2,376 research outputs found
Second-Order Belief Hidden Markov Models
Hidden Markov Models (HMMs) are learning methods for pattern recognition. The
probabilistic HMMs have been one of the most used techniques based on the
Bayesian model. First-order probabilistic HMMs were adapted to the theory of
belief functions such that Bayesian probabilities were replaced with mass
functions. In this paper, we present a second-order Hidden Markov Model using
belief functions. Previous works in belief HMMs have been focused on the
first-order HMMs. We extend them to the second-order model
Evidence Propagation and Consensus Formation in Noisy Environments
We study the effectiveness of consensus formation in multi-agent systems
where there is both belief updating based on direct evidence and also belief
combination between agents. In particular, we consider the scenario in which a
population of agents collaborate on the best-of-n problem where the aim is to
reach a consensus about which is the best (alternatively, true) state from
amongst a set of states, each with a different quality value (or level of
evidence). Agents' beliefs are represented within Dempster-Shafer theory by
mass functions and we investigate the macro-level properties of four well-known
belief combination operators for this multi-agent consensus formation problem:
Dempster's rule, Yager's rule, Dubois & Prade's operator and the averaging
operator. The convergence properties of the operators are considered and
simulation experiments are conducted for different evidence rates and noise
levels. Results show that a combination of updating on direct evidence and
belief combination between agents results in better consensus to the best state
than does evidence updating alone. We also find that in this framework the
operators are robust to noise. Broadly, Yager's rule is shown to be the better
operator under various parameter values, i.e. convergence to the best state,
robustness to noise, and scalability.Comment: 13th international conference on Scalable Uncertainty Managemen
A unified view of some representations of imprecise probabilities
International audienceSeveral methods for the practical representation of imprecise probabilities exist such as Ferson's p-boxes, possibility distributions, Neumaier's clouds, and random sets . In this paper some relationships existing between the four kinds of representations are discussed. A cloud as well as a p-box can be modelled as a pair of possibility distributions. We show that a generalized form of p-box is a special kind of belief function and also a special kind of cloud
A Random Matrix Approach to VARMA Processes
We apply random matrix theory to derive spectral density of large sample
covariance matrices generated by multivariate VMA(q), VAR(q) and VARMA(q1,q2)
processes. In particular, we consider a limit where the number of random
variables N and the number of consecutive time measurements T are large but the
ratio N/T is fixed. In this regime the underlying random matrices are
asymptotically equivalent to Free Random Variables (FRV). We apply the FRV
calculus to calculate the eigenvalue density of the sample covariance for
several VARMA-type processes. We explicitly solve the VARMA(1,1) case and
demonstrate a perfect agreement between the analytical result and the spectra
obtained by Monte Carlo simulations. The proposed method is purely algebraic
and can be easily generalized to q1>1 and q2>1.Comment: 16 pages, 6 figures, submitted to New Journal of Physic
A reliability-based approach for influence maximization using the evidence theory
The influence maximization is the problem of finding a set of social network
users, called influencers, that can trigger a large cascade of propagation.
Influencers are very beneficial to make a marketing campaign goes viral through
social networks for example. In this paper, we propose an influence measure
that combines many influence indicators. Besides, we consider the reliability
of each influence indicator and we present a distance-based process that allows
to estimate the reliability of each indicator. The proposed measure is defined
under the framework of the theory of belief functions. Furthermore, the
reliability-based influence measure is used with an influence maximization
model to select a set of users that are able to maximize the influence in the
network. Finally, we present a set of experiments on a dataset collected from
Twitter. These experiments show the performance of the proposed solution in
detecting social influencers with good quality.Comment: 14 pages, 8 figures, DaWak 2017 conferenc
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