1. Machine learning and advanced statistics: photometric classification of SNe
Machine learning and advanced statistics:
photometric classification of SNe
Marco De Pascale1,2,3
Baruffolo A.3, Cappellaro E.3, Patat F.2
1Department of Physics and Astronomy – University of Padova
2European Southern Observatory
2Astronomical Observatory of Padova – INAF
November, 28th 2014
2. Machine learning and advanced statistics: photometric classification of SNe
Outline
1 Surveys and data
2 Data-flood
3 Solution
Data smoothing
Dimensionality reduction
Classification
3. Machine learning and advanced statistics: photometric classification of SNe
Surveys and data
Supernovae . . .
• Among the brightest objects in the Universe
• Universe expansion
• Star formation rate evolution
4. Machine learning and advanced statistics: photometric classification of SNe
Surveys and data
. . . and photometric surveys
• DES and PanSTARSS, ongoing
SNe surveys
• LSST, planned survey
• Huge amount of data produced
5. Machine learning and advanced statistics: photometric classification of SNe
Data-flood
A problem for classification
• Can not be done “by hand”
• Can not use spectra
• Need for an automatic technique
6. Machine learning and advanced statistics: photometric classification of SNe
Solution
Information from data
• Large data set can describe itself
• Combine advanced statistics and
machine learning
• data driven classification
7. Machine learning and advanced statistics: photometric classification of SNe
Solution
Backwards outline
8. Machine learning and advanced statistics: photometric classification of SNe
Solution
Backwards outline
9. Machine learning and advanced statistics: photometric classification of SNe
Solution
Backwards outline
10. Machine learning and advanced statistics: photometric classification of SNe
Solution
Data set
• Simulated in four bands griz
• From Supernova Photometric Classification Challenge
(Kessler+ 2010)
• Biased towards SN Ia
• Real data from SUDARE survey
11. Machine learning and advanced statistics: photometric classification of SNe
Solution
Data smoothing
Smoothing with few assumption
• Data speak for themselves = no templates
• Non-parametric smoothing techniques
• Only constraint: main features of underlining function
12. Machine learning and advanced statistics: photometric classification of SNe
Solution
Data smoothing
Gaussian processes (or kriging)
• Measurements described
by infinite number of
functions
• Gaussian probability
distribution over functions
f(x) ∼ GP(µ(x), k(xi, xj))
13. Machine learning and advanced statistics: photometric classification of SNe
Solution
Data smoothing
Covariance function
• Covariance among measurements
k(xi, xj) = h2
exp −
|xi − xj|2
2 2
• Hyper parameters
• h: magnitude of the function
• : length scale
• Optimised through likelihood maximisation
14. Machine learning and advanced statistics: photometric classification of SNe
Solution
Data smoothing
Smoothing results
15. Machine learning and advanced statistics: photometric classification of SNe
Solution
Dimensionality reduction
Next step
• Describe light curves with few parameters
• Capture the important features
• Diffusion maps, Coifam & Lafon (2006)
16. Machine learning and advanced statistics: photometric classification of SNe
Solution
Dimensionality reduction
Measuring similarities
• Euclidean metric to
measure similarities
• Weighted by smoothing
errors
17. Machine learning and advanced statistics: photometric classification of SNe
Solution
Dimensionality reduction
Diffusion map
• Non-linear dimensionality
reduction technique
• Captures intrinsic
geometry of data set
• Similarity measure
→ diffusion distance
19. Machine learning and advanced statistics: photometric classification of SNe
Solution
Classification
Identify clusters
• Diffusion coordinates = parameters
• Hopefully we have clusters in diffusion space
• Associate clusters to SN type
20. Machine learning and advanced statistics: photometric classification of SNe
Solution
Classification
Random forests. . .
• Set of classification trees
• Committee with majority
vote
• Successful
21. Machine learning and advanced statistics: photometric classification of SNe
Solution
Classification
. . . at work
• Trained on labelled observations
SNIa SNIbc SNII class.error
SNIa 536 5 17 0.03
SNIbc 74 50 20 0.65
SNII 18 4 378 0.05
• Tested on test observations
SNIa SNIbc SNII class.error
SNIa 3791 162 568 0.16
SNIbc 1467 680 506 0.74
SNII 4296 350 8382 0.35
