresholding. We demonstrate the performance of both
algorithms experimentally on synthetic data, grayscale and color images, and
several benchmark data sets such as MNIST, COIL and WebKB. We also make use of
fast numerical solvers for finding the eigenvectors and eigenvalues of the
graph Laplacian, and take advantage of the sparsity of the matrix. Experiments
indicate that the results are competitive with or better than the current
state-of-the-art multiclass segmentation algorithms.Comment: 14 page
GEMs and amplitude bounds in the colored Boulatov model
In this paper we construct a methodology for separating the divergencies due
to different topological manifolds dual to Feynman graphs in colored group
field theory. After having introduced the amplitude bounds using propagator
cuts, we show how Graph-Encoded-Manifolds (GEM) techniques can be used in order
to factorize divergencies related to different parts of the dual topologies of
the Feynman graphs in the general case. We show the potential of the formalism
in the case of 3-dimensional solid torii in the colored Boulatov model.Comment: 20 pages; 20 Figures; Style changed, discussion improved and typos
corrected, citations added; These GEMs are not related to "Global Embedding
Minkowskian spacetimes
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