The principle of maximum entropy (MaxEnt principle) provides a valuable methodology for reasoning with probabilistic conditional knowledge bases realizing an idea of information economy in the sense of adding a minimal amount of assumed information. The conditional structure of such a knowledge base allows for classifying possible worlds regarding their influence on the MaxEnt distribution. In this paper, we present an algorithm that determines these equivalence classes and computes their cardinality by performing satisfiability tests of propositional formulas built upon the premises and conclusions of the conditionals. An example illustrates how the output of our algorithm can be used to simplify calculations when drawing nonmonotonic inferences under maximum entropy. For this, we use a characterization of the MaxEnt distribution in terms of conditional structure that completely abstracts from the propositional logic underlying the conditionals.

A continuous time Bayesian network is a graphical model capable of describing discrete state systems that evolve in continuous time. Unfortunately, the number of parameters required for each node in the graph is exponential in the number of parents of the node, which can be prohibitively large for many real-world systems. To mitigate this problem, we propose a Noisy-OR model for continuous time Bayesian networks, which can reduce the number of required parameters from exponential to linear. We describe the model, as well as the process required to compute the remaining unspecified parameters. Finally, we experimentally validate the correctness of the proposed Noisy-OR formulation.

The majority of Bayesian networks learning and inference algorithms rely on the assumption that all random variables are discrete, which is not necessarily the case in real-world problems. In situations where some variables are continuous, a trade-off between the expressive power of the model and the computational complexity of inference has to be done: on one hand, conditional Gaussian models are computationally efficient but they lack expressive power; on the other hand, mixtures of exponentials (MTE), bases or polynomials are expressive but this comes at the expense of tractability. In this paper, we propose an alternative model that lies in between. It is composed of a "discrete" Bayesian network (BN) combined with a set of monodimensional conditional truncated densities modeling the uncertainty over the continuous random variables given their discrete counterpart resulting from a discretization process. We show that inference computation times in this new model are close to those in discrete BNs. Experiments confirm the tractability of the model and highlight its expressive power by comparing it with MTE.

Testing independencies in Bayesian networks (BNs) is a fundamental task in probabilistic reasoning. In this paper, we propose inaugural-separation (i-separation) as a new method for testing independencies in BNs. We establish the correctness of i-separation. Our method has several theoretical and practical advantages. There are at least five ways in which i-separation is simpler than d-separation, the classical method for testing independencies in BNs, of which the most important is that "blocking" works in an intuitive fashion. In practice, our empirical evaluation shows that i-separation tends to be faster than d-separation in large BNs.

Possibilistic networks are important tools for reasoning under uncertainty. They are compact representations of joint possibility distributions that encode available expert knowledge. The first part of the paper defines the concept of negated possibilistic network which will be used to encode the reverse of a joint possibility distribution. The second part of the paper proposes a propagation algorithm to compute a possibility degree of each event in the negated possibilistic network. Our algorithm is based on the use of a junction tree associated to the initial graphical structure.

Continuous streaming Electrocardiogram (ECG) data inthe Intensive Care Unit (ICU) is highly susceptible tonoise artifacts and signal corruption. Currently, the publicizedalgorithms for QRS detection do not account forunreliable lead information; waveform detection is typicallycontingent upon information from a single lead;and uncertainty metrics are not provided regarding thedetection accuracy. We propose a cross-correlation fusionmethod for multi-component ECG templates usingDempster-Shafer (DS) Theory. Our experiments usingclinical data were compared to benchmark nonsyntacticdetection algorithms where the detection accuracywas comparable at high signal-to-noise ratio (SNR). However, the fusion approach demonstrated asuperior increase in accuracy when the SNR degraded.Addressing these downfalls for the detection of QRScomplexes and other waveforms has potential to improvepatient risk prediction in the ICU.

We propose Simple Propagation (SP) as a new join tree propagation algorithm for exact inference in discrete Bayesian networks. We establish the correctness of SP. The striking feature of SP is that its message construction exploits the factorization of potentials at a sending node, but without the overhead of building and examining graphs as done in Lazy Propagation (LP). Experimental results on numerous benchmark Bayesian networks show that SP is often faster than LP.

A general method of building a predictive model requires least square estimation at first. Then we need work on the residuals, find the confidence interval of parameters and test how well the model fits the data which are based on the normally distributed assumption of the residuals (or noises). But unfortunately the assumption is not guaranteed. Most of the time, you will have a graph of residuals that looks like another distribution rather than the normal. At this moment you could add one more factor term to your model so as to filter out the non-normal distributed noise, and then calculate the LSE again.

We consider a distributed learning setup where a network of agents sequentially access realizations of a set of random variables with unknown distributions. The network objective is to find a parametrized distribution that best describes their joint observations in the sense of the Kullback-Leibler divergence. Apart from recent efforts in the literature, we analyze the case of countably many hypotheses and the case of a continuum of hypotheses. We provide non-asymptotic bounds for the concentration rate of the agents' beliefs around the correct hypothesis in terms of the number of agents, the network parameters, and the learning abilities of the agents. Additionally, we provide a novel motivation for a general set of distributed Non-Bayesian update rules as instances of the distributed stochastic mirror descent algorithm.

This study suggests a new prediction model for chaotic time series inspired by the brain emotional learning of mammals. We describe the structure and function of this model, which is referred to as BELPM (Brain Emotional Learning-Based Prediction Model). Structurally, the model mimics the connection between the regions of the limbic system, and functionally it uses weighted k nearest neighbors to imitate the roles of those regions. The learning algorithm of BELPM is defined using steepest descent (SD) and the least square estimator (LSE). Two benchmark chaotic time series, Lorenz and Henon, have been used to evaluate the performance of BELPM. The obtained results have been compared with those of other prediction methods. The results show that BELPM has the capability to achieve a reasonable accuracy for long-term prediction of chaotic time series, using a limited amount of training data and a reasonably low computational time.