Foundations

Epp, Susanna S.; Riley, David; Dalal, Mukesh

doi:10.1201/9781439832905.ch1

Cited by 20 publications

(30 citation statements)

References 0 publications

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“…Indeed, the inference matrix is more akin to a (probabilistic) correlation matrix. The relations represented by (9) can be shown to be reflexive, symmetric and transitive [9], albeit with inverse probabilities rather than 1 in the non-diagonal elements. The inference matrices can also be augmented with the priors, represented as flows from a fictitious "external" domain, to give the augmented inference matrices:…”

Section: -2mentioning

confidence: 99%

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Bayesian cyclic networks, mutual information and reduced-order Bayesian inference

Niven¹,

Noack

Cattafesta³

et al. 2016

AIP Conference Proceedings

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Abstract. We examine Bayesian cyclic networks, here defined as complete directed graphs in which the nodes, representing the domains of discrete or continuous variables, are connected by directed edges representing conditional probabilities between all pairs of variables. The prior probabilities associated with each domain are also included as probabilistic edges into each domain. Such networks provide a graphical representation of the inferential connections between variables, and substantially extend the standard definition of "Bayesian networks", usually defined as one-directional (acyclic) directed graphs. In a binary system, the proposed representation provides a graphical expression of Bayes' theorem. In higher-dimensional systems, further probabilistic relations can be recovered from the network cyclic properties and the joint probability of all variables. In particular, adopting a Markovian assumption leads to the theorem that the mutual information between any pair of variables on the network must be equivalent. Analysis of a hybrid Bayesian cyclic network of two continuous and two discrete variables -of the form of a commutative diagram -provides a framework for more computationally efficient reduced-order Bayesian inference, involving initial simplification by an order reduction process.

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Section: -2mentioning

confidence: 99%

“…Relations (27) are again reflexive, symmetric and transitive [9], but again with inverse non-diagonal elements.…”

Section: Ternary Cyclesmentioning

confidence: 99%

Bayesian cyclic networks, mutual information and reduced-order Bayesian inference

Niven¹,

Noack

Cattafesta³

et al. 2016

AIP Conference Proceedings

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show abstract

“…The information given for target nodes may include GPS position. Thus specific distances can be calculated based on the entrance point of the robot; and since the end of the overall path plan often includes returning to the entrance, this often becomes a typical Traveling Salesman Problem (TSP) [11]. By solving the TSP for the given set, a solution will exist that is minimal in distance (and likely to be traversable by the robot).…”

Section: A Classical Approach -Explicit Methodsmentioning

confidence: 99%

O3: An optimal and opportunistic path planner (with obstacle avoidance) using voronoi polygons

Coleman

Wunderlich

2008

2008 10th IEEE International Workshop on Advanced Motion Control

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Abstract-Traditional mobile robot research focuses on a robot navigating its environment to reach a single goal while avoiding obstacles. This paper proposes a new method called O 3 to solve the challenges presented at the Intelligent Ground Vehicle Competition (IGVC) where a navigation course includes multiple goals to be found in an optimal order. The O 3 technique includes improvements on traditional path planning and obstacle avoidance techniques while providing an explicit ability to change course as obstacles are discovered. This method uses modern trajectories such as minimum-weighted Hamiltonian circuits, A* algorithm for obstacle avoidance, and local points of opportunity to update the globally optimal path using Voronoi polygons. Environmental mapping is also used to speed up the search algorithms in static environments. Overall, the O 3 technique exploits local points of opportunity while avoiding obstacles and ultimately finding a globally optimal path through an unknown environment.This methodology will be implemented on an autonomous web-based tour guide robot to serve the Internet community reviewing Elizabethtown College. This methodology can be extended to other research areas where multiple locations need to be traversed independent of their order such as city map, trip planners, and distribution networks (power, internet, etc) due to its balance between weighted graphs and obstacle avoidance (objects, traffic, construction, etc).

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“…Next, the metric has (n-k+1) 2 operations, shown in section IV.A. Hence, by the theorem on Polynomial orders [10] this leads to a complexity of O((…”

Section: B Full Searchmentioning

confidence: 99%