11,024 research outputs found
Evaluation of the Performance of the Markov Blanket Bayesian Classifier Algorithm
The Markov Blanket Bayesian Classifier is a recently-proposed algorithm for
construction of probabilistic classifiers. This paper presents an empirical
comparison of the MBBC algorithm with three other Bayesian classifiers: Naive
Bayes, Tree-Augmented Naive Bayes and a general Bayesian network. All of these
are implemented using the K2 framework of Cooper and Herskovits. The
classifiers are compared in terms of their performance (using simple accuracy
measures and ROC curves) and speed, on a range of standard benchmark data sets.
It is concluded that MBBC is competitive in terms of speed and accuracy with
the other algorithms considered.Comment: 9 pages: Technical Report No. NUIG-IT-011002, Department of
Information Technology, National University of Ireland, Galway (2002
Estimating Diffusion Network Structures: Recovery Conditions, Sample Complexity & Soft-thresholding Algorithm
Information spreads across social and technological networks, but often the
network structures are hidden from us and we only observe the traces left by
the diffusion processes, called cascades. Can we recover the hidden network
structures from these observed cascades? What kind of cascades and how many
cascades do we need? Are there some network structures which are more difficult
than others to recover? Can we design efficient inference algorithms with
provable guarantees?
Despite the increasing availability of cascade data and methods for inferring
networks from these data, a thorough theoretical understanding of the above
questions remains largely unexplored in the literature. In this paper, we
investigate the network structure inference problem for a general family of
continuous-time diffusion models using an -regularized likelihood
maximization framework. We show that, as long as the cascade sampling process
satisfies a natural incoherence condition, our framework can recover the
correct network structure with high probability if we observe
cascades, where is the maximum number of parents of a node and is the
total number of nodes. Moreover, we develop a simple and efficient
soft-thresholding inference algorithm, which we use to illustrate the
consequences of our theoretical results, and show that our framework
outperforms other alternatives in practice.Comment: To appear in the 31st International Conference on Machine Learning
(ICML), 201
Penalized Estimation of Directed Acyclic Graphs From Discrete Data
Bayesian networks, with structure given by a directed acyclic graph (DAG),
are a popular class of graphical models. However, learning Bayesian networks
from discrete or categorical data is particularly challenging, due to the large
parameter space and the difficulty in searching for a sparse structure. In this
article, we develop a maximum penalized likelihood method to tackle this
problem. Instead of the commonly used multinomial distribution, we model the
conditional distribution of a node given its parents by multi-logit regression,
in which an edge is parameterized by a set of coefficient vectors with dummy
variables encoding the levels of a node. To obtain a sparse DAG, a group norm
penalty is employed, and a blockwise coordinate descent algorithm is developed
to maximize the penalized likelihood subject to the acyclicity constraint of a
DAG. When interventional data are available, our method constructs a causal
network, in which a directed edge represents a causal relation. We apply our
method to various simulated and real data sets. The results show that our
method is very competitive, compared to many existing methods, in DAG
estimation from both interventional and high-dimensional observational data.Comment: To appear in Statistics and Computin
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