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Computational Complexity in the Social Sciences II

Dive into the spectrum of computational modeling - theory-driven and data-driven approaches in social sciences. Understand neural networks, regressions, and interaction effects in predictive analysis. Learn about artificial neural networks and their applications in forecasting and learning algorithms. Gain insights into the complexities and potential of neural nets in research and data analysis.

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Computational Complexity in the Social Sciences II

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  1. Computational Complexity in the Social Sciences II Will Tracy Rensselaer Polytechnic Institute CSSS 2008

  2. The Spectrum of Computational Modeling Theory Driven Data Driven ?

  3. The Spectrum of Computational Modeling Theory Driven Data Driven ?

  4. The Spectrum of Computational Modeling Theory Driven Data Driven ? 1

  5. The Spectrum of Computational Modeling Theory Driven Data Driven ? 2 1

  6. The Spectrum of Computational Modeling Theory Driven Data Driven ? 2 1 3

  7. Neural Networks Theory Driven Data Driven ? 1 2 3

  8. Before Neural Networks -Regressions • Will person A make a good borrower? Income Debt

  9. Before Neural Networks -Regressions YES Income YES Debt NO Will person A make a good borrower?

  10. Before Neural Networks -Regressions NO Income NO Debt YES Will person A make a good borrower?

  11. Before Neural Networks -Regressions YES Income Maybe? Debt YES • Perhaps some sort of weighting could help? Will person A make a good borrower?

  12. Before Neural Networks -Regressions • Will person A make a good borrower? Income (+) β1 0 ≤ Y ≤ 1 Debt (-) β2 • Using Logit or Probit we can analytically estimate the the coefficients. • (1/(1+e-X) • X =β0 + β1(Income) + β2(debt) • β coefficients have “meaning” • Assuming conditions are met – Good Science?

  13. Regressions and Interaction Effects • Will a fulltime Y1 doctoral student still be in their current grad program 7 years from now? PhD Student MD Student

  14. Regressions and Interaction Effects • Will a fulltime Y1 doctoral student still be in their current grad program 7 years from now? PhD Student YES NO MD Student NO • Well, “MAYBE” might be a better answer, but let’s say “NO” to make ourselves feel good, and make this example work.

  15. Regressions and Interaction Effects • Will a fulltime Y1 doctoral student still be in their current grad program 7 years from now? PhD Student NO NO MD Student YES

  16. Regressions and Interaction Effects • Will a fulltime Y1 doctoral student still be in their current grad program 7 years from now? PhD Student YES YES! MD Student YES

  17. Regressions and Interaction Effects • Will a fulltime Y1 doctoral student still be in their current grad program 7 years from now? PhD Student (?) β1 ? MD Student (?) β2 • Hard to fit a Logit to this (XOR) problem. • This is a silly example of an extreme case, but these types of interaction effects impact lots of things firms would like to predict.

  18. (FF) Artificial Neural Networks • Will a fulltime Y1 doctoral student still be in their current grad program 7 years from now? PhD Student MD Student • Weights • Thresholds • Output = Weight if Input > Threshold.

  19. (FF) Artificial Neural Networks • Will a fulltime Y1 doctoral student still be in their current grad program 7 years from now? w = 1 Threshold = 1 w = 1 PhD Student w = .5 w = 1 w = .5 w = -1.5 MD Student w = 1 w = 1 • If the last node sends “1” answer = “No” • Trainable with learning algorithms

  20. (FF) Artificial Neural Networks 1 w = 1 Threshold = 1 w = 1 PhD Student 1 w = .5 w = 1 1 .5 1 w = .5 w = -1.5 MD Student 0 0 w = 1 w = 1 • If the last node sends “1” answer = “No” • Trainable with learning algorithms Will a fulltime doctoral student still be in their current grad program 7 years from now?

  21. (FF) Artificial Neural Networks w = 1 Threshold = 1 w = 1 PhD Student 0 w = .5 w = 1 w = .5 w = -1.5 MD Student 1 w = 1 w = 1 • If the last node sends “1” answer = “No” • Trainable with learning algorithms Will a fulltime doctoral student still be in their current grad program 7 years from now?

  22. (FF) Artificial Neural Networks 0 w = 1 Threshold = 1 w = 1 PhD Student 0 w = .5 w = 1 1 .5 1 w = .5 w = -1.5 MD Student 1 1 w = 1 w = 1 • If the last node sends “1” answer = “No” • Trainable with learning algorithms Will a fulltime doctoral student still be in their current grad program 7 years from now?

  23. (FF) Artificial Neural Networks w = 1 Threshold = 1 w = 1 PhD Student 1 w = .5 w = 1 w = .5 w = -1.5 MD Student 1 w = 1 w = 1 • If the last node sends “1” answer = “No” • Trainable with learning algorithms Will a fulltime doctoral student still be in their current grad program 7 years from now?

  24. (FF) Artificial Neural Networks 1 w = 1 Threshold = 1 w = 1 PhD Student 1 w = .5 w = 1 .5 0 1 w = .5 w = -1.5 MD Student 1 1 w = 1 w = 1 • If the last node sends “1” answer = “No” • Trainable with learning algorithms Will a fulltime doctoral student still be in their current grad program 7 years from now?

  25. Some Thoughts on Neural Nets • Learning algorithm could be a GA • Each gene in the chromosome is a weight • Mutation draws a new real number from some distrabution • Learning algorithms could also be less stochastic • Incremental Improvements + Multiple Iterations • e.g. backpropagation, or propagation of error • Not as easy are regressions to interpret • Often better than regressions at forecasting

  26. Some Thoughts on Neural Nets • Learning algorithm could be a GA • Each gene in the chromosome is a weight • Mutation draws a new real number from some distrabution • Learning algorithms could also be less stochastic • Incremental Improvements + Multiple Iterations • e.g. backpropagation, or propagation of error • Not as easy are regressions to interpret • Often better than regressions at forecasting

  27. Review: A GA to Fit a FF Neural Net • The genes are weight: • Ex: (1.0, 1.6, 1.6, 1.0, 1.0, -1.5, 1.0, 1.0) • Assign each chromosome a fitness score • How good does it predict on test sample? • Randomly sample + tournament selection • Lower fitness score might be better! • Generate new population (crossover & mutation) • Repeat untill your Neural Net is “well trained.”

  28. Some Thoughts on Neural Nets • Learning algorithm could be a GA • Each gene in the chromosome is a weight • Mutation draws a new real number from some distrabution • Learning algorithms could also be less stochastic • Incremental Improvements + Multiple Iterations • e.g. backpropagation, or propagation of error • Not as easy are regressions to interpret • Often better than regressions at forecasting

  29. Some Thoughts on Neural Nets • Learning algorithm could be a GA • Each gene in the chromosome is a weight • Mutation draws a new real number from some distrabution • Learning algorithms could also be less stochastic • Incremental Improvements + Multiple Iterations • e.g. backpropagation, or propagation of error • Not as easy are regressions to interpret • Often better than regressions at forecasting

  30. Uses in Firm Decision Making • First Commerce Corporation – Junk Mail (Brokaw, 1997) • Time Series Forecasting (Hill, O’Conner & Remus 1996) • I-Banks Currency Crisis Model • Private Investment Helper • http://www.tradingsolutions.com (NNs + GAs) • http://neuralinvesting.com • NN based Investment Funds and News Letters • http://www.calsci.com/Stock.html • www.legendgroup.com

  31. More on Computational Finance • Algorithmic trading accounts for a third of all share trades in America (The Economist, June 2007) • Algo trading accounts for ~ 40 per cent of trades in US markets (FT March 2008) • Increase volatility • Jan. 23 2007 - 600 points roundtrip in 90 minutes. • What if the world changes?

  32. Some Thoughts on Neural Nets • Learning algorithm could be a GA • Each gene in the chromosome is a weight • Mutation draws a new real number from some distrabution • Learning algorithms could also be less stochastic • Incremental Improvements + Multiple Iterations • e.g. backpropagation, or propagation of error • Not as easy are regressions to interpret • Often better than regressions at forecasting

  33. Binding Parameter Space Theory Driven Data Driven ? 2 2 1 3

  34. Consider a Simple ABM of City Traffic • City Layout • Traffic Light Timing • Agent Rules • Start Points, Destinations, and Timing • Road Knowledge / Decision Rules • Driving Rules • Many Uses • Light timing / driving rules / new intersections

  35. The Problem of Pudong • (Largely) planned new section of Shanghai • Before 1990 East of the Huangpu River was mostly farm land • In 1990 the central government declared it an New Open Economic Development Zone. • By 2007 almost 2 million residence (~ 10%)

  36. Roads for Pudong • What type of road grid? • Assume we all agree on the metric • Energy efficiency • Accident minimization • Traffic minimization • Assume 2 Plans – One designed by you! • Assume my ABM says reject your plan.

  37. Is My Model Cooked? • Maybe … • Robustness of Results • Parametric Sensitivity • Natural parameters • Parameterizing mechanisms

  38. Are all Social Science ABMs just BS? • Many say “yes, they are.” • Parameters’ impact on ABM results are a real problem for computational modeling in the social sciences. • Solution: AMBs do not provide answers. ABMs associate answers with regions of the model’s parameter space.

  39. What is an ABM’s parameter space? 1 Probability Agent Moves 0.5 0.5 1 0 Probability Agent Moves Forward

  40. What is an ABM’s parameter space?

  41. What is an ABM’s parameter space? B A

  42. What is an ABM’s parameter space? B A

  43. Problems with this Approach • We’re assuming there exists a distance metric on the parameter space s.t. the probability with which neighboring points yield qualitatively similar emergent phenomena is high. • Also assuming that there are “somewhat well-behaved” boarders separating regions that yield different emergent phenomena • Validity of these assumptions depends on the system being studied.

  44. A Weaker Set of Assumptions ? B A

  45. A Weaker Set of Assumptions ? B A

  46. A Weaker Set of Assumptions ? A

  47. Where we could go wrong. Y Emergent Phenomena B Z Emergent Phenomena A X

  48. New Problem – New Solution • Problem: Most ABMs are too complex for an exhaustive search of their parameter space. • Solution: Apply a stochastic, non-linear, search algorithm to the parameter space. • Only works if the weaker assumptions on the previous slide hold. • Danger: If these assumptions do not hold, this approach might lead us to make false conclusions!

  49. Example: Miller’s ANTs Algorithm • Uses evolutionary computation to “help” bind an area in parameter space (1) - Define the Chromosome (2) - Fitness Function >> “rewards” deviation from desired emergent phenomena. (3) - Run Algorithm (4) - Return to Step 1, restricting the parameter space allowed by the Chromosome

  50. Thoughts on the Frontier Theory Driven Data Driven ? 3 2 1 3

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