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Chapter 11 Analysis and Explanation

Chapter 11 Analysis and Explanation. Chapter 11 Outline. Explain how CI systems do what they do Only a few methodologies are discussed here Sensitivity analysis Relation factors Zurada sensitivity analysis Hinton diagrams Applications of EC to explanation facilities.

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Chapter 11 Analysis and Explanation

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  1. Chapter 11Analysis and Explanation

  2. Chapter 11 Outline • Explain how CI systems do what they do • Only a few methodologies are discussed here • Sensitivity analysis • Relation factors • Zurada sensitivity analysis • Hinton diagrams • Applications of EC to explanation facilities

  3. Sensitivity Analysis • Provides a method for assessing relative importance of CI system inputs • One definition is true positive ratio: TP/(TP+FN) • Another approach is that of relation factors, which depict strengths between individual inputs and individual outputs of a CI system • Still another approach is the Zurada sensitivity analysis, designed originally for neural networks

  4. Relation Factor One Relation factor one: Effect of a given input on a given output when other inputs are held constant (often 0); switch input over dynamic range (0–1 for NN, dynamic range for fuzzy system) With i inputs and o outputs, there are i * o relation factors one Can clamp values to something other than 0, say 0.5 (or the midpoint of the dynamic range, for fuzzy systems).

  5. Relation Factor Two • Measures average effect of given input on given output over a set of patterns • For each pattern, calculate the change in the output when the input is switched over its range while other inputs have value defined by the pattern • Repeat for all patterns • Sum of changes divided by number of patterns gives the factor for a given input-output pair • Again, there are i * o such factors • Can use relation factors to make CI system more intelligent about what input is requested next

  6. Zurada Sensitivity Analysis The sensitivity of a trained output zkj with respect to an input aki is defined as The sensitivity must therefore be determined for each input for each pattern, resulting in a sensitivity matrix.

  7. Zurada Sensitivity Three sensitivity measures are defined over the entire training set: The mean square average sensitivity matrix Savgis defined as: The absolute value average sensitivity matrix Sabsis defined as: The maximum sensitivity matrix Smaxis defined as:

  8. Zurada Sensitivity, Simplified • Calculate mean value for each input parameter • Hold all but 1 input at mean, vary other over dynamic range in steps (10-15 steps), then iterate for each input. • Sensitivity of an input with respect to an output is max – min over this range of inputs: Sji,e • Calculate a sensitivity for each input Si,e in one of three ways.

  9. Zurada Sensitivity, Simplified Now calculate a sensitivity for each input in one of three ways: The mean square average estimated sensitivitySi,eavis defined as: The absolute value average estimated sensitivitySi,eabis defined as: The maximum estimated sensitivity Si,emxis defined as:

  10. Using Zurada Sensitivities • Rank order sensitivities • Delete input with lowest sensitivity and retrain network • If results are good, keep result and try deleting another input • More scientific approach: • Retrain network with a random variable as an additional input • Calculate Zurada sensitivities • Remove any input with sensitivity lower that that of random input • Retrain (without random input) • Same method can be adapted for fuzzy systems

  11. Hinton Diagrams Must exercise care when interpreting weights in a neural network (large weights aren’t always important) Numeric representations of weight matrixes are difficult to interpret Geoffrey Hinton developed a graphical representation technique Size of shape is magnitude of weight Color or shading represents sign In Figure, a 9-4-2 backprop net weight matrix is shown Input to hidden weights on top Hidden to output weights on bottom Bias weights on left A number of variations exist (activation values can be displayed, for example; can be used to prune networks

  12. Hinton diagram for a 9-4-2 feedforward neural network

  13. EC Tools for Explanation Facilities • Explanation facilities make CI systems understandable to users • Explanation facilities should have consistent user interfaces • Functions can include: • Cite reasons for decision • Make system actions clear • Provide examples • Cite logical relationships

  14. Explanation Facility Justification • Main justification often is to provide reasons for system conclusions • Also sometimes justified by need for info on: • System limitations • System knowledge domain(s) • Codebook vectors • Decision hypersurface information • The bottom line is that the user wants to TRUST the system!

  15. Explanation Facility Design and Functions • Design of interface important • Design should be responsive to level of users, especially novices • Trace functions used mainly for debugging • NN explanation facilities can provide user with “codebook vectors” • which are quintessential examples (online or offline) • NN facilites can also provide information on decision hypersurface including distance to it • Fuzzy System facilities can list rules that fired, ranked by contribution

  16. Explanation Facility Shortcomings • Sequence of rule firings not intuitive for many users • Typical backward chaining system doesn’t give information on decision hypersurface • Some explanation facilities require rule firing information • Systems that have parallel aspects, such as evolutionary fuzzy expert systems, present special challenges

  17. Evolutionary Computation Tools • Use trained NN weight matrix to calculate fitness and EA to find input patterns that illustrate: • Codebook vectors • Decision hypersurface • Some kind of rank ordering of EA is often beneficial • Fuzzy systems can also act as fitness functions

  18. Modular Approach to Explanation Facilities • “Look and feel” should be consistent among modules despite using codebook vectors, relation factors, etc. • A (fuzzy) rule-based shell can provide a common interface and consistency

  19. Modular Medical Diagnostic System Could represent three main modules: abdominal disorders, chest pain, and ocular complaints.

  20. Example Neural Network Explanation Facility Uses particle swarm optimization Works on the Iris data set Can be used with any back-propagation neural net weight file obtained using the back-propagation implementation in this book Run it by invoking the program with two run files: nnexp bp.run pso.run

  21. PSO Run File Similar to that for the evolutionary NN application Example: 1 0 1 0 0 = minimize 18 Use evaluation function 18 1 1 0.0 1.0 0.5 1.0 1000 30 0.9 0

  22. BP.RUNExample iris.wts neural network weight file 3number of layers in NN 4number of PE in hidden layer 4 number of network inputs 3number of network outputs 0.9 0.1 0.1what you are looking for examples of 0.011acceptable sum-squared error irisexp.outresults file for output Note: Don’t use 1 and 0 as your targets with a sigmoidal activation function.

  23. Sample Output Format: inp1 inp2 inp3 inp4 targval1 targval2 targval3 error 0.18607 0.37378 0.29725 0.15496 0.90000 0.10000 0.10000 0.010015 To get values near the decision hypersurface for classes 2 and 3, use target values of: 0.1 0.5 0.5

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