Investment Science Corp.

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Investment Science Corp.
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Symbolic Regression

• Large Scale
• 1M rows x 20 columns
• Single computer
• Less than 50 hours computation time
• Server Farm Scaling
• Assume a 100 server farm
• The Farm can manage 1000 symbolic regressions of
  1M rows x 20 cols
• Elapsed computation time will be 500 hours
• Trading System Deployment
• Training weekly requires one large scale symbolic
  regression
• To deploy, must get approval from trading
  committee
• Blind forward 20 year history requires 1000 large
  scale symbolic regressions

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DeepGreenTM WorkFlow
The CTO provides hands on direction to Tiger
teams developing advanced analytics.
Weekly Securities Buy-Sell Account Traders
Account Traders See only The weekly HTML reports.
Weekly Production Run Green Team
Weekly HTML Reports Account Traders
What-If Blind-Forward Testing Investment Science
Department Green Team
New Algorithm Integration Scoring Investment
Science Department Green Team

• New Algorithm Research Development
• Engineering Department
• Green Team
• Development Teams

Development Teams See only their own projects.
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Weekly Production Run

• Produces Thousands of HTML Pages
• Analyses pages for each of 1,500 stocks
• Performance history for each of top 150 trader
  agents
• Product strategy performance for each of top 35
  product strategies
• Requires Retraining of all 40M Agents
• Currently uses 50 weekend hours for computation
• Deployment of new models requires a server farm
• Data Collection
• Weekly data feed from Valueline
• Weekly data feed from DownloadQuotes.com
• Weekly data feed from First Call
• Weekly data feed from Standard Poors
• Data cleansing is automated but requires some
  human intervention
• Valueline once asked to re-purchase our cleansed
  data (we declined)

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Automating New Product Development

• Marketing Defines New Product Requirements
• Type of risk management required (Structural,
  Statistical)
• Competitive rates of return available in market
• Competitive risk levels available in market
• Engineering Product Mock Ups
• Review top trader performance (each of 40M trader
  agents)
• Review product strategy performance (each of 35
  product strategies)
• Can we fulfill with a mixture of existing product
  strategies traders?
• Product Research (fulfilling the future)
• Review top academic algorithm performance
• Review additional data requirements for market
  penetration
• Can we fulfill with a mixture of new algorithms
  new data?
• Acquire test additional data and new academic
  algorithms

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Symbolic Regression

• Linear Regression
• Gaussian substitution
• Least Squares
• Multivariate polynomial models
• Non-Linear Regression
• Logit regression
• Support Vector Regression
• A growing but very limited set of tools models
• The Growing Need
• Scientific problems are growing in complexity
• All current regression tools are ON2
  computational complexity or greater
• Generalized, scalable, symbolic regression is
  badly needed
• It could change the practice of science

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Large Scale Symbolic Regression

• Why chose evolutionary technology?
• Algorithms are ON1 computational complexity (they
  scale well)
• Just-in-time algorithms
• Algorithms are creative
• Multiple techniques available
• Genetic Programming
• Grammatical Evolution
• Grammatical Swarm Optimization
• Reaching scalability
• Challenge basic assumptions
• Recombine disparate techniques into powerful
  partnerships
• Use statistics
• Use computer science

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Experimental Combinations

• Combined Hybrid combination of particle swarm
  agents and GP
• Combined Hybrid combination of grammar and
  tree-based GP
• Combined Hybrid fitness measure supporting
  symbolic regression and classification long/short
  candiudates
• Combined Hybrid combination of multiple island
  populations and boosting with GP

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Techniques Employed

• Experimental setup with separate training
  testing data sets
• Generate training data with simple complex
  models noise
• High speed compiler generating register speed
  individuals
• Fitness measure rewards accuracy first then tail
  classification
• Standard GP using the abstract grammar
• Abstract grammars implemented as particle swarm
  agents
• Vertical slicing (sort by Y then use every nth
  training example)
• Hill climbing mutation added to crossover
  operator
• Context Aware Crossover added to crossover
  operator
• Standard GP using the MVL grammar
• Island GP using multiple grammars
• Separate island for each boosting run
• Exhaustively search abstract roots in each run
• Standard GP using abstract grammar
• Tournament-of-Champions every five training runs

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Simplified Concept Flow
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Abstract Grammar

• Little Fine-Grain Control log(x3.2392)/sin(x10
  56.341)
• More Fine-Grain Control log(V1C1)/sin(V2C2)
• Abstract Substitution Vi choose from X1 thru
  XN, Ci choose any real number
• Swarm Intelligence Use particle swarm or
  differential evolution for fine-grain control

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Remaining Big Issues

• Time Constraint Abstract grammars produce better
  results when given more time.
• Poor Performance on Multi-model Test Cases GP
  still having problems on more difficult cases.
• Search Coverage GP still prematurely converging
  on local minima.

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Future Research Steps

• Age-Layered Population Structure as an attempt to
  avoid premature convergence?
• A Posteriori Fitness Subsets as a directed search
  for better performance on more difficult
  multi-model test cases?
• Information Theoretic Fitness Measures as a tool
  for improving performance on more difficult
  multi-model test cases?

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Reviewer Questions Part1

• Which market index was used for this market
  neutral study? (and all other questions of this
  nature)
• Is a fixed five-year training window adequate
  for all changing market regimes?
• Are there other advantages of Vertical Slicing
  beyond saving training time?
• Why do you claim classification was good in most
  cases?

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Reviewer Questions Part2

• What is the time scale used - which is better
  one month hold, one quarter hold, etc?
• Is the possibility under consideration that the
  tool could evolve itself or that it could adapt?
  
• What is the motivation for retraining on all
  1250 samples, when only the latest 5 of them are
  new each week, is unclear?
• Does this extended context-aware crossover yield
  a number of evaluations significantly less than
  that of enumerative search by a constructive
  procedure that simply builds successively more
  complex canonical forms?

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Audience QA

• What are the audience questions?

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Investment Science Corp.