New Techniques in Light Curve Analysis Joseph Richards UC Berkeley Department of Astronomy Department of Statistics jwrichar stat berkeley edu High Energy Astrophysics Division Meeting September 7 2011 Center for Time Domain Informatics UC Berkeley UCB Faculty Staff Josh Bloom Dan Starr Astro John Rice Noureddine El Karoui Stats Martin Wainwright Masoud Nikravesh CS Post Docs Dovi Poznanski Brad Cenko Nat Butler Berian James JWR Grad Students Dan Perley Adam Miller Adam Morgan Chris Klein James Long Tamara Broderick Sahand Negahban John Brewer Henrik Brink Sharmo Bhattacharyya Undergrads Maxime Rischard Justin Higgins Rachel Kennedy Jason Chu Arien Crellin Quick Pierre Christian Tatyana Gavrilchenko Stuart Gegenheimer Anthony Paredes Benjamin Gerard Lawrence Berkeley National Laboratory LBNL Peter Nugent David Schlegel Nic Ross Horst Simon Visit our website http cftd info J Richards Techniques in LC Analysis 2 Motivation A road map for light curve classification Context See Richards et al 2011 arXiv 1101 1959 Bloom Richards 2011 arXiv 1104 3142 J Richards Techniques in LC Analysis 3 Motivation Automated Learning on Light Curves Need machine learned classification of light curves for 1 detection and discovery of events in real time condensing a data deluge into a trickle of astrophysical goodness 2 optimal allocation of expensive follow up resources often in real time 3 construction of pure complete samples of e g Type Ia Supernovae expansion history of Universe RR Lyrae Variable Stars structure of Milky Way Eclipsing star systems stellar mass radius age distance 4 outlier detection to find objects from new or rare classes Bhattacharyya et al 2011 in prep semi supervised anomaly detection Discovery on massive data streams is not assured J Richards Techniques in LC Analysis 4 Example Optimal Resource Allocation Classification drives resource allocation RATE GRBz web tool for GRB follow up 0 8 0 6 0 4 Fraction of high z 4 GRBs observed 0 2 Based only on early time metrics random 0 0 Problem statement Given limited follow up time maximize the time spent on high redshift GRBs 1 0 EfficiencyEfficiency Classification 0 0 0 2 0 4 0 6 0 8 of GRBs followed up 1 0 Fraction of GRBs Followed Up Normalized reduced Morgan et al 2011 in prep J Richards Techniques in LC Analysis 5 Machine Learned Classification of Light Curves with Josh Bloom Dan Starr Nat Butler Darren Homrighausen Chad Schafer Peter Freeman Dovi Poznanski Bloom Richards 2011 arXiv 1104 3142 Overview of ML LC Class Richards et al 2011 arXiv 1101 1959 VarStar Classification Richards et al 2011 arXiv 1103 6034 SN Typing Bloom et al 2011 arXiv 1106 5491 Classification for PTF J Richards Techniques in LC Analysis 6 Light Curve Features Domain knowledge drives choice of features Periodic Metrics Use generalized Lomb Scargle method to find frequencies amplitudes phase offsets of fundamental freqs and harmonics Variability Metrics Stetson indices damped random walk QSO model of Butler Bloom 2011 point to point metrics J Richards Shape Analysis marginals std skewness kurtosis ratios of quantiles Low D embeddings of LCs e g diffusion map LLE Context Features e g distance to nearest galaxy type of nearest galaxy location in the ecliptic plane SDSS etc Techniques in LC Analysis 7 Diffusion Map for Photometric SN Typing Diffusion map non linear method to uncover low dimensional structure in data Lafon Lee 2006 I I Map each light curve x into m dimensional diffusion space x 7 1 x m x Features for classification are the diffusion map coordinates Richards et al 2011 arXiv 1103 6034 J Richards Techniques in LC Analysis 8 From Features to Classification Classification We describe each light curve with a vector of features x Goal Using known labels y1 yn estimate model b f x to predict class probabilities for new light curves Class wise distribution of features a Mira a Mira b Semireg PV b Semireg PV c RV Tauri c RV Tauri d Classical Cepheid d Classical Cepheid e Pop II Cepheid e Pop II Cepheid f Multi Mode Cepheid f Multi Mode Cepheid g RR Lyrae FM g RR Lyrae FM h RR Lyrae FO h RR Lyrae FO i RR Lyrae DM i RR Lyrae DM j Delta Scuti j Delta Scuti k Lambda Bootis k Lambda Bootis l Beta Cephei l Beta Cephei m Slowly Puls B m Slowly Puls B n Gamma Doradus n Gamma Doradus o Pulsating Be o Pulsating Be p Per Var SG p Per Var SG q Chem Peculiar q Chem Peculiar r Wolf Rayet r Wolf Rayet s T Tauri s T Tauri t Herbig AE BE t Herbig AE BE u S Doradus u S Doradus v Ellipsoidal v Ellipsoidal w Beta Persei w Beta Persei x Beta Lyrae x Beta Lyrae y W Ursae Maj y W Ursae Maj 3 2 1 0 1 2 log freq1 harmonics freq 0 3 2 5 2 1 5 1 0 5 0 0 5 1 log freq1 harmonics amplitude 0 Frequency Amplitude J Richards Techniques in LC Analysis 9 Classification Decision Trees Classification Learn model bf x that maps a feature vector x to a vector of class probabilities Classification Trees I Binary partitions of feature space I Each split minimizes node impurity I Within each node model class probabilities b f x as constant Advantages 1 Able to capture complex interactions 2 Robust to outliers 3 Handle multi class problems 4 Immune to irrelevant features 5 Cope with missing values 6 Computationally efficient scalable Hastie Tibshirani Friedman 2009 J Richards Techniques in LC Analysis 10 Classification Ensemble Methods Drawback of Classification Trees Classification trees are usually unbiased if grown deep enough but have high variance Note Expected classification error is variance plus bias squared I I I Bagging averages trees from bootstrapped versions of x Boosting averages a series of trees iteratively up weighting mis classified data Random Forest averages B P de correlated bootstrapped trees b fRF B1 Bi 1 b fi 1 Var b fRF Var b fi Var b fi B where is the correlation between trees b fi J Richards Techniques in LC Analysis 11 Classification Structured Classification Idea Let class taxonomy guide classifier HSC Hierarchical single label classification I Fit separate classifier at each non terminal node J Richards HMC Hierarchical multi label classification I Fit one classifier where L y b f x w0depth Techniques in LC Analysis 12 Classification of Hipparcos OGLE VarStars 0 34 Cross validated classification error rates 0 30 0 28 0 26 0 24 J Richards HSC RF RF non LS Feat this work RF pw RF pw Techniques in LC Analysis HSC RF LS Features this work RF HSC RF RF HSC RF RF LS Features Debosscher RF pw SVM pw HMC RF Boost pw CART pw KNN Boost C4 5 CART LS non LS Features this work