Reflections of a Keen Modeler

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    Reflections of a Keen Modeler - Presentation Transcript

    1. Some Reflections of a Keen Modeler David E. Goldberg Illinois Genetic Algorithms Laboratory University of Illinois at Urbana-Champaign Urbana, Illinois 61801 [email_address]
    2. A Life in Models
      • What should I talk about?
      • Started engineering college in 1971.
      • Calculus was cool, and differential equations were amazing
      • Really dug making models with computers.
      • Bumped into fluid mechanics my junior year at Michigan.
      • Didn’t understand impact of that collision then.
      • Started to understand it when I bumped into GAs in 1980.
      • Bumped into more models as chief scientist of web startup.
      • Reflections on life in models.
    3. Roadmap
      • What’s a model?
      • An economic model of models.
      • Models in GAs.
      • From GAs to PMBGAs/EDAs.
      • Models in PMBGA/EDAs.
      • Models in the education of the creative genetic algorithmist.
    4. What is a Model?
      • A model is a system that represents one or more facets of some other system.
      • Typical model  facet combinations:
        • Drawing or solid model  geometry.
        • Prototype  geometry & operation.
        • Graph  variation of variable with independent variable (time, space, etc.).
        • Equilibrium equation  select state variables at steady state.
        • Dynamic equation  variation of select state variables with time.
        • Simulation  similar to equations, but uses an intermediate artifact to calculate..
    5. Words and Models
      • Foregoing examples typical engineering models.
      • Language is also used in modeling.
      • Many first models are verbal.
      • Types of verbal models:
        • Single word or noun phrase.
        • Description of an object/process.
        • Feature list.
        • Dimension list.
        • Set of engineering specifications.
    6. An Economy of Models
      • Have many models with different precision-accuracy and different costs.
      • Can we evaluate model usage rationally?
      • Consider economics of intellection and spectrum of models.
    7. Fundamental Modeling Tradeoff
      • Error versus cost of modeling
      ε , Error C, Cost of Modeling Engineer/Inventor Scientist/Mathematician
    8. Marginal Analysis
      • Optimal thinking, when marginal cost of a thought equals marginal benefit to design.
      •  C =  B
      • If cost higher than advance in design, thinking is uneconomic.
      • Science: model is the end.
      • Engineering; model is instrumental.
      • Match model complexity to ends required.
    9. A Spectrum of Models The Modeling Spectrum Low Cost/ High Error High Cost/ Low Error Unarticulated Wisdom Articulated Qualitative Model Dimensional Models Facetwise Models Equations of Motion
    10. Disciplines: Mature & Immature
      • Mature disciplines are mature partially because they have developed sense of models.
      • GAs circa 1980: Immature discipline.
      • Few models available.
      • Hodgepodge of religious beliefs (xover v. mutation, etc.).
      • Some qualitative notions of what is important.
    11. What Are Models Good For?
      • Many uses for models:
        • Description: describe the ways things are (were).
        • Prediction: describe the ways things will be.
        • Prescription: describe the way things should be.
      • Key variables: time and change.
      • Usually assumes have extant object to model.
      • Oftentimes assumes extant models.
    12. Crossing Qual-Quant Divide
      • Needed quantitative understanding of qualitative theories/experience.
      • How do you cross the qual-quant divide?
      • Do not expect full equations of motion to provide answers.
    13. Models in GAs
      • Our interest is in models that are
        • Principled
        • Quantitative
        • Not equations of motion
      • Call them little models , where “little” is a term of approbation.
      • Little models simplified, not universal.
      • Where do little models come from?
    14. Sources of Little Models
      • Dimensional analysis (more in moment)
      • Construction of model for single facet.
      • Reduction of equation of motion for one or small number of facets.
      • Incorporation of qualitative reasoning.
      • Extremum principle.
      • Data usage (data-influenced), but empirical fit alone not enough.
    15. Aside on Dimensional Analysis
      • Common in physics and engineering, but not CS.
      • Buckingham PI theorem: n dimensional parameters, m dimensions  n – m independent dimensionless parameters.
      • [ V ] = L/T, [ D ] = L, [ ν ] = L 2 /T n = 3, m = 2, n – m = 1 R = VD / ν , the Reynolds number
      • One difference: many CS parameters are pure numbers. Must derive time, spatial, or other scale, then renormalize.
      • Can play the same game for GAs, AI, & AL.
    16. A LM of Selection Alone
      • Choose truncation selection because it is easy to analyze.
      • Truncation selection: make s copies each of top 1/ s th of the population.
      • Want to know time for good individual to “takeover” population: takeover time.
    17. Takeover Time Under Truncation
      • Let P be proportion of best individuals.
      • How many more next generation? s
      • P ( t +1) = s P ( t ) until P ( t )=1.
      • P ( t ) = s t P (0).
      • Solve for takeover time t *: time to go from one good guy to all or all but one good guys.
      • t* = ln n/ ln s
    18. So What?
      • Who cares about selection alone?
      • I want to analyze a “real GA.”
      • How can selection only analysis help me?
      • Answer: Imagine another characteristic time, the innovation time.
    19. A LM of Innovation Time
      • Assume using crossover-based innovation with probability p c .
      • Assume that crossover event gives improvement with probability p i in population of size n.
      • Can calculate the expected time of arrival of next improvement.
    20. The Innovation Time, t i
      • Define innovation time as the expected time to create an individual better than one so far.
      • t i = ( p c p i n ) -1
      • Model is facetwise, probabilistic & incomplete ( p i unknown).
      • p i estimated in Goldberg, Deb, & Thierens (1993) and Thierens & Goldberg (1993).
    21. The Race: Integrating 2 Models
      • Have two facetwise models, but want integrated understanding.
      • Putting models in t terms gives us an idea.
      • Consider relative magnitudes of the two times: a dimensional argument.
      • Consider which is favorable to innovation: a qualitative argument.
    22. Schematic of the Race
    23. Dimensional & Qualitative Argument
      • This argument results in an integrated little model.
      • Define innovation number G = t* / t i
      • G = p c p i n ln n/ ln s.
      • Want takeover time greater than innovation time or G > 1.
      • Quantity like Reynolds number in fluids.
    24. A Simple Control Map
      • Draw success region in GA parameter space.
      • Control map.
      • p c > c ( m, n ) ln s.
      • For p c versus ln s a straight line .
    25. 1993 Empirical Result
      • Easy problems are no problem.
      • GA has a large “sweet spot”.
      • A monkey can set cross probability & selection pressure
      [Goldberg, Deb, & Theirens, 1993]
    26. Lessons of LMing
      • Facetwise approach is fast.
      • Requires some skill in identifying correct facets and in integrating them.
      • Payoff in understanding is out of proportion to complexity of the effort.
      • Do not waste time on needless parametric study.
      • Verify expected behavior and move on.
      • Facetwise understanding improves pedagogy and ability to explain things simply.
    27. Models in PMBGA/EDAs
      • Baluja & others recognized key thing that Holland had identified earlier.
      • Population + genetic operators  Probability distribution over possible structures.
      • Early PMBGA/EDAs used fixed models.
      • Later ones built models.
      • What is going on?
    28. Primary Effect: Good Solutions Current population Selection New population Bayesian network
    29. Secondary: Structural Knowledge
      • Mental models give us flexibility to think about world without paying big price.
      • Built models can be used to speed up evolution of good structures:
        • Parallelism
        • Time continuation
        • Hybridization
        • Evaluation relaxation
      • Usually think of them independently.
    30. Supermultiplicative Speedup
      • Speed-Up: Ratio of # function evaluations without efficiency enhancement to that with it.
      • Only 1-15% individuals need evaluation
      • Speed-Up: 30–53
      • Have decision tree & ECGA versions.
      Fitness modeling in BOA
    31. Use of Structural/Fitness Surrogates
      • Parallelism: decomposition of problem for efficient parallelism.
      • Time continuation: understanding of problem sequencing and parameterization.
      • Hybridization: What neighborhood operators appropriate when & information for optimal division of labor.
      • Estimation of algorithm parameters.
    32. Important Frontier PMBGA/EDAs
      • Extending the notion of model building.
      • Pervade every aspect of algorithm coordination.
      • Already movement in that direction.
      • More still needs to be done.
    33. Education of Creative GAmist
      • Early 60s-80s pioneering years.
      • Years where categories genetic algorithms and evolutionary computation were created.
      • How do we rekindle that creativity moving forward?
      • How do we educate creative genetic algorithmists of the future?
      • Crossed qual-quant divide.
      • Need to go back to qual.
    34. Key Distinction
      • Modeling of imagined or desired objects versus extant objects.
      • What can we draw on?
        • Existing objects that fail in some regard.
        • Similar or related objects.
        • Analogically related objects.
        • Creatively concocted objects.
      • Takes us back to the tabula rasa problem.
      • How do we even discuss that which does not exist?
    35. Tabula Rasa: Curse & Blessing of Category Creator
      • How do we design when we don’t know how to talk about what we are designing?
      • Let’s start at the human beginnings of conceptual clarity.
      • Let’s start at the beginning of formal philosophy.
      • Let’s start with two key techniques from Athens.
    36. What Examples of New Thought?
      • Clearest examples are from philosophy.
      • Presocratic  Socrates  Plato  Aristotle.
      • Mechanisms of the new thought:
        • Socratic dialectic
        • Aristotelian data mining
    37. Socrates and Dialectic
      • Socrates was a pain in the neck.
      • Walked around Athens asking everyone impossible questions.
      • Then proved their answers were wrong, but rarely gave an answer himself.
      • Nonetheless, Socrates’s method was useful.
      • Conversation trying to probe what things really are (or might be).
      • Questions were the rights ones. Whitehead’s famous remark.
      Socrates (470-399 BCE)
    38. The Probing of Dialectic
      • Questions directed at the essence of things.
      • What is the meaning of a common phrase? “What is virtue?”
      • Answers often betray our lack of knowledge and understanding.
      • Examine answers critically, often with more questions.
      • Ask penetrating questions about the answers.
    39. What’s This Got to Do with GAs?
      • Questions & conversation is at roots of new inventions.
      • Research on tech visionaries shows that problem finding is the main activity of successful TVs
      • Spark of insight may come as flash, but dialectic necessary in new product creation.
      • Three roles of questions:
        • Probe field needs.
        • Probe biases or politics of the field..
        • Probe developmental hurdles.
    40. Tactics of Dialectic
      • Critical:
        • Equivocation: use of term in different senses.
        • Question begging: assuming the conclusion.
        • Infinite regress: infinite sequence implying incoherence.
        • Loss of contrast & emptiness: distinction with little or no difference.
      • Creative:
        • Definition: Seek essential distinctions.
        • Analogies: Certain dialectical similarities.
        • Thought experiments: Hypothetical w/ true premises that does not follow.
      http://www.amazon.com/Practice-Philosophy-Handbook-Beginners-3rd/dp/0132308487
    41. Aristotelian Data Mining
      • Called The Philosopher by some.
      • Amazing range and scope of work.
      • Created many of basic categories of college curriculum.
      • Founded a school the Lyceum.
      • We have 1/3 his output (2000 pages in 30 books).
      • Categories and Metaphysics.
      • Method very modern:
        • Empirical search for data.
        • Considered attributes, which he named.
        • Classified data according to his attributes.
      Aristotle (384-322 BCE)
    42. Analysis is More than Pretty Math
      • Sons & daughters of Newton spoiled by equations of motion.
      • Put too much faith in sets of equations.
      • Complexity demands heavy lifting of the facets for understanding.
      • Range of modeling skills, particularly qualitative reasoning.
      • Necessary for creative activity that is genetic and evolutionary computation.
    43. Summary
      • Models generally:
        • Economy of models.
        • Modeling spectrum.
      • Models in GAs w/ emphasis on little models.
      • Models in PMBGA/EDAs.
      • Models in education of the creative genetic algorithmist.
    44. Conclusions
      • Modeling is central to our business.
      • But simple view of modeling limits progress.
      • Need sophisticated, flexible approach to advance state of the art most quickly.
      • Still many opportunities for model advance in PMBGA/EDAs.
      • Mastery of the spectrum of models from qual to quant, from little to equations of motion holds hope for continued vibrancy and creativity of the field.
    45. More Information
      • DoI, the book
      • TEE, the book. http://eu.wiley.com/WileyCDA/WileyTitle/productCd-0470007230.html
      • TEE, the blog. www.entrepreneurialengineer.blogspot.com
      • TEE, the course. http://online.engr.uiuc.edu/webcourses/ge498tee/index.html
      • MTV, the course. http://online.engr.uiuc.edu/webcourses/ge498tv/index.html
      • GAs, the course http://online.engr.uiuc.edu/webcourses/ge531/index.html
      • 2007 Workshop on Philosophy & Engineering (WPE) http://www- illigal.ge.uiuc.edu/wpe
      • Illinois Genetic Algorithms Lab http://www-illigal.ge.uiuc.edu/

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