Using data sets to simulate evolution within complex environments Bruce Edmonds Centre for Policy Modelling Manchester Metropolitan University

Main Issue Does the complexity of the environment significantly affect evolutionary processes? Where “complexity” means that there are exploitable patterns in the environment but these are difficult to discover Adding randomness to an environment and/or fitness is not satisfactory NK model of fitness adjusts the difficulty of a fitness space (second order uniformity) Using data sets to simulate evolution, Bruce Edmonds, Complexity of Evolutionary Processes, Manchester, June 13 th 2011, slide 2

Idea of Talk Evolutionary data-mining is where ideas from biological evolution are applied to data-mining – finding patterns in data Data sets exist for the purpose of testing different ML algorithms that have patterns in them, albeit difficult to discover Reversing this... I am suggesting the use of complex data sets as a test bed to investigate how the complexity of the environment might affect evolution Using data sets to simulate evolution, Bruce Edmonds, Complexity of Evolutionary Processes, Manchester, June 13 th 2011, slide 3

The Data Set Environment Find a rich data set (preferably one derived from a naturally complex system) with many independent variables The gene of an individual is an arbitrary arithmetic expression stored as a tree (or similar technique) Resource in the model is modelled by distributing to individuals predicting the outcome variable of local data better than its competitors The gene are mutated and crossed as the simulation progresses Individuals are selected for/against depending on their total success in predicting Using data sets to simulate evolution, Bruce Edmonds, Complexity of Evolutionary Processes, Manchester, June 13 th 2011, slide 4

Cleveland Heart Disease Data 281 Data Points 13 Diagnostic variables: age, sex, cp (chest pain), trestbps (resting blood pressure), chol (cholesteral), fbs (fasting blood sugar), restecg (resting ecg type), thalach (max heart rate), exang (exercise induced angina), oldpeak (ST depression induced by exercise), slope (slope of exercise), ca (num blood vessels), thal Predicts severity of Heart Attack (0-4) Using data sets to simulate evolution, Bruce Edmonds, Complexity of Evolutionary Processes, Manchester, June 13 th 2011, slide 5

The Evolutionary Model I Using data sets to simulate evolution, Bruce Edmonds, Complexity of Evolutionary Processes, Manchester, June 13 th 2011, slide 6 Data Space Individuals each with genes composed of an arithmetic expression to predict HD based on the other 13 variables For each data point (or a random subset of them) evaluate (a random selection of) near individuals to determine the share of fitness each receive (depending on predictive success) Sum of fitness determines which breed and die

The Evolutionary Model II Using data sets to simulate evolution, Bruce Edmonds, Complexity of Evolutionary Processes, Manchester, June 13 th 2011, slide 7 Data Space N times: 1.probabilistically select a winner on fitness 2.probabilistically select a loser on lack of fitness 3.kill loser Either 4.propagate winner locally with possible mutation 5.mate with another local based on fitness 8.1

Start of Simulation (HD Data) Using data sets to simulate evolution, Bruce Edmonds, Complexity of Evolutionary Processes, Manchester, June 13 th 2011, slide 8 Individuals each with gene which is an arithmetic expression, e.g.: Data points from set distributed over space dependent on 2 variables chol (x) & thalach (y)

After 25 ticks (HD Data) Using data sets to simulate evolution, Bruce Edmonds, Complexity of Evolutionary Processes, Manchester, June 13 th 2011, slide 9

After 50 ticks (HD Data) Using data sets to simulate evolution, Bruce Edmonds, Complexity of Evolutionary Processes, Manchester, June 13 th 2011, slide 10

After 75 ticks (HD Data) Using data sets to simulate evolution, Bruce Edmonds, Complexity of Evolutionary Processes, Manchester, June 13 th 2011, slide 11

After 300 then 100 w/o Variation Using data sets to simulate evolution, Bruce Edmonds, Complexity of Evolutionary Processes, Manchester, June 13 th 2011, slide 12 ca 1 sex slope restecg+fbs+1fbs/oldpeak

Illustrative Results Heart Disease Data Set 20 runs with each setting 1000 individuals, 1000 iterations Locality parameter 0.1 (radius) Comparison of Original vs Ersatz Data Sets Fixed normal noise (0, 0.1) added to both data sets Using data sets to simulate evolution, Bruce Edmonds, Complexity of Evolutionary Processes, Manchester, June 13 th 2011, slide 13

Ersatz Data Set Comparison Data Set For each variable separately: approximate a normal distribution of its values Then reconstruct a data set using this distribution for each value independently Results in a Data Set with similar shape and randomness But without the predictive variable being linked in to the explanatory variables Using data sets to simulate evolution, Bruce Edmonds, Complexity of Evolutionary Processes, Manchester, June 13 th 2011, slide 14

Fitness (HD Data) Using data sets to simulate evolution, Bruce Edmonds, Complexity of Evolutionary Processes, Manchester, June 13 th 2011, slide 15

Spread (HD Data) Using data sets to simulate evolution, Bruce Edmonds, Complexity of Evolutionary Processes, Manchester, June 13 th 2011, slide 16

Gene Complexity/Depth (HD Data) Using data sets to simulate evolution, Bruce Edmonds, Complexity of Evolutionary Processes, Manchester, June 13 th 2011, slide 17

All Runs’ Complexity Using data sets to simulate evolution, Bruce Edmonds, Complexity of Evolutionary Processes, Manchester, June 13 th 2011, slide 18 Original Ersatz

Fitness (White Wine Data) Using data sets to simulate evolution, Bruce Edmonds, Complexity of Evolutionary Processes, Manchester, June 13 th 2011, slide 19

Depth (White Wine Data) Using data sets to simulate evolution, Bruce Edmonds, Complexity of Evolutionary Processes, Manchester, June 13 th 2011, slide 20

Depth (White Wine Data) Using data sets to simulate evolution, Bruce Edmonds, Complexity of Evolutionary Processes, Manchester, June 13 th 2011, slide 21 Original Original with 0.1 noise

Depth – locality 0.1 (HD Data) Using data sets to simulate evolution, Bruce Edmonds, Complexity of Evolutionary Processes, Manchester, June 13 th 2011, slide 22

Depth – locality 0.2 (HD Data) Using data sets to simulate evolution, Bruce Edmonds, Complexity of Evolutionary Processes, Manchester, June 13 th 2011, slide 23

Depth – locality 0.4 (HD Data) Using data sets to simulate evolution, Bruce Edmonds, Complexity of Evolutionary Processes, Manchester, June 13 th 2011, slide 24

Concluding Questions When mighty the complexity of the environment effect evolutionary processes? How might the complexity of the environment effect evolutionary processes? Will models with a simple environment tell us about evolution in the wild? –When and about what aspects will models with simple environments be sufficient? –In what ways might evolution differ when in complex environments? What kind of complexity might we need? How might one measure this complexity in the wild (if this is even possible)? Using data sets to simulate evolution, Bruce Edmonds, Complexity of Evolutionary Processes, Manchester, June 13 th 2011, slide 25

The End Bruce Edmonds Centre for Policy Modelling

White Wine Quality Data 4898 Data Points 11 Diagnostic variables: fixed acidity, volatile acidity, citric acid, residual sugar, chlorides, free sulfur dioxide, total sulfur dioxide, density, pH, sulphates, alcohol Predicts judged quality of wine (0-10) Using data sets to simulate evolution, Bruce Edmonds, Complexity of Evolutionary Processes, Manchester, June 13 th 2011, slide 27