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prof. dr. Lambert Schomaker

KI2 – 8. Heterogeneous-Information Integration. prof. dr. Lambert Schomaker. Kunstmatige Intelligentie / RuG. Heterogeneous-information integration. aka multi-sensor fusion multi-expert combination multi-agent collaboration

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prof. dr. Lambert Schomaker

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  1. KI2 – 8 Heterogeneous-Information Integration prof. dr. Lambert Schomaker Kunstmatige Intelligentie / RuG

  2. Heterogeneous-information integration • aka • multi-sensor fusion • multi-expert combination • multi-agent collaboration • The improved use of multiple information sources which are of different unit and scale

  3. Heterogeneous-information integration • Examples: • terrorist & weapon classification • friend or foe • forensic evidence collection • finding oil sources • pattern classification by multiple experts • audio-visual speech recognition

  4. … different units … • Celsius • microgram • Volt • Ampere • Lumen • probability • pseudo-probability • integer count

  5. 0.0 A B … different scale … • ratio scale • interval scale • ordinal scale (1st 2nd 3rd 4th 5th 6th … ) • nominal scale • yes/no • green red purple • good bad ugly • true/false A B

  6. Architecture, example Expert 1, NN Expert 2, Rule-based real world Expert 3, Bayesian COMBINE Measurementi DECISION Measurement j agent k agent l agent m

  7. How to combine heterogeneous information? • trained parameter-estimation methods • context-free methods

  8. Trained, parametric combination methods • Use a trainable function approximator: • mean field (linear, weights) • multi-layer perceptron (NN) • polynomial • Bayes! • cumbersome: train individual components, train the combination • if a new module or expert is added, the system must be completely retrained! • independent training sets are needed for the single functions and for the combination function

  9. Context-free combination methods • majority voting • plurality voting • product rule • sum rule • rank combination schemes

  10. Voting • A candidate ci is a person, object or proposal, and C is the set of all possible candidates, and Ce is the set of candidates taking place in a particular election • A voter is a function vj : Ce  R, in words, each candidate partaking in the election obtains a real- valued confidence of vjinci

  11. Election • An election is a tuple (Ce,Ve) where Ce C and Ve V, such that vjVe vj : Ce  R yielding |Ve| orderings of the candidates, in R

  12. Voting system criteria • Condorcet winner: will win from all candidates if elections were held in a pairwise fashion. A Condorcet loser could exist too • Consistency: if ciis a winner for voters Vk and for voters Vm, then ci should also be the winner if the election is based on {Vk Vm}

  13. More voting-system criteria • Monotonicity: if votes become available, this should not affect the existing valuation (humans often react non-monotonously in a sequential voting procedure). Also, voting procedures which eliminate candidates one by one are non monotonous. • Pareto optimality: the voting system choses cx over cy if all voters choose cxover cy

  14. Example: majority vote in unreliable but independent experts

  15. Special case: Borda rank combination • Each of N voters ranks Mcandidates • The assumption is that an optimal ranking exists • Individual voters utilize an unknown evaluation function vj : Ce  R where j=[1,N], e=[1,M] • Evaluations are sorted, such that the ‘best’ evaluation ranks 1, etc. up to M, ‘worst’

  16. Example: Evaluation scores 0-100

  17. Example: Ranks

  18. Example: Ranks

  19. How to combine rankings? • Several models are possible • standard Borda: take the average (best guess) • also: • median rank (disregard outlying ranks) • mode of ranks (plurality of ranks) • min of ranks (optimistic) • max of ranks (pessimistic)

  20. standard Borda: mean rank

  21. modal rank

  22. min rank

  23. min rank How to solve ties?

  24. max rank

  25. How to solve ties in the combined Borda ranking? • Random choice of candidates • If the validity of the voters’ judgment is known: take the rank of the best voter • But: then we digress towards knowledge-based and probabilistic schemes

  26. Example non-stochastic tie solving: Voter C is known to be superior to A, B

  27. How to choose for a combination method? • mean? mode? median? min? max? • Empirical tests are needed, mostly • The type of question to be answered is important • Example: “sportsperson of the year contest”

  28. How to choose for a combination method? • The type of question to be answered is important • Example: “sportsperson of the year contest” • Not the average rank over N sports for M sportspersons • but the minimum rank (best played sport) is indicative

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