85 research outputs found
Dynamic importance sampling in Bayesian networks based on probability trees
In this paper we introduce a new dynamic importance sampling propagation algorithm for
Bayesian networks. Importance sampling is based on using an auxiliary sampling distribution
from which a set of configurations of the variables in the network is drawn, and the performance
of the algorithm depends on the variance of the weights associated with the simulated
configurations. The basic idea of dynamic importance sampling is to use the simulation of a
configuration to modify the sampling distribution in order to improve its quality and so reducing
the variance of the future weights. The paper shows that this can be achieved with a low
computational effort. The experiments carried out show that the final results can be very good
even in the case that the initial sampling distribution is far away from the optimum.
2004 Elsevier Inc. All rights reserved.Spanish Ministry of Science and Technology, project Elvira II
(TIC2001-2973-C05-01 and 02
Dynamic Importance Sampling in Bayesian Networks Based on Probability Trees
In this paper we introduce a new dynamic importance sampling propagation algorithm for Bayesian networks. Importance sampling is based on using an auxiliary sampling distribution from which a set of con gurations of the variables in the network is drawn, and the performance of the algorithm depends on the variance of the weights associated with the simulated con gurations. The basic idea of dynamic importance sampling is to use the simulation of a con guration to modify the sampling
distribution in order to improve its quality and so reducing the variance of the future weights. The paper shows that this can be achieved with a low computational effort. The experiments carried out show that the nal results can be very good even in the case that the initial sampling distribution is far away from the optimum
Maximum of entropy for belief intervals under Evidence Theory
The Dempster-Shafer Theory (DST) or Evidence Theory has been commonly used to
deal with uncertainty. It is based on the basic probability assignment concept (BPA). The upper entropy
on the credal set associated with a BPA is the only uncertainty measure in DST that verifies all the
necessary mathematical properties and behaviors. Nonetheless, its computation is notably complex. For this
reason, many alternatives to this measure have been recently proposed, but they do not satisfy most of the
mathematical requirements and present some undesirable behaviors. Belief intervals have been frequently
employed to quantify uncertainty in DST in the last years, and they can represent the uncertainty-basedinformation
better than a BPA. In this research, we develop a new uncertainty measure that consists of the
maximum of entropy on the credal set corresponding to belief intervals for singletons. It verifies all the
crucial mathematical requirements and presents good behavior, solving most of the shortcomings found in
uncertainty measures proposed recently. Moreover, its calculation is notably easier than the upper entropy
on the credal set associated with the BPA. Therefore, our proposed uncertainty measure is more suitable to
be used in practical applications.Spanish Ministerio de Economia y Competitividad
TIN2016-77902-C3-2-PEuropean Union (EU)
TEC2015-69496-
Required mathematical properties and behaviors of uncertainty measures on belief intervals
The Dempster–Shafer theory of evidence (DST) has
been widely used to handle uncertainty‐based information.
It is based on the concept of basic probability
assignment (BPA). Belief intervals are easier to
manage than a BPA to represent uncertainty‐based
information. For this reason, several uncertainty measures
for DST recently proposed are based on belief
intervals. In this study, we carry out a study about the
crucial mathematical properties and behavioral requirements
that must be verified by every uncertainty
measure on belief intervals. We base on the study
previously carried out for uncertainty measures on
BPAs. Furthermore, we analyze which of these properties
are satisfied by each one of the uncertainty
measures on belief intervals proposed so far. Such a
comparative analysis shows that, among these measures,
the maximum of entropy on the belief intervals
is the most suitable one to be employed in practical
applications since it is the only one that satisfies all the
required mathematical properties and behaviors
Upgrading the Fusion of Imprecise Classifiers
Imprecise classification is a relatively new task within Machine Learning. The difference
with standard classification is that not only is one state of the variable under study determined, a set
of states that do not have enough information against them and cannot be ruled out is determined
as well. For imprecise classification, a mode called an Imprecise Credal Decision Tree (ICDT) that
uses imprecise probabilities and maximum of entropy as the information measure has been presented.
A difficult and interesting task is to show how to combine this type of imprecise classifiers.
A procedure based on the minimum level of dominance has been presented; though it represents a
very strong method of combining, it has the drawback of an important risk of possible erroneous
prediction. In this research, we use the second-best theory to argue that the aforementioned type of
combination can be improved through a new procedure built by relaxing the constraints. The new
procedure is compared with the original one in an experimental study on a large set of datasets, and
shows improvement.UGR-FEDER funds under Project A-TIC-344-UGR20FEDER/Junta de Andalucía-Consejería de Transformación Económica, Industria, Conocimiento
y Universidades” under Project P20_0015
A Monte-Carlo Algorithm for Probabilistic Propagation in Belief Networks based on Importance Sampling and Stratified Simulation Techniques
A class of Monte Carlo algorithms for probability propagation in belief networks is given.
The simulation is based on a two steps procedure. The first one is a node deletion technique
to calculate the ’a posteriori’ distribution on a variable, with the particularity that when
exact computations are too costly, they are carried out in an approximate way. In the second
step, the computations done in the first one are used to obtain random configurations for the
variables of interest. These configurations are weighted according to the importance sampling
methodology. Different particular algorithms are obtained depending on the approximation
procedure used in the first step and in the way of obtaining the random configurations. In
this last case, a stratified sampling technique is used, which has been adapted to be applied
to very large networks without problems with round-off errors
New strategies for finding multiplicative decompositions of probability trees
Probability trees are a powerful data structure for representing probabilistic potentials. However, their complexity can become intractable if they represent a probability distribution over a large set of variables. In this paper, we study the problem of decomposing a probability tree as a product of smaller trees, with the aim of being able to handle bigger probabilistic potentials. We propose exact and approximate approaches and evaluate their behaviour through an extensive set of experiments
Recent advances in probabilistic graphical models
Probabilistic graphical models constitute a fundamental tool for the development
of intelligent systems
Computation of Kullback–Leibler Divergence in Bayesian Networks
Kullback–Leibler divergence KL(p, q) is the standard measure of error when we have a
true probability distribution p which is approximate with probability distribution q. Its efficient
computation is essential in many tasks, as in approximate computation or as a measure of error
when learning a probability. In high dimensional probabilities, as the ones associated with Bayesian
networks, a direct computation can be unfeasible. This paper considers the case of efficiently
computing the Kullback–Leibler divergence of two probability distributions, each one of them
coming from a different Bayesian network, which might have different structures. The paper is based
on an auxiliary deletion algorithm to compute the necessary marginal distributions, but using a cache
of operations with potentials in order to reuse past computations whenever they are necessary. The
algorithms are tested with Bayesian networks from the bnlearn repository. Computer code in Python
is provided taking as basis pgmpy, a library for working with probabilistic graphical models.Spanish Ministry of Education and Science
under project PID2019-106758GB-C31European Regional Development Fund (FEDER
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