19,279 research outputs found
A Branch-and-Bound Algorithm for MDL Learning Bayesian Networks
This paper extends the work in [Suzuki, 1996] and presents an efficient
depth-first branch-and-bound algorithm for learning Bayesian network
structures, based on the minimum description length (MDL) principle, for a
given (consistent) variable ordering. The algorithm exhaustively searches
through all network structures and guarantees to find the network with the best
MDL score. Preliminary experiments show that the algorithm is efficient, and
that the time complexity grows slowly with the sample size. The algorithm is
useful for empirically studying both the performance of suboptimal heuristic
search algorithms and the adequacy of the MDL principle in learning Bayesian
networks.Comment: Appears in Proceedings of the Sixteenth Conference on Uncertainty in
Artificial Intelligence (UAI2000
Generating Markov Equivalent Maximal Ancestral Graphs by Single Edge Replacement
Maximal ancestral graphs (MAGs) are used to encode conditional independence
relations in DAG models with hidden variables. Different MAGs may represent the
same set of conditional independences and are called Markov equivalent. This
paper considers MAGs without undirected edges and shows conditions under which
an arrow in a MAG can be reversed or interchanged with a bi-directed edge so as
to yield a Markov equivalent MAG.Comment: Appears in Proceedings of the Twenty-First Conference on Uncertainty
in Artificial Intelligence (UAI2005
Identifying Dynamic Sequential Plans
We address the problem of identifying dynamic sequential plans in the
framework of causal Bayesian networks, and show that the problem is reduced to
identifying causal effects, for which there are complete identi cation
algorithms available in the literature.Comment: Appears in Proceedings of the Twenty-Fourth Conference on Uncertainty
in Artificial Intelligence (UAI2008
Identifying Conditional Causal Effects
This paper concerns the assessment of the effects of actions from a
combination of nonexperimental data and causal assumptions encoded in the form
of a directed acyclic graph in which some variables are presumed to be
unobserved. We provide a procedure that systematically identifies cause effects
between two sets of variables conditioned on some other variables, in time
polynomial in the number of variables in the graph. The identifiable
conditional causal effects are expressed in terms of the observed joint
distribution.Comment: Appears in Proceedings of the Twentieth Conference on Uncertainty in
Artificial Intelligence (UAI2004
A Criterion for Parameter Identification in Structural Equation Models
This paper deals with the problem of identifying direct causal effects in
recursive linear structural equation models. The paper establishes a sufficient
criterion for identifying individual causal effects and provides a procedure
computing identified causal effects in terms of observed covariance matrix.Comment: Appears in Proceedings of the Twenty-Third Conference on Uncertainty
in Artificial Intelligence (UAI2007
Boundedness and exponential convergence of a chemotaxis model for tumor invasion
We revisit the following chemotaxis system modeling tumor invasion
\begin{equation*} \begin{cases} u_t=\Delta u-\nabla \cdot(u\nabla v),&
x\in\Omega, t>0,\\ v_t=\Delta v+wz,& x\in\Omega, t>0,\\ w_t=-wz,& x\in\Omega,
t>0,\\ z_t=\Delta z-z+u, & x\in\Omega, t>0,\\ \end{cases} \end{equation*} in a
smooth bounded domain with homogeneous
Neumann boundary and initial conditions. This model was recently proposed by
Fujie et al. \cite{FIY14} as a model for tumor invasion with the role of
extracellular matrix incorporated, and was analyzed by Fujie et al.
\cite{FIWY16}, showing the uniform boundedness and convergence for .
In this work, we first show that the -boundedness of the system can
be reduced to the boundedness of
for some
alone, and then, for , if the initial data
, and are sufficiently small, we are able to establish the
-boundedness of the system. Furthermore, we show that boundedness
implies exponential convergence with explicit convergence rate, which resolves
the open problem left in \cite{FIWY16}.Comment: 15pages, Submmitte
Local Markov Property for Models Satisfying Composition Axiom
The local Markov condition for a DAG to be an independence map of a
probability distribution is well known. For DAGs with latent variables,
represented as bi-directed edges in the graph, the local Markov property may
invoke exponential number of conditional independencies. This paper shows that
the number of conditional independence relations required may be reduced if the
probability distributions satisfy the composition axiom. In certain types of
graphs, only linear number of conditional independencies are required. The
result has applications in testing linear structural equation models with
correlated errors.Comment: Appears in Proceedings of the Twenty-First Conference on Uncertainty
in Artificial Intelligence (UAI2005
Probabilities of Causation: Bounds and Identification
This paper deals with the problem of estimating the probability that one
event was a cause of another in a given scenario. Using structural-semantical
definitions of the probabilities of necessary or sufficient causation (or
both), we show how to optimally bound these quantities from data obtained in
experimental and observational studies, making minimal assumptions concerning
the data-generating process. In particular, we strengthen the results of Pearl
(1999) by weakening the data-generation assumptions and deriving theoretically
sharp bounds on the probabilities of causation. These results delineate
precisely how empirical data can be used both in settling questions of
attribution and in solving attribution-related problems of decision making.Comment: Appears in Proceedings of the Sixteenth Conference on Uncertainty in
Artificial Intelligence (UAI2000
Causal Discovery from Changes
We propose a new method of discovering causal structures, based on the
detection of local, spontaneous changes in the underlying data-generating
model. We analyze the classes of structures that are equivalent relative to a
stream of distributions produced by local changes, and devise algorithms that
output graphical representations of these equivalence classes. We present
experimental results, using simulated data, and examine the errors associated
with detection of changes and recovery of structures.Comment: Appears in Proceedings of the Seventeenth Conference on Uncertainty
in Artificial Intelligence (UAI2001
Polynomial Constraints in Causal Bayesian Networks
We use the implicitization procedure to generate polynomial equality
constraints on the set of distributions induced by local interventions on
variables governed by a causal Bayesian network with hidden variables. We show
how we may reduce the complexity of the implicitization problem and make the
problem tractable in certain causal Bayesian networks. We also show some
preliminary results on the algebraic structure of polynomial constraints. The
results have applications in distinguishing between causal models and in
testing causal models with combined observational and experimental data.Comment: Appears in Proceedings of the Twenty-Third Conference on Uncertainty
in Artificial Intelligence (UAI2007
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