Pan-STARRS1 Photometric Classifica7on of Supernovae using Ensemble Decision Tree Methods

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1 Pan-STARRS1 Photometric Classifica7on of Supernovae using Ensemble Decision Tree Methods George Miller, Edo Berger Harvard-Smithsonian Center for Astrophysics

2 PS1 Medium Deep Survey 1.8m f/4.4 telescope with 3.2 degree FOV and 1.6 Gpix camera PS1 Sky Surveys: May 2010 March 2014 Medium Deep 10 fields of 7 sq. deg. with a 3-day staggered cadence and grizy filters Currently the best precursor and source of training data for LSST classifica7on tools Similar cadence (~3 days) and sensi7vity Similar grizy band-passes (+u for LSST) Wide variety of science drivers and a large distributed collabora7on

3 PS1/MDS Spectroscopic Sample Sample of 514 events with spectroscopic follow up (~150 nights on MMT, Magellan, Gemini by the Harvard PS1 team) 69% Ia 22% IIP/n 4% Ib/c 4% ULSN, TDE, etc. 1% Unclassified

4 Goals To develop a machine learning algorithm capable of: 1. Classifying all types of supernovae subtypes, including rare or exo7c events. 2. Classifying quickly in real 7me

5 Model Fikng F (t) = 8 A+ (t t 0 ) >< + c if t<t 1+e (t t 0 )/ rise 1 >: (A+ (t 1 t 0 )) e (t t 1 )/ fall 1+e (t t 0 )/ rise + c if t t 1 Adapted from the non-ia lightcurve model (Bazin+ 2009) Required a func7onal form sufficiently generic to fit a wide array of possible SN lightcurves Added second 7me parameter and linear decay func7on to allow for plateau effect near and ajer maximum light

6 Non-Ia Model (Bazin+ 2009) Double Peak Model (Karpenka+ 2013) Linear Decline Model (This work)

7 Individual fits using PyMC MH Confirmed Type IIP F F F F Flu[ 1000 Flu[ 3000 Flu[ 1000 Flu[ JD [+55500] JD [+55500] JD [+55500] JD [+55500] Confirmed Type Ia F F F F Flu[ Flu[ Flu[ Flu[ JD [+55500] JD [+55500] JD [+55500] JD [+55500]

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11 F (t) = 8 A+ (t t 0 ) >< + c if t<t 1+e (t t 0 )/ rise 1 >: (A+ (t 1 t 0 )) e (t t 1 )/ fall 1+e (t t 0 )/ rise + c if t t 1 Careful Considera;ons: A degeneracy exists between a fast exponen7al decline and a steep linear decline. Fix: Set priors to favor exponen7al declines. We set the slope (β) as a normal centered at low values We set the lag 7me (t 1 -t 0 ) as a double-normal composed of a narrow, low-valued and a broad, high-valued Gaussian

12 F (t) = 8 A+ (t t 0 ) >< + c if t<t 1+e (t t 0 )/ rise 1 >: (A+ (t 1 t 0 )) e (t t 1 )/ fall 1+e (t t 0 )/ rise + c if t t 1 Careful Considera;ons: A degeneracy exists between a fast exponen7al decline and a steep linear decline. Fix: Set priors to favor exponen7al declines. We set the slope (β) as a normal centered at low values We set the lag 7me (t 1 -t 0 ) as a double-normal composed of a narrow, low-valued and a broad, high-valued Gaussian The parameters A and lag (t 1 -t 0 ) don t actually represent the maximum amplitude and linear decline dura7on respec7vely. Fix: Use post-processing to fit the maximum amplitude of the posterior model and define lag as t max t 0

13 Imbalanced Classes Type Ia supernovae will consist of the majority class for any survey. 70% Type Ia for PS1 MD On a superficial level, this affects our performance measure. Cannot simply state overall accuracy. On a deeper level, imbalanced class distribu7on will affect the machine learning algorithm. If the algorithm tries to adap7vely maximize the overall predic7ve accuracy of the sample, it tends to ignore minority classes if this hurts the accuracy of the major class. If we wish to iden;fy unique/exo;c transients, we must rec;fy the inherently imbalanced supernovae class rates

14 SMOTE Synthe7c Minority Over-sampling Technique (SMOTE) proposed by Chawla et. al SMOTE creates synthe7c samples in the feature space by randomly sampling anywhere along the line segments joining the k minority class nearest neighbors Also allows us to more freely explore a broader poten7al feature space of the minority class

15 Boos7ng t fall,i > 40 t rise,g >20 lag r > 10 M i > -18 SN Ia SN IIn SN IIp SN Ia SN Ib/c Freund & Schapire 1995

16 Boos7ng Advantages of Boos7ng Decision Trees can incorporate features from a wide array of sources. They do not need to be numerically related, and can even use mul7- class labeling features (is the host galaxy a spiral or ellip7cal, etc.) The combina7on of mul7ple weak learners, as opposed to a deeper decision tree, reduces overfikng the data and does not rely upon axisaligned par77oning of the features Boos7ng can be efficiently applied to large datasets with many variables, resul7ng in faster computa7onal 7mes

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19 Sub-type classifica7on results Overall Accuracy of 88.4% Must account for 70% type Ia

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24 Future Plans Don t rely on spectroscopic redshijs Use photo-z, or create a redshij independent model Incorporate colors into model fikng Genera7ve: Use a K-correc7on model Discrimina7ve: Add a Bayesian Hyperprior Incorporate external informa7on as features Host galaxy type, host galaxy offset, etc. Real 7me classifica7on Need to be more sensi7ve to rise phase

25 Discussion Ques7ons 1. How can we dis7nguish new/rare/exo7c transient events? 2. How can we incorporate fikng errors into our machine learning algorithms?