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

Ephemeral properties and the illusion of microscopic particles

Founding our analysis on the Geneva-Brussels approach to quantum mechanics, we use conventional macroscopic objects as guiding examples to clarify the content of two important results of the beginning of twentieth century: Einstein-Podolsky-Rosen's reality criterion and Heisenberg's uncertainty principle. We then use them in combination to show that our widespread belief in the existence of microscopic particles is only the result of a cognitive illusion, as microscopic particles are not particles, but are instead the ephemeral spatial and local manifestations of non-spatial and non-local entities

Supraventriculaire tachycardie met isoritmische atrioventriculaire dissociatie bij een labrador-retriever

A neutered, seven-year-old, female Labrador retriever was presented with complaints of tachypnea, gagging and abdominal distension. A left apical systolic murmur with an intensity of 3/6, tachycardia, weak femoral pulses and positive undulation were observed on physical examination. After echocar-diographic and electrocardiographic examination, dilated cardiomyopathy (primary or secundary) and supraventricular tachycardia were diagnosed. At a later control visit, after initiation of treatment with digoxin, electrocardiography revealed isorhythmic atrioventricular dissociation (IAVD) and poor control of the SVT. After transition to diltiazem, the tachycardia was well-controlled. A full recovery of the heart was observed on echocardiographic examination. Twenty-four months later, the dog showed no more cardiac signs. In this case report, a rare arrhythmia, i.e. IAVD in combination with SVT is described. It shows the importance of SVT as a reversible cause of a DCM-like phenotype on echo-cardiography

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

Regularization of point vortices for the Euler equation in dimension two

In this paper, we construct stationary classical solutions of the incompressible Euler equation approximating singular stationary solutions of this equation. This procedure is carried out by constructing solutions to the following elliptic problem [ -\ep^2 \Delta u=(u-q-\frac{\kappa}{2\pi}\ln\frac{1}{\ep})_+^p, \quad & x\in\Omega, u=0, \quad & x\in\partial\Omega, ] where $p>1$, $\Omega\subset\mathbb{R}^2$ is a bounded domain, $q$ is a harmonic function. We showed that if $\Omega$ is simply-connected smooth domain, then for any given non-degenerate critical point of Kirchhoff-Routh function $\mathcal{W}(x_1,...,x_m)$ with the same strength $\kappa>0$, there is a stationary classical solution approximating stationary $m$ points vortex solution of incompressible Euler equations with vorticity $m\kappa$. Existence and asymptotic behavior of single point non-vanishing vortex solutions were studied by D. Smets and J. Van Schaftingen (2010).Comment: 32page

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