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Register a new userInclusion within Continuous Belief Functions
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Added by
Arnaud Martin
Publication date
2015
fields
Informatics Engineering
and research's language is
English
Authors
Dorra Attiaoui
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Defining and modeling the relation of inclusion between continuous belief function may be considered as an important operation in order to study their behaviors. Within this paper we will propose and present two forms of inclusion: The strict and the partial one. In order to develop this relation, we will study the case of consonant belief function. To do so, we will simulate normal distributions allowing us to model and analyze these relations. Based on that, we will determine the parameters influencing and characterizing the two forms of inclusion.
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The theory of belief functions manages uncertainty and also proposes a set of combination rules to aggregate opinions of several sources. Some combination rules mix evidential information where sources are independent; other rules are suited to combine evidential information held by dependent sources. In this paper we have two main contributions: First we suggest a method to quantify sources degree of independence that may guide the choice of the more appropriate set of combination rules. Second, we propose a new combination rule that takes consideration of sources degree of independence. The proposed method is illustrated on generated mass functions.
The aim of this paper is to show the interest in fitting features with an $alpha$-stable distribution to classify imperfect data. The supervised pattern recognition is thus based on the theory of continuous belief functions, which is a way to consider imprecision and uncertainty of data. The distributions of features are supposed to be unimodal and estimated by a single Gaussian and $alpha$-stable model. Experimental results are first obtained from synthetic data by combining two features of one dimension and by considering a vector of two features. Mass functions are calculated from plausibility functions by using the generalized Bayes theorem. The same study is applied to the automatic classification of three types of sea floor (rock, silt and sand) with features acquired by a mono-beam echo-sounder. We evaluate the quality of the $alpha$-stable model and the Gaussian model by analyzing qualitative results, using a Kolmogorov-Smirnov test (K-S test), and quantitative results with classification rates. The performances of the belief classifier are compared with a Bayesian approach.
The standard problem setting in Dec-POMDPs is self-play, where the goal is to find a set of policies that play optimally together. Policies learned through self-play may adopt arbitrary conventions and implicitly rely on multi-step reasoning based on fragile assumptions about other agents actions and thus fail when paired with humans or independently trained agents at test time. To address this, we present off-belief learning (OBL). At each timestep OBL agents follow a policy $pi_1$ that is optimized assuming past actions were taken by a given, fixed policy ($pi_0$), but assuming that future actions will be taken by $pi_1$. When $pi_0$ is uniform random, OBL converges to an optimal policy that does not rely on inferences based on other agents behavior (an optimal grounded policy). OBL can be iterated in a hierarchy, where the optimal policy from one level becomes the input to the next, thereby introducing multi-level cognitive reasoning in a controlled manner. Unlike existing approaches, which may converge to any equilibrium policy, OBL converges to a unique policy, making it suitable for zero-shot coordination (ZSC). OBL can be scaled to high-dimensional settings with a fictitious transition mechanism and shows strong performance in both a toy-setting and the benchmark human-AI & ZSC problem Hanabi.
In this work, we introduce a new approach for the efficient solution of autonomous decision and planning problems, with a special focus on decision making under uncertainty and belief space planning (BSP) in high-dimensional state spaces. Usually, to solve the decision problem, we identify the optimal action, according to some objective function. We claim that we can sometimes generate and solve an analogous yet simplified decision problem, which can be solved more efficiently; a wise simplification method can lead to the same action selection, or one for which the maximal loss can be guaranteed. Furthermore, such simplification is separated from the state inference, and does not compromise its accuracy, as the selected action would finally be applied on the original state. First, we present the concept for general decision problems, and provide a theoretical framework for a coherent formulation of the approach. We then practically apply these ideas to BSP problems, which can be simplified by considering a sparse approximation of the initial (Gaussian) belief. The scalable belief sparsification algorithm we provide is able to yield solutions which are guaranteed to be consistent with the original problem. We demonstrate the benefits of the approach in the solution of a highly realistic active-SLAM problem, and manage to significantly reduce computation time, with practically no loss in the quality of solution. This work is conceptual and fundamental, and holds numerous possible extensions.
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