13,871 research outputs found
A hybrid algorithm for Bayesian network structure learning with application to multi-label learning
We present a novel hybrid algorithm for Bayesian network structure learning,
called H2PC. It first reconstructs the skeleton of a Bayesian network and then
performs a Bayesian-scoring greedy hill-climbing search to orient the edges.
The algorithm is based on divide-and-conquer constraint-based subroutines to
learn the local structure around a target variable. We conduct two series of
experimental comparisons of H2PC against Max-Min Hill-Climbing (MMHC), which is
currently the most powerful state-of-the-art algorithm for Bayesian network
structure learning. First, we use eight well-known Bayesian network benchmarks
with various data sizes to assess the quality of the learned structure returned
by the algorithms. Our extensive experiments show that H2PC outperforms MMHC in
terms of goodness of fit to new data and quality of the network structure with
respect to the true dependence structure of the data. Second, we investigate
H2PC's ability to solve the multi-label learning problem. We provide
theoretical results to characterize and identify graphically the so-called
minimal label powersets that appear as irreducible factors in the joint
distribution under the faithfulness condition. The multi-label learning problem
is then decomposed into a series of multi-class classification problems, where
each multi-class variable encodes a label powerset. H2PC is shown to compare
favorably to MMHC in terms of global classification accuracy over ten
multi-label data sets covering different application domains. Overall, our
experiments support the conclusions that local structural learning with H2PC in
the form of local neighborhood induction is a theoretically well-motivated and
empirically effective learning framework that is well suited to multi-label
learning. The source code (in R) of H2PC as well as all data sets used for the
empirical tests are publicly available.Comment: arXiv admin note: text overlap with arXiv:1101.5184 by other author
ACCAMS: Additive Co-Clustering to Approximate Matrices Succinctly
Matrix completion and approximation are popular tools to capture a user's
preferences for recommendation and to approximate missing data. Instead of
using low-rank factorization we take a drastically different approach, based on
the simple insight that an additive model of co-clusterings allows one to
approximate matrices efficiently. This allows us to build a concise model that,
per bit of model learned, significantly beats all factorization approaches to
matrix approximation. Even more surprisingly, we find that summing over small
co-clusterings is more effective in modeling matrices than classic
co-clustering, which uses just one large partitioning of the matrix.
Following Occam's razor principle suggests that the simple structure induced
by our model better captures the latent preferences and decision making
processes present in the real world than classic co-clustering or matrix
factorization. We provide an iterative minimization algorithm, a collapsed
Gibbs sampler, theoretical guarantees for matrix approximation, and excellent
empirical evidence for the efficacy of our approach. We achieve
state-of-the-art results on the Netflix problem with a fraction of the model
complexity.Comment: 22 pages, under review for conference publicatio
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