Related papers: Deriving And Combining Continuous Possibility Func…
Approaches to decision-making under uncertainty in the belief function framework are reviewed. Most methods are shown to blend criteria for decision under ignorance with the maximum expected utility principle of Bayesian decision theory. A…
Dempster-Shafer Theory (DST) generalizes Bayesian probability theory, offering useful additional information, but suffers from a high computational burden. A lot of work has been done to reduce the complexity of computations used in…
An algorithm is proposed, analyzed, and tested for solving continuous nonlinear-equality-constrained optimization problems where the objective and constraint functions are defined by expectations or averages over large, finite numbers of…
By elaborating on the notion of linear belief functions (Dempster 1990; Liu 1996), we propose an elementary approach to knowledge representation for expert systems using linear belief functions. We show how to use basic matrices to…
The problem of guessing a random string is revisited. A close relation between guessing and compression is first established. Then it is shown that if the sequence of distributions of the information spectrum satisfies the large deviation…
The Hilbert space of probability mass functions (pmf) is introduced in this thesis. A factorization method for multivariate pmfs is proposed by using the tools provided by the Hilbert space of pmfs. The resulting factorization is special…
Standard maximum likelihood estimation cannot be applied to discrete energy-based models in the general case because the computation of exact model probabilities is intractable. Recent research has seen the proposal of several new…
The article presents mathematical generalization of results which originated as solutions of practical problems, in particular, the modeling of transitional processes in electrical circuits and problems of resource allocation. However, the…
In this paper, we propose a general method for testing composite hypotheses. Our idea is to use confidence limits to define stopping and decision rules. The requirements of operating characteristic function can be satisfied by adjusting the…
In this paper, we present two methods to provide explanations for reasoning with belief functions in the valuation-based systems. One approach, inspired by Strat's method, is based on sensitivity analysis, but its computation is simpler…
Many applications require that we learn the parameters of a model from data. EM is a method used to learn the parameters of probabilistic models for which the data for some of the variables in the models is either missing or hidden. There…
A theoretical framework is developed to describe the transformation that distributes probability density functions uniformly over space. In one dimension, the cumulative distribution can be used, but does not generalize to higher…
Maximum composite likelihood estimation is a useful alternative to maximum likelihood estimation when data arise from data generating processes (DGPs) that do not admit tractable joint specification. We demonstrate that generic composite…
Determining the reliability of evidence sources is a crucial topic in Dempster-Shafer theory (DST). Previous approaches have addressed high conflicts between evidence sources using discounting methods, but these methods may not ensure the…
Vibration-based quality monitoring of manufactured components often employs pattern recognition methods. Albeit developing several classification methods, they usually provide high accuracy for specific types of datasets, but not for…
Inspired by empirical work in neuroscience for Bayesian approaches to brain function, we give a unified probabilistic account of various types of symbolic reasoning from data. We characterise them in terms of formal logic using the…
We show a general relation between the spatially disjoint product of probability density functions and the sum of their Fisher information metric tensors. We then utilise this result to give a method for constructing the probability density…
In this paper, we suggest marrying Dempster-Shafer (DS) theory with Knowledge Representation (KR). Born out of this marriage is the definition of "Dempster-Shafer Belief Bases", abstract data types representing uncertain knowledge that use…
Belief function theory provides a flexible way to combine information provided by different sources. This combination is usually followed by a decision making which can be handled by a range of decision rules. Some rules help to choose the…
This work presents a new methodology to obtain probabilistic interval predictions of a dynamical system. The proposed strategy uses stored past system measurements to estimate the future evolution of the system. The method relies on the use…