?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.title=Approximate+Discrete+Probability+Distribution+Representation+using+a+Multi-ResolutionBinary+Tree&rft.creator=Bellot%2C+Dr+D&rft.creator=Bessiere%2C+Dr+P&rft.subject=Robotics&rft.description=Computing+and+storing+probabilities+is+a+hard+problem+as+soon+as+one+has+to+deal+with+complex+distributions+over+multiples+random+variables.+The+problem+of+efficient+representation+of+probability+distributions+is+central+in+term+of+computational+efficiency+in+the+field+of+probabilistic+reasoning.+The+main+problem+arises+when+dealing+with+joint+probability+distributions+over+a+set+of+random+variables%3A+they+are+always+represented+using+huge+probability+arrays.+In+this+paper%2C+a+new+method+based+on+a+binary-tree+representation%0Ais+introduced+in+order+to+store+efficiently+very+large+joint+distributions.+Our+approach+approximates+any+multidimensional+joint+distributions+using+an+adaptive+discretization+of+the+space.+We+make+the+assumption+that+the+lower+is+the+probability+mass+of+a+particular+region+of+feature+space%2C+the+larger+is+the+discretization+step.+This+assumption+leads+to+a+very+optimized+representation+in+term+of+time+and+memory.+The+other+advantages+of+our+approach+are+the+ability+to+refine+dynamically+the+distribution+every+time+it+is+needed+leading+to+a+more+accurate+representation+of+the+probability%0Adistribution+and+to+an+anytime+representation+of+the+distribution.&rft.date=2003&rft.type=Conference+Paper&rft.type=NonPeerReviewed&rft.format=application%2Fpdf&rft.identifier=http%3A%2F%2Fcogprints.org%2F3752%2F1%2FBellot03.pdf&rft.identifier=++Bellot%2C+Dr+D+and+Bessiere%2C+Dr+P++(2003)+Approximate+Discrete+Probability+Distribution+Representation+using+a+Multi-ResolutionBinary+Tree.++%5BConference+Paper%5D+++++&rft.relation=http%3A%2F%2Fcogprints.org%2F3752%2F