1. Artificial Intelligence as a Technology of Approximation Derek Partridge, University of Exeter, UK d.partridge@exeter.ac.uk

2. Maybe Most likely Seems to be the case Unlikely to be true Possibly not Yes No Certainly Certainly not Key Idea: if we can systematically compute all reasonable answers, then the distribution of this set of answers is the trust in the answer + 0.7 + 0.4 + 0.3 +0.9

3. Systematic (from 2.) recomputation (from 1.)

4. A classifier system: input a feature vector & it outputs a class 1. If specification of how the target classes are computed from the feature vector, then program it 2. But if all we have is samples of data (observed or desired) Patient 1 Symptoms/Features Disease X Patient 2 Symptoms/Features Not Disease X Etc. Train classifier system (i.e. optimize model parameters) using a sample set.

5. k=7 get 6 red, 1 green therefore unknown is red k=30 get 12 red, 18 green Therefore unknown is green k is one parameter of knn model, maybe distance, , should be another? 2 classes: red or green

6. The data (defining the problem) D The classifier model to be used, M with params  (e.g. K nearest neighbours with  =(k,  ) ) The input pattern/vector x The output class y Use training data to find optimal values for 

7. T.C.Bailey, R.M. Everson, W.J.Krzanowski, A. Hernandez, J. Fieldsend and V. Schetinin using MCMC methods we can draw samplesfrom use Bayes

8. 6 accepted states omitted chain converged to stationary distribution S1 k1,  1 S2 k2,  2 S3 k3,  3 S4 k4,  4 S5 k5,  5 S6 k6,  6 S13 k13,  13 Markov Chain & Metropolis- Hastings Alg. & Green’s Reversible Jump  (6)  (13) 1.At any state Si, generate new proposed state, Sj 2.Probabilistically accept or reject Sj as new state 3.Go to step 1 00.51.0 10000 Count of Probability p

9. 1,000s of recomputations using parameter values generated by the Markov chain `trust’ in the answer delivered

10. (7 output classes, 1-7 top to bottom) Maybe Class 1 or Class 3 Most probably Class 3

11. To compare our system with previously published examples we must transform our sets of histograms into a discrete classification choice If most probable classifications are the same on 95% or greater of alternative computations then that classification is selected as SURE else majority classification is selected as UNSURE

12. Bayesian system test results UCI data set Number of classes Training set size Test set size Correct (%) A SURE(%) Correct B UNSURE (%) C SURE(%) but Incorrect D Wisconsin245522899.188.611.40.0 Ionosphere220015194.058.941.10.0 Votes23914495.581.815.92.3 Sonar21387088.620.080.00.0 Vehicle456428267.747.542.69.9 Image7210210014.30.0100.00.0 Wisconsin245522899.188.611.40.0 2.3 9.9 100

13. estimates of the 2 target classes for 1 input vector: 88.6% SURE correct & 11.4% UNSURE vs 98.3% correct probability

14. it does seem to be possible to extract trustworthiness of a result from a systematic distribution of recomputations it does seem useful to so localize decision uncertainty never eliminate uncertainty and extra problems when a trusted result is incorrect, i.e. trust is misplaced

15. Intelligent decisions are (by definition?) not always correct