875 research outputs found
Active Semi-Supervised Learning Using Sampling Theory for Graph Signals
We consider the problem of offline, pool-based active semi-supervised
learning on graphs. This problem is important when the labeled data is scarce
and expensive whereas unlabeled data is easily available. The data points are
represented by the vertices of an undirected graph with the similarity between
them captured by the edge weights. Given a target number of nodes to label, the
goal is to choose those nodes that are most informative and then predict the
unknown labels. We propose a novel framework for this problem based on our
recent results on sampling theory for graph signals. A graph signal is a
real-valued function defined on each node of the graph. A notion of frequency
for such signals can be defined using the spectrum of the graph Laplacian
matrix. The sampling theory for graph signals aims to extend the traditional
Nyquist-Shannon sampling theory by allowing us to identify the class of graph
signals that can be reconstructed from their values on a subset of vertices.
This approach allows us to define a criterion for active learning based on
sampling set selection which aims at maximizing the frequency of the signals
that can be reconstructed from their samples on the set. Experiments show the
effectiveness of our method.Comment: 10 pages, 6 figures, To appear in KDD'1
Semi-supervised Learning based on Distributionally Robust Optimization
We propose a novel method for semi-supervised learning (SSL) based on
data-driven distributionally robust optimization (DRO) using optimal transport
metrics. Our proposed method enhances generalization error by using the
unlabeled data to restrict the support of the worst case distribution in our
DRO formulation. We enable the implementation of our DRO formulation by
proposing a stochastic gradient descent algorithm which allows to easily
implement the training procedure. We demonstrate that our Semi-supervised DRO
method is able to improve the generalization error over natural supervised
procedures and state-of-the-art SSL estimators. Finally, we include a
discussion on the large sample behavior of the optimal uncertainty region in
the DRO formulation. Our discussion exposes important aspects such as the role
of dimension reduction in SSL
A High-Throughput Solver for Marginalized Graph Kernels on GPU
We present the design and optimization of a linear solver on General Purpose GPUs for the efficient and high-throughput evaluation of the marginalized graph kernel between pairs of labeled graphs. The solver implements a preconditioned conjugate gradient (PCG) method to compute the solution to a generalized Laplacian equation associated with the tensor product of two graphs. To cope with the gap between the instruction throughput and the memory bandwidth of current generation GPUs, our solver forms the tensor product linear system on-the-fly without storing it in memory when performing matrix-vector dot product operations in PCG. Such on-the-fly computation is accomplished by using threads in a warp to cooperatively stream the adjacency and edge label matrices of individual graphs by small square matrix blocks called tiles, which are then staged in registers and the shared memory for later reuse. Warps across a thread block can further share tiles via the shared memory to increase data reuse. We exploit the sparsity of the graphs hierarchically by storing only non-empty tiles using a coordinate format and nonzero elements within each tile using bitmaps. Besides, we propose a new partition-based reordering algorithm for aggregating nonzero elements of the graphs into fewer but denser tiles to improve the efficiency of the sparse format.We carry out extensive theoretical analyses on the graph tensor product primitives for tiles of various density and evaluate their performance on synthetic and real-world datasets. Our solver delivers three to four orders of magnitude speedup over existing CPU-based solvers such as GraKeL and GraphKernels. The capability of the solver enables kernel-based learning tasks at unprecedented scales
The CoNLL 2007 shared task on dependency parsing
The Conference on Computational Natural Language Learning features a shared task, in which participants train and test their learning systems on the same data sets. In 2007, as in 2006, the shared task has been devoted to dependency parsing, this year with both a multilingual track and a domain adaptation track. In this paper, we define the tasks of the different tracks and describe how the data sets were created from existing treebanks for ten languages. In addition, we characterize the different approaches of the participating systems, report the test results, and provide a first analysis of these results
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