Principle Components & Neural Networks. How I finished second in Mapping Dark Matter Challenge Sergey Yurgenson , Harvard University Pasadena, 2011. T o measure the ellipticity of 60,000 simulated galaxies. Scientific view. Kitching , 2011. Data mining view. Training set
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How I finished second inMapping Dark Matter Challenge
Sergey Yurgenson, Harvard University
40,000 training examples
g: P -> e
•Regression function g does not need to be justified in any scientific way!
•Supervised learning is used to find g
Too many inputs parameters.
Many parameters are nothing more than noise.
Result is not very good
Reduce number of parameters
Make parameters “more meaningful”
Neural Network with PC as inputs : RMSE~0.0155
Center pictures using spline interpolation.
Recalculate principle components
Fine dune center position using amplitude of antisymmetrical components
Implicit use of additional information about data set:
2D matrixes are images of objects
Objects have meaningful center.
Color – 2theta
Color – (a-b)/(a+b)
Linear regression using only components 2,3 => RMSE~0.02
38 (galaxies PC) + 8 (stars PC) inputs
2 Hidden Layers -12 neurons (linear transfer function) and 8 neurons(sigmoid transfer function)
2 outputs – e1 and e2 as targets
80% random training subset, 20% validation subset
•Multiple trainings with numerous networks achieving training RMSE<0.015
•Typical test RMSE =0.01517 – 0.0152
•Small score improvement by combining prediction of many networks (simple mean):
Combination of multiple networks, training RMSE ~0.0149
public RMSE ~0.01505-0.01509
private RMSE ~0.01512-0.01516
Benefit of network combination is ~0.00007-0.0001
•Best submission – mean of 35 NN predictions
Method is strongly data depended. How method will perform for more diverse data set and real data ?
Is there a place for this kind of methods in cosmology?