Joshua Bloom: Machine Learning and Classification in the Synoptic Survey Era
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The document provides information about a workshop on classification of astronomical time-series data held at UC Berkeley on May 7, 2012. It discusses the challenges of classifying large amounts of time-series data from current and upcoming astronomical surveys, and how machine learning can help address these challenges by making rapid classifications of light curves to identify interesting transient events and variable object types. Specifically, it describes how machine learning has been used to identify supernovae in real-time from large surveys, and how features extracted from light curves can be used to classify variable stars and other astronomical objects.
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Joshua Bloom: Machine Learning and Classification in the Synoptic Survey Era
- 1. January 7 - March 2, 1610
- 2. Classification of Astronomical Time-Series Data in the Synoptic Survey Era Josh Bloom Joseph Richards University of California, Berkeley Berkeley Streaming Workshop; 7 May 2012
- 3. Center for Time-Domain Informatics UC Berkeley (UCB): Faculty/Staff JSB, Dan Starr (Astro), John Rice, Noureddine El Karoui (Stats), Martin Wainwright, Masoud Nikravesh (CS) Postdocs Joey Richards (stat/astro), Berian James, Damian Eads, Dovi Poznanski (→Tel Aviv), Brad Cenko, Nat Butler, Nino Cucchiara, Damian Eads (→Cambridge) Grad Students Dan Perley (→Caltech), Adam Miller, Adam Morgan, Chris Klein, James Long, Tamara Broderick (stats), Sahand Negahban (EECS), John Brewer (→Yale), Henrik Brink (←Copenhagen) Undergrads Anthony Paredes, Tatyana Gavrilchenko, Stuart Gegenheimer, Maxime Rischard, Justin Higgins, Rachel Kennedy, Arien Crellin-Quick, Michelle Kislak (→UCLA), Allison Merritt (→Yale) Lawrence Berkeley National Laboratory (LBNL): Peter Nugent, David Schlegel, Nic Ross, Horst Simon Visit our website: http://cftd.info/
- 4. Text Understanding & Exploiting the Dynamic Universe
- 5. Text Understanding & Exploiting the Dynamic Universe •Twinkle, twinkle... Everything changes at some level (brightness, color, position, ...)
- 6. Text Understanding & Exploiting the Dynamic Universe •Twinkle, twinkle... Everything changes at some level (brightness, color, position, ...) • Stars die...and blow up supernovae, gamma-ray bursts, new phenomena ...
- 7. Text Understanding & Exploiting the Dynamic Universe •Twinkle, twinkle... Everything changes at some level (brightness, color, position, ...) • Stars die...and blow up supernovae, gamma-ray bursts, new phenomena ... • Discovery is only the start
- 8. Text Understanding & Exploiting the Dynamic Universe •Twinkle, twinkle... Everything changes at some level (brightness, color, position, ...) • Stars die...and blow up supernovae, gamma-ray bursts, new phenomena ... • Discovery is only the start Greatest insights require follow-up (imaging, spectroscopy, archive introspection)
- 9. Text Understanding & Exploiting the Dynamic Universe •Twinkle, twinkle... Everything changes at some level (brightness, color, position, ...) • Stars die...and blow up supernovae, gamma-ray bursts, new phenomena ... • Discovery is only the start Greatest insights require follow-up (imaging, spectroscopy, archive introspection) Follow-up is EXPENSIVE (ie., people, time, telescope, resources, $)
- 10. Gamma-Ray Burst Transients “static” γ-ray sky
- 11. Gamma-Ray Burst Transients • Short-lived blasts of high energy light (γ-rays & X-rays)
- 12. Gamma-Ray Burst Transients • Short-lived blasts of high energy light (γ-rays & X-rays) “static” γ-ray sky
- 13. Gamma-Ray Burst Transients • Short-lived blasts of high energy light (γ-rays & X-rays) • random & rare - found by specialized satellites “static” γ-ray “static” γ-ray sky
- 14. Gamma-Ray Burst Transients • Short-lived blasts of 106 high energy light (γ-rays & X-rays) 10,000 • random & rare - found by specialized satellites 100 • also: brightest optical events in universe power 1 (transient “afterglow”) 0.01
- 15. Gamma-Ray Burst Transients • Short-lived blasts of 106 high energy light (γ-rays & X-rays) 10,000 • random & rare - found by specialized satellites 100 • also: brightest optical events in universe power 1 (transient “afterglow”) • two origins: exploding 0.01 massive stars & colliding compact objects
- 16. Gamma-Ray Burst Transients • Short-lived blasts of 106 high energy light (γ-rays & X-rays) 10,000 • random & rare - Challenge: how can we found by specialized satellites maximize our science 100 return power • also: brightest optical on discovery with events in universe optimized follow up? 1 (transient “afterglow”) • two origins: exploding 0.01 massive stars & colliding compact objects
- 17. Follow-Up-Resource-Aware Classification collect burst data from satellite feed predict which events are “high redshift” "high redshift" GRBs in real-time less interesting unclassified "immediately" available data
- 18. Follow-Up-Resource-Aware Classification Efficiency vs α 1.0 predicted fraction of high-redshift GRBs improvement (90% c.l.) 0.8 Fraction of high (z>4) GRBs observed “59% (86%) of high-z GRBs can 0.6 be captured from om following up the nd top 20% (40%) of 0.4 ra the ranked candidates” 0.2 0.0 0.0 0.2 0.4 0.6 0.8 1.0 followed-up fraction Fraction of GRBs Followed Up: α Morgan+11 reduced
- 19. Extragalactic Transient Universe: Explosive Systems -22 -20 Pair Production Supernovae z=0.45 log(brightness) -18 Type Ia MH -16 Type IIp -14 IMBH + WD Collision 200Mpc -12 NS + RSG Collision NS + NS Mergers -10 50 100 150 200 Days Since Explosion E. Ramirez-Ruiz (UCSC)
- 20. Text Data Deluge Challenge Large Synoptic Survey Telescope (LSST) - 2018 ! Light curves for 800M sources every 3 days 106 supernovae/yr, 105 eclipsing binaries 3.2 gigapixel camera, 20 TB/night LOFAR & SKA 150 Gps (27 Tflops) → 20 Pps (~100 Pflops) Gaia space astrometry mission - 2013 1 billion stars observed ∼70 times over 5 years Will observe 20K supernovae Many other astronomical surveys are already producing data: SDSS, PTF, CRTS, Pan-STARRS, Hipparcos, OGLE, ASAS, Kepler, LINEAR, DES (soon) etc., etc.
- 21. Text Data Deluge Challenge Large Synoptic Survey Telescope (LSST) - 2018 ! Light curves for 800M sources every 3 days 106 supernovae/yr, 105 eclipsing binaries 3.2 gigapixel camera, 20 TB/night LOFAR & SKA 150 Gps (27 Tflops) → 20 Pps (~100 Pflops) Gaia space astrometry mission - 2013 1 billion stars observed ∼70 times over 5 years Will observe 20K supernovae Many other astronomical surveys are already producing data: SDSS, PTF, CRTS, Pan-STARRS, Hipparcos, OGLE, ASAS, Kepler, LINEAR, DES (soon) etc., etc.
- 22. Text Data Deluge Challenge Large Synoptic Survey Telescope (LSST) - 2018 ! Light curves for 800M sources every 3 days 106 supernovae/yr, 105 eclipsing binaries 3.2 gigapixel camera, 20 TB/night LOFAR & SKAHow do we do discovery, follow-up, and inference when 150 Gps (27 Tflops) → 20 Pps (~100 Pflops) the data rates (& requisite Gaia space astrometry mission - 2013 1 billiontimescales) precludeyears stars observed ∼70 times over 5 human involvement? Will observe 20K supernovae Many other astronomical surveys are already producing data: SDSS, PTF, CRTS, Pan-STARRS, Hipparcos, OGLE, ASAS, Kepler, LINEAR, DES (soon) etc., etc.
- 23. Machine Learning As Surrogate - trained to quickly make concrete, deterministic, & repeatable statements about abstract concepts “Is this varying source astrophysical in nature or spurious?”
- 24. Machine Learning As Surrogate - trained to quickly make concrete, deterministic, & repeatable statements about abstract concepts “Is this varying source astrophysical Discovery in nature or spurious?”
- 25. Machine Learning As Surrogate - trained to quickly make concrete, deterministic, & repeatable statements about abstract concepts PTF: 1.5M candidate/night “Is this varying 1:1000 are astrophysical source astrophysical machine has opined on in nature or 800M candidates Bloom+11 spurious?” Poznanski, Brink, this workshop Discovery
- 26. Reference New Difference 11kly 11kx also, cf., Bailey+07
- 27. 2011fe identified w/ Machine-Learned Discovery Algorithms Discovery image was ~11 hours after explosion Within a few hours, a spectrum confirmed it to be a SN Ia Nearest SN Ia in more than 3 decades 5th brightest supernova in 100 years
- 28. Machine Learning As Surrogate - trained to quickly make concrete, deterministic, & repeatable statements about abstract concepts “What is the nature (origin/reason...) of the variability?”
- 29. Machine Learning As Surrogate - trained to quickly make concrete, deterministic, & repeatable statements about abstract concepts “What is the nature Classification (origin/reason...) of the variability?”
- 30. Pulsating Alpha Cygni (ACYG) Short Period (BCEPS) Beta Cephei (BCEP) Anomalous (BLBOO) Pulsating Stars Multiple Modes (CEPB) Cepheids (CEP) Long Period (CWA) W Virginis (CW) Short Period (CWB) Delta Cep (DCEP) Symmetrical (DCEPS) Delta Scuti (DSCT) Low Amplitude (DSCTC) Slow Irregular (L) Late Spectral Type (K, M, C, S) (LB) Mira (M) Supergiants (LC) Dual Mode (RRB) PV Telescopii (PVTEL) Asymmetric (RRAB) RR Lyrae (RR) Near Symmetric (RRC) Constant Mean Magnitude (RVA) RV Tauri (RV) Variable Mean Magnitude (RVB) Persistent Periodicity (SRA) Semiregular (SR) Poorly Defined Periodicity (SRB) Pulsating Subdwarfs (SXPHE) Supergiants (SRC) F, G, or K (SRD) Only H Absorption (ZZA) ZZ Ceti (ZZ) Only He Absorption (ZZB) HeII Absoption (ZZO) Cataclysmic Variables Cataclysmic Variables SS Cygni U Geminorum (UG) SU Ursae Majoris SNIa Z Camelopardalis SNIb Type I Supernovae (SNI) SNIc Supernovae (SN) SNIIL Type II Supernovae (SNII) SNIIN Fast Novae (NA) Slow Novae (NB) SNIIP Novae (N) Very Slow Novae (NC) Novalike Variables (NL) Recurrent Novae (NR) Gamma-ray Bursts (GRB) Long Gamma-ray Burst (LSB) Soft Gamma-ray Repeater (SGR) Symbiotic Variables (ZAND) Short Gamma-ray Burst (SHB) Eclipsing Eclipsing Systems Systems with White Dwarfs (WD) Semidetached (SD) Early (O-A) (KE) RS Canum Venaticorum (RS) W Ursa Majoris (KW) Planetary Nebulae (PN) Contact Systems (K) Algol (Beta Persei) (EA) Systems with Supergiant(s) (GS) Eclipsing Binary Systems (E) Beta Lyrae (EB) W Ursae Majoris (EW) Main Sequence (DM) Detached (D) With Subgiant (DS) Detached - AR Lacertae (AR) W Ursa Majoris (DW) Wolf-Rayet Stars (WR)
- 31. Considerable Complications with Time-Series Data • noisy, irregularly sampled
- 32. Considerable Complications with Time-Series Data • noisy, irregularly sampled • spurious data
- 33. Considerable Complications with Time-Series Data • noisy, irregularly sampled • spurious data • telltale signature event may not have happened yet
- 34. Machine-Learning Approach to Classification Features: homogenize the data; real-number metrics that describe the time-domain characteristics & context of a source ~100 features computed in < 1 sec (including periodogram analysis) Wózniak et al. 2004; Protopapas+06, Willemsen & Eyer 2007; Debosscher et al. 2007; Mahabal et al. 2008; Sarro et al. 2009; Blomme et al. 2010; Kim+11, Richards+11
- 35. Machine-Learning Approach to Classification Features: homogenize the data; real-number metrics that describe the time-domain characteristics & context of a source ~100 features computed in < 1 sec (including periodogram analysis) periodic variability metrics: e.g. domi metrics nant freq : e.g. Stetson indices, χ 2/dof Lomb- uencies in Scargle, p hase offs (constant hypothesis) between ets periods shape analysis wness, kurtosis, context metrics e.g. ske Gaussianity e.g. distance to nearest galaxy, type of nearest galaxy, locatio n in the ecliptic plane Wózniak et al. 2004; Protopapas+06, Willemsen & Eyer 2007; Debosscher et al. 2007; Mahabal et al. 2008; Sarro et al. 2009; Blomme et al. 2010; Kim+11, Richards+11
- 36. Variable Star Classification Confusion True Class Richards+11
- 37. Variable Star Classification Confusion pulsating True Class eruptive multi-star Richards+11
- 38. Variable Star Classification Confusion pulsating - global classification errors on well-observed sources approaching True 15% Class - random forest with missing data eruptive imputation emerging as superior e.g., Dubath+11,Richards+11 multi-star Richards+11
- 39. StructuredLearning Structured Classification Structured Classification: Let class taxonomy guide classifier. 5% gross mis- classification rate! HSC: Hierarchical single-label HMC: Hierarchical multi-label classification. classification. I Fit separate classifier at I Fit one classifier, where depth each non-terminal node. L(y , f (x)) w0 Richards+11
- 40. Decision Boundaries are Survey Specific How do we transfer learning from one survey to the next? –3– (a) (b) feature #2 feature #1 feature #1 Hipparcos OGLE-III Fig. 1.— (a) The grey lines represent the CART classifier constructed using Hipparcos data. The points are Hipparcos sources. This classifier separates Hipparcos sources well (0.6% error as measured by cross-validation). (b) Here the OGLE sources are plotted over the Long+12; Richards+11 same decision boundaries. There is now significant class overlap (30% error rate). This is
- 41. Decision Boundaries are Survey Specific – 31 – How do we transfer learning from one survey to the next? “Expert” ASAS (testing) OGLE+Hip (training) Fig. 8.— Long+12; Richards+11 Active learning samples on a single iteration of the algorithm. Yellow circles signify points that at least 65% of users were able to classify. These points are included
- 42. Decision Boundaries are Survey Specific How do we transfer learning from one survey to the next? ● ● ● ● ● 0.40 ● ● ● ● Percent of Confident ASAS RF Labels ● ● 0.35 ● ● ● 0.30 ● 0.25 ● ● 0.20 ● 0.15 ● 2 4 6 8 0 2 4 6 8 AL Iteration AL Iteration Long+12; eft: Percent agreement of the Random Forest classifier with the ACVS labels, Richards+11 of AL iteration. Right: Percent of ASAS data with confident RF classification
- 43. Classification Statements are Inherently Fuzzy - classification probabilities should reflect uncertainty in the data & training - higher confidence with greater proximity to training data - calibration of classification probability vector E.g.: 20% of transients classified as supernova of type “Ib” with P=0.2 should be supernova of type “Ib”
- 44. Classification Statements are Inherently Fuzzy - classification probabilities should reflect uncertainty in the data & training - higher confidence with greater proximity to training data - calibration of classification probability vector E.g.: 20% of transients classified as supernova of type “Ib” with P=0.2 should be supernova of type “Ib” Catalogs of Transients and Variable Stars Must Become Probabilistic
- 46. Doing Science with Probabilistic Catalogs Demographics (with little followup): trading high purity at the cost of lower efficiency e.g., using RRL to find new Galactic structure Novelty Discovery (with lots of followup): trading high efficiency for lower purity e.g., discovering new instances of rare classes
- 47. Discovery of Bright Galactic R Coronae Borealis and DY Persei Variables: Rare Gems Mined from ASAS A. A. Miller1,⇤ , J. W. Richards1,2 , J. S. Bloom1 , S. B. Cenko1 , J. M. Silverman1 , arXiv:1204.4181v1 [astro-ph.SR] 18 Apr 2012 D. L. Starr1 , and K. G. Stassun3,4 ABSTRACT – 13 – We present the results of a machine-learning (ML) based search for new R Coronae Borealis (RCB) stars and DY Persei-like stars (DYPers) in the Galaxy using cataloged light curves obtained by the All-Sky Automated Survey (ASAS). RCB stars—a rare class of hydrogen-deficient carbon-rich supergiants—are of great interest owing to the insights they can provide on the late stages of stellar evolution. DYPers are possibly the low-temperature, low-luminosity analogs to the RCB phenomenon, though additional examples are needed to fully estab- lish this connection. While RCB stars and DYPers are traditionally identified by epochs of extreme dimming that occur without regularity, the ML search framework more fully captures the richness and diversity of their photometric behavior. We demonstrate that our ML method recovers ASAS candidates that would have been missed by traditional search methods employing hard cuts on amplitude and periodicity. Our search yields 13 candidates that we consider likely RCB stars/DYPers: new and archival spectroscopic observations confirm that four of these candidates are RCB stars and four are DYPers. Our discovery of four new DYPers increases the number of known Galactic DYPers from two to six; noteworthy is that one of the new DYPers has a measured parallax and is m ⇡ 7 mag, making it the brightest known DYPer to date. Future observations of these new DYPers should prove instrumental in establishing the RCB con- Fig. 2.— ASAS V nection. We consider these results, derived from a machine-learned probabilistic -band light curves of newly discovery RCB stars and DYPers. Note t di↵ering magnitude ranges shown for each light curve. Spectroscopic observations confi 1 Department of Astronomy, University of California, Berkeley, CA 94720-3411, USA the top four candidates to RCB/DY California, Berkeley, CA, bottomUSA are DYPers. 17 known Galactic be Universitystars, while the 94720-7450, four Statistics Department, RCB of Per 2 3
- 48. Discovery of Bright Galactic R Coronae Borealis and DY Persei Variables: Rare Gems Mined from ASAS A. A. Miller1,⇤ , J. W. Richards1,2 , J. S. Bloom1 , S. B. Cenko1 , J. M. Silverman1 , arXiv:1204.4181v1 [astro-ph.SR] 18 Apr 2012 D. L. Starr1 , and K. G. Stassun3,4 ABSTRACT We present the results of a machine-learning (ML) based search for new R Coronae Borealis (RCB) stars and DY Persei-like stars (DYPers) in the Galaxy using cataloged light curves obtained by the All-Sky Automated Survey (ASAS). RCB stars—a rare class of hydrogen-deficient carbon-rich supergiants—are of great interest owing to the insights they can provide on the late stages of stellar evolution. DYPers are possibly the low-temperature, low-luminosity analogs to the RCB phenomenon, though additional examples are needed to fully estab- lish this connection. While RCB stars and DYPers are traditionally identified by epochs of extreme dimming that occur without regularity, the ML search framework more fully captures the richness and diversity of their photometric behavior. We demonstrate that our ML method recovers ASAS candidates that would have been missed by traditional search methods employing hard cuts on amplitude and periodicity. Our search yields 13 candidates that we consider likely RCB stars/DYPers: new and archival spectroscopic observations confirm that four of these candidates are RCB stars and four are DYPers. Our discovery of four new DYPers increases the number of known Galactic DYPers from two to six; noteworthy is that one of the new DYPers has a measured parallax and is m ⇡ 7 mag, making it the brightest known DYPer to date. Future observations of these new DYPers should prove instrumental in establishing the RCB con- nection. We consider these results, derived from a machine-learned probabilistic 1 Department of Astronomy, University of California, Berkeley, CA 94720-3411, USA 17 known Galactic RCB/DY California, Berkeley, CA, 94720-7450, USA Statistics Department, University of Per 2 3
- 49. Variety of Open Questions 1. How do bootstrap learning from one survey to the next, given inherent differences? “active learning” (e.g., Richards+11b) 2. How do we detect and quantify real outliers? e.g. clustering, semi-supervised learning (e.g., Protopapas+06, Rebbapragada+09, Bhattacharyya+, in prep) 3. How do imbue domain knowledge into classifiers? hybridization, metalearning 4. How do we weigh classification value with computational cost? resource allocation
- 50. Summary science maximization with synoptic surveys demands a more distant human role than before machine learning in time-domain astrophysics is not just talk...it’s working and enabling novel science yet, real-time discovery & classification is far from solved helpful to view endeavor as a resource-limited problem
- 51. See you tomorrow! food starting 8am talks starting 9am group picture before lunch
Hinweis der Redaktion
- * time-domain in astronomy\n* Crucial. new discoveries Looking at the sky with new tools (new eyes). Ptlometic order - planets were suppose to be fixed spherical orbs not with their own moons -- that didn&#x2019;t fit the world view. opportunistic tools\n* emphasizes the crucial roles of humans both in the data collection side, data analysis, and inference. \n\n\n
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- happy to acknowledge. big effort. industry support.\n
- needle in the haystack\n
- needle in the haystack\n
- needle in the haystack\n
- needle in the haystack\n
- needle in the haystack\n
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- contrained in time. decisions with incomplete information. Extreme rarities -- maybe a few a year of interest. imbalance and robust\n
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- Teaming with things we know and dont know about. exploration of the known and the unknowns.\n\nRumsfeldian\nshort timescales.\n
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- Simply must understand that our roles must change.\n
- Simply must understand that our roles must change.\n
- identification different than discovery: Galeilio \nGalileo's drawings show that he first observed Neptune on December 28, 1612, and again on January 27, 1613. On both occasions, Galileo mistook Neptune for a fixed star when it appeared very close&#x2014;inconjunction&#x2014;to Jupiter in the night sky;[20] hence, he is not credited with Neptune's discovery.\n\n253 year later\n\nJohann Gottfried Galle\n 23 September 1846\n
- identification different than discovery: Galeilio \nGalileo's drawings show that he first observed Neptune on December 28, 1612, and again on January 27, 1613. On both occasions, Galileo mistook Neptune for a fixed star when it appeared very close&#x2014;inconjunction&#x2014;to Jupiter in the night sky;[20] hence, he is not credited with Neptune's discovery.\n\n253 year later\n\nJohann Gottfried Galle\n 23 September 1846\n
- identification different than discovery: Galeilio \nGalileo's drawings show that he first observed Neptune on December 28, 1612, and again on January 27, 1613. On both occasions, Galileo mistook Neptune for a fixed star when it appeared very close&#x2014;inconjunction&#x2014;to Jupiter in the night sky;[20] hence, he is not credited with Neptune's discovery.\n\n253 year later\n\nJohann Gottfried Galle\n 23 September 1846\n
- identification different than discovery: Galeilio \nGalileo's drawings show that he first observed Neptune on December 28, 1612, and again on January 27, 1613. On both occasions, Galileo mistook Neptune for a fixed star when it appeared very close&#x2014;inconjunction&#x2014;to Jupiter in the night sky;[20] hence, he is not credited with Neptune's discovery.\n\n253 year later\n\nJohann Gottfried Galle\n 23 September 1846\n
- 1.5 M per night, \n
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- it should be easy -- there&#x2019;s a bunch of classes of objects which vary, we measure their light curves and that&#x2019;s it. Even remarkably homogeneous classes such as Ia and RRL exhibit huge variations. \n\n
- it should be easy -- there&#x2019;s a bunch of classes of objects which vary, we measure their light curves and that&#x2019;s it. Even remarkably homogeneous classes such as Ia and RRL exhibit huge variations. \n\n
- it should be easy -- there&#x2019;s a bunch of classes of objects which vary, we measure their light curves and that&#x2019;s it/\n
- however, in practice\n
- however, in practice\n
- however, in practice\n
- however, in practice\n
- however, in practice\n
- however, in practice\n
- dynamic time warping\nhundreds of features: n log n, n^2, etc. some of these are results of external queries.\n\nSame things we, as experts, look at in a light curve and ancillary data.\n
- dynamic time warping\nhundreds of features: n log n, n^2, etc. some of these are results of external queries.\n\nSame things we, as experts, look at in a light curve and ancillary data.\n
- dynamic time warping\nhundreds of features: n log n, n^2, etc. some of these are results of external queries.\n\nSame things we, as experts, look at in a light curve and ancillary data.\n
- dynamic time warping\nhundreds of features: n log n, n^2, etc. some of these are results of external queries.\n\nSame things we, as experts, look at in a light curve and ancillary data.\n
- discovery of physical intuition, like what Alex talked about.\n
- discovery of physical intuition, like what Alex talked about.\n
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- how you observed the data impacts what you think it is. This is obvious.\n\napproach is to craft ground truth from one survey to look like another. Either in light curve space\nor in feature space.\n
- how you observed the data impacts what you think it is. This is obvious.\n\napproach is to craft ground truth from one survey to look like another. Either in light curve space\nor in feature space.\n
- how you observed the data impacts what you think it is. This is obvious.\n\napproach is to craft ground truth from one survey to look like another. Either in light curve space\nor in feature space.\n
- how you observed the data impacts what you think it is. This is obvious.\n\napproach is to craft ground truth from one survey to look like another. Either in light curve space\nor in feature space.\n
- say good bye to black and white catalogs, \n
- posterior probabilities\nnot liklihoods -- convolved with the priors\nprescription for adapation\n
- best way to find needles in teh haystack is to get really good a finding and identifying hay.\n
- 8 of 13\n&#x2206;mV up to &#x223C;8 mag), aperiodic declines in brightness\nAt maximum light RCB stars are bright supergiants,\n\nMerrill-Sanford bands of SiC2 in three of our candidates: ASAS 162232&#x2212;5349.2, ASAS 065113+0222.1, and ASAS 182658+0109.0. To our knowledge this is the first identification of SiC2 in a DYPer spectrum\n\n
- last one not so important if we can wait for the answer.\n
- richer\n
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