Belief Functions Based on Probabilistic Multivalued Random Variables
نویسندگان
چکیده
In this paper, we would like to give Dempster and Shafer's belief function theory an interpretation based on probabilistic multivalued random vari-ables(PMRV). While a random variable is a function from the sample space to the target space, a PMRV maps each point in the sample space to a probability distribution on the target one. By such interpretation , the belief and plausibility measures are respectively the lower and upper estimations of the probability on the sample space. Dempster's combination rule is also considered under the interpretation. It is then shown that normalization is not necessary at all, because connicts will not arise under the independence assumption.
منابع مشابه
Support vector regression with random output variable and probabilistic constraints
Support Vector Regression (SVR) solves regression problems based on the concept of Support Vector Machine (SVM). In this paper, a new model of SVR with probabilistic constraints is proposed that any of output data and bias are considered the random variables with uniform probability functions. Using the new proposed method, the optimal hyperplane regression can be obtained by solving a quadrati...
متن کاملMulti-robot Markov Random Fields (Short Paper)
We propose Markov random fields (MRFs) as a probabilistic mathematical model for unifying approaches to multi-robot coordination or, more specifically, distributed action selection. The MRF model is well-suited to domains in which the joint probability over latent (action) and observed (perceived) variables can be factored into pairwise interactions between these variables. Specifically, these ...
متن کاملBelief function and multivalued mapping robustness in statistical estimation
We consider the case in which the available knowledge does not allow to specify a precise probabilistic model for the prior and/or likelihood in statistical estimation. We assume that this imprecision can be represented by belief functions models. Thus, we exploit the mathematical structure of belief functions and their equivalent representation in terms of closed convex sets of probabilities t...
متن کاملLearning Multivalued Multithreshold Functions
This paper concerns multivalued multithreshold functions, {0, 1, . . . , k}-valued functions on Rn that may be considered as generalizations of (linear) threshold functions, or as discretized versions of artificial neurons. Such functions have arisen in the context of multiple-valued logic and artificial neural networks. For any fixed k, we present two procedures which, given a set of points la...
متن کاملDirected graphical models
for some functions f and g. Probabilistic graphical models are a way of representing conditional independence assumptions using graphs. Nodes represent random variables and lack of edges represent conditional independence assumptions, in a way which we will define below. There are many kinds of graphical model, but the two most popular are Bayesian (belief) networks1, which are based on directe...
متن کامل