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1 CORE DATA PROCESSING SOFTWARE PLAN REVIEW | SEATTLE, WA | SEPTEMBER 19-20, 2013 Name of Meeting Location Date - Change in Slide Master Object Characterization and MultiFit Jim Bosch Princeton University September 19, 2013 CDP FINAL DESIGN REVIEW September 19 - 20, 2013

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2 CORE DATA PROCESSING SOFTWARE PLAN REVIEW | SEATTLE, WA | SEPTEMBER 19-20, 2013 Review Charge (11) Is the MultiFit approach to multi-epoch object characterization algorithmically sound and justified? (12) Is the choice of MultiFit as the default shape measurement algorithm scientifically justified, given the current state of the art?

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3 CORE DATA PROCESSING SOFTWARE PLAN REVIEW | SEATTLE, WA | SEPTEMBER 19-20, 2013 Data Products From Data Products Definition Document (Section 5.2.1): − Point source model fit. The observed object is modeled as a point source with finite proper motion and parallax and constant flux (allowed to be different in each band). This model is a good description for stars and other unresolved sources. Its 11 parameters will be simultaneously constrained using information from all available observations in all bands. − Bulge-disk model fit. The object is modeled as a sum of a de Vaucouleurs (Sersic n = 4) and an exponential (Sersic n = 1) component. This model is intended to be a reasonable description of galaxies. The object is assumed not to move. The components share the same ellipticity and center. One effective radius is fit for each component (that is, the radius is not a function of band). The central surface brightness is allowed to vary from band to band. There are a total of 18 free parameters, which will be simultaneously constrained using information from all available epochs and bands. Where there's insufficient data to constrain the likelihood (eg., small, poorly resolved, galaxies, or very few epochs), priors will be adopted to limit the range of its sampling. In addition to the maximum likelihood values of fitted parameters and their covariance matrix, a number (currently planned to be 200, on average) of independent samples from the likelihood function will be provided. These will enable use-cases sensitive to departures from the Gaussian approximation.

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4 CORE DATA PROCESSING SOFTWARE PLAN REVIEW | SEATTLE, WA | SEPTEMBER 19-20, 2013 Outline − Limitations of coadd-based measurement − (Re-)introducing MultiFit: multi-epoch simultaneous fitting − Data products produced via MultiFit methods − Shape measurement for weak lensing The algorithmic landscape, and LSST’s approach to it Computational challenges and optimization − Implementation: current prototypes and roadmap for construction

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5 CORE DATA PROCESSING SOFTWARE PLAN REVIEW | SEATTLE, WA | SEPTEMBER 19-20, 2013 Coadd Limitations: Optimal Weights How do we optimally combine these two images? Kaiser: formally possible in Fourier space − requires stationary noise, spatially constant PSF, no bad pixels, no distortion between images... − worth investigating, but never demonstrated in practice Just a signal-to-noise issue – not a source of systematic error Exposure TimeSeeing A30s0.6” B100s1.0”

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6 CORE DATA PROCESSING SOFTWARE PLAN REVIEW | SEATTLE, WA | SEPTEMBER 19-20, 2013 Coadd Limitations: Correlated Noise Warping and resampling images correlates pixel noise − correlations are spatially coherent across the image: dangerous for weak lensing − measurement in the presence of correlated noise is more challenging (most often it’s just ignored, which at the very least will produce incorrect uncertainty estimates) − propagating full covariance information through the coaddition process is impractical for lanczos2 resampling, we’d have approximately 12 unique nonzero covariance elements per coadd pixel Potentially a source of systematic error

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7 CORE DATA PROCESSING SOFTWARE PLAN REVIEW | SEATTLE, WA | SEPTEMBER 19-20, 2013 Coadd Limitations: PSF − The effective point-spread function on a coadd is discontinuous at the edges of the input frames − When pixels are rejected from the coadd due to clipping or masks, there is no well-defined effective PSF on the coadd worst case: stars that are saturated only in good seeing Partial solution from Jee and Tyson (2011): compute PSF model on the coadd by warping/coadding PSF models from individual frames (a.k.a. StackFit, CoaddPsf) − only valid when object footprints do not contain missing pixels or frame boundaries − unknown whether this can fully account for DCR effects − still a substantial improvement over attempting to do PSF determination from coadd star images

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8 CORE DATA PROCESSING SOFTWARE PLAN REVIEW | SEATTLE, WA | SEPTEMBER 19-20, 2013 MultiFit vs. Coadd Measurement Exposure 1 Exposure 2 Exposure 3 Coadd Galaxy / Star Models Fitting Warp, Convolve Coadd Measurement Exposure 1 Exposure 2 Exposure 3 Galaxy / Star Models Transformed Model 1 Transformed Model 2 Warp, Convolve Fitting MultiFit (Simultaneous Multi-Epoch Fitting) Hard, but we only have to do it once. Easy; relatively few data points. Easier (depends on model), but we have to do it every iteration! Same number of parameters, but with orders of magnitude more data points.

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9 CORE DATA PROCESSING SOFTWARE PLAN REVIEW | SEATTLE, WA | SEPTEMBER 19-20, 2013 (Re-)introducing MultiFit − Most coadd problems occur because we attempt to transform noisy data; instead we want to transform perfectly known models and compare to all the original data. − We want to combine data by multiplying likelihood surfaces, not combining data points. This is not a new idea: − Stetson 1987 (proposed for use in stellar photometry) − Roat 2004 (proposed for use in shape measurement, prototype implementation, coined “MultiFit” term) − Lang 2009 (used for astrometry in SDSS Stripe 82) − Miller 2013 (used for shape measurement in CFHTLenS)

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10 CORE DATA PROCESSING SOFTWARE PLAN REVIEW | SEATTLE, WA | SEPTEMBER 19-20, 2013 MultiFit Limitations − Computationally expensive, especially when the number of exposures is large model convolution and evaluation is typically the dominant computational component, and in MultiFit, this is multiplied by the number of exposures − Many traditional measurements are difficult (impossible?) to map to a model/likelihood framework: image moments with analytic PSF corrections (i.e. KSB) common morphological classifiers (i.e. CAS, Gini) Flux-fraction isophotes (i.e. half-light ellipse) − NOT a limitation: degrees of freedom – we don’t add new parameters for per-exposure centroids and/or fluxes

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11 CORE DATA PROCESSING SOFTWARE PLAN REVIEW | SEATTLE, WA | SEPTEMBER 19-20, 2013 Data Products From Data Products Definition Document (Section 5.2.1): − Point source model fit. The observed object is modeled as a point source with finite proper motion and parallax and constant flux (allowed to be different in each band). This model is a good description for stars and other unresolved sources. Its 11 parameters will be simultaneously constrained using information from all available observations in all bands. − Bulge-disk model fit. The object is modeled as a sum of a de Vaucouleurs (Sersic n = 4) and an exponential (Sersic n = 1) component. This model is intended to be a reasonable description of galaxies. The object is assumed not to move. The components share the same ellipticity and center. One effective radius is fit for each component (that is, the radius is not a function of band). The central surface brightness is allowed to vary from band to band. There are a total of 18 free parameters, which will be simultaneously constrained using information from all available epochs and bands. Where there's insufficient data to constrain the likelihood (eg., small, poorly resolved, galaxies, or very few epochs), priors will be adopted to limit the range of its sampling. In addition to the maximum likelihood values of fitted parameters and their covariance matrix, a number (currently planned to be 200, on average) of independent samples from the likelihood function will be provided. These will enable use-cases sensitive to departures from the Gaussian approximation.

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12 CORE DATA PROCESSING SOFTWARE PLAN REVIEW | SEATTLE, WA | SEPTEMBER 19-20, 2013 Data Products: Stellar Astrometry Within LSST, “MultiFit” has traditionally implied “shape measurement”, but that’s an incomplete perspective – it’s the formally optimal approach for any deep measurement; the question is whether there are any equivalent or “good enough” approaches. Stellar astrometry is a case in point. − Point source models include proper motion and parallax It’s simply impossible to measure motion on the coadd. If we measure centroids independently on single frames, we miss out on the population with 24.5 < r < 27.5, and our measurements have lower SNRs. − Not including motion in the point source models would be hugely damaging to LSST’s galactic science goals: all nearby stars move. − Including motion in point source models also benefits extragalactic science and cosmology: better classification w.r.t. small galaxies.

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13 CORE DATA PROCESSING SOFTWARE PLAN REVIEW | SEATTLE, WA | SEPTEMBER 19-20, 2013 Data Products: Stellar Astrometry Lang (2009): Fit point source models to SDSS Stripe 82, including proper motion and parallax. Individual exposures: objects are undetected or marginally detected Moving point-source and galaxy models are indistinguishable on the coadd

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14 CORE DATA PROCESSING SOFTWARE PLAN REVIEW | SEATTLE, WA | SEPTEMBER 19-20, 2013 Data Products: Galaxy Model Fitting − Current baseline is similar to lensfit (Miller 2013): restricted bulge+disk model -same ellipticity for both components -radius ratio between components is fixed -amplitude of components can vary independently Bayesian: posterior = prior ×likelihood will sample from posterior, rather than rely on maximum likelihood fit with 2 nd -derivative covariance estimate − Will explore modifications with more/fewer free parameters − Will store posterior samples in the database, using a weak prior; users can apply a stronger prior later if desired

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15 CORE DATA PROCESSING SOFTWARE PLAN REVIEW | SEATTLE, WA | SEPTEMBER 19-20, 2013 Shape Measurement: Algorithmic Landscape − adaptive moments + corrections KSB 1995 (etc) − forward fitting, Bayesian sampling lensfit (Miller 2013) − forward fitting, max-likelihood e.g. im3shape (Zuntz 2013) − Fourier-domain methods Bernstein & Armstrong 2013 − object-stacking methods Lewis 2009 (etc) Easy computationally; no longer state- of-the-art in systematics control Very similar to sampling, but easier computationally Unproven on real data; likely easier computationally State-of-the-art in systematics control, battle-tested on real data, and likely the most computationally challenging

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16 CORE DATA PROCESSING SOFTWARE PLAN REVIEW | SEATTLE, WA | SEPTEMBER 19-20, 2013 Shape Measurement: Work Yet To Do − lensfit shear biases were acceptable for CFHTLenS; will need improvement for LSST due to smaller statistical uncertainties better priors? use posterior samples differently? more flexible galaxy models? marginalization over PSF/distortion uncertainties? fitting multiple galaxies simultaneously? − lensfit is already too slow to be practical for LSST as-is approximately 0.7s per epoch (in many-epoch limit) LSST computation budget for shape measurement is ~0.017s per epoch – we need to speed things up by a factor of 40. Most of these increase the number of parameters in the galaxy model.

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17 CORE DATA PROCESSING SOFTWARE PLAN REVIEW | SEATTLE, WA | SEPTEMBER 19-20, 2013 Shape Measurement: lensfit in detail − Galaxy models are evaluated and convolved directly in Fourier- space, using pre-computed profiles − Centroid and amplitude parameters are analytically marginalized, reducing dimensionality of parameter space − Radius and complex ellipticity are sampled on an adaptive grid requires approximately 500 samples per galaxy – much less than MCMC sampling, which can require up to 8000 if we need to add more parameters to the model, a grid approach doesn’t scale Fast, and by no means naive – but can we do better? Monte Carlo sampling would scale better with additional parameters

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18 CORE DATA PROCESSING SOFTWARE PLAN REVIEW | SEATTLE, WA | SEPTEMBER 19-20, 2013 Multi-Shapelet Model Evaluation Approximate Sérsic profiles using sums of Gaussians: See Hogg and Lang (2013), Bosch (2010) for more information

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19 CORE DATA PROCESSING SOFTWARE PLAN REVIEW | SEATTLE, WA | SEPTEMBER 19-20, 2013 Multi-Shapelet Model Evaluation...and approximate the PSF using sums of shapelets: − Galaxy profiles are approximate......but in a straightforward and controllable way. − Convolution is exact and fast: Model evaluation in 0.56ms; lensfit is very approximately 1.4ms Room for more improvement with custom CPU instruction sets, GPUs ( ≠ )

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20 CORE DATA PROCESSING SOFTWARE PLAN REVIEW | SEATTLE, WA | SEPTEMBER 19-20, 2013 Adaptive Importance Sampling See Wraith et al (2013) for more information

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21 CORE DATA PROCESSING SOFTWARE PLAN REVIEW | SEATTLE, WA | SEPTEMBER 19-20, 2013 Adaptive Importance Sampling iteration=1, perplexity=0.263365, essf=0.115455

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22 CORE DATA PROCESSING SOFTWARE PLAN REVIEW | SEATTLE, WA | SEPTEMBER 19-20, 2013 Adaptive Importance Sampling iteration=2, perplexity=0.872371, essf=0.737913

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23 CORE DATA PROCESSING SOFTWARE PLAN REVIEW | SEATTLE, WA | SEPTEMBER 19-20, 2013 Adaptive Importance Sampling iteration=3, perplexity=0.939877, essf=0.893093

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24 CORE DATA PROCESSING SOFTWARE PLAN REVIEW | SEATTLE, WA | SEPTEMBER 19-20, 2013 Adaptive Importance Sampling iteration=4, perplexity=0.964655, essf=0.934239

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25 CORE DATA PROCESSING SOFTWARE PLAN REVIEW | SEATTLE, WA | SEPTEMBER 19-20, 2013 Using coadd measurements to feed MultiFit

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26 CORE DATA PROCESSING SOFTWARE PLAN REVIEW | SEATTLE, WA | SEPTEMBER 19-20, 2013 Implementation: Current Prototype − Coaddition of PSF models fully implemented − Prototype implemented this summer: Multi-Shapelet model evaluation -one round of profiling: new convolution relation → 3.4x speedup adaptive importance sampling start from coadd, use to feed MultiFit − No shear systematics tests using this code yet; just looking at likelihood surfaces, measuring computational performance. − Next up: use greedy optimization to initialize proposal distributions for importance sampling. − Currently fast enough that we have time for ~30 posterior samples; with expected 4x future speedup, we can do 120, which we think will be enough using importance sampling.

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27 CORE DATA PROCESSING SOFTWARE PLAN REVIEW | SEATTLE, WA | SEPTEMBER 19-20, 2013 Implementation: Construction Roadmap Pipeline Release DateFeatures 8/2014greedy optimizer fitting and importance sampling with single- epoch data and coadds; model photometry; morphological star- galaxy separation 8/2015greedy optimizer fitting and importance sampling in MultiFit mode; micro-optimization of model evaluation code 8/2016moving point source models; fitting in presence of charge- transport effects; decision on hardware architecture 8/2017feed MultiFit using coadd results; shear estimation analysis 8/2018fitting blending objects; computational performance improvements Some features will likely arrive early in the codebase, just as a result of good code design and scientific interest by developers; this roadmap gives us plenty time to make them work well.

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28 CORE DATA PROCESSING SOFTWARE PLAN REVIEW | SEATTLE, WA | SEPTEMBER 19-20, 2013 Summary: the Baseline Plan − Our best deep measurements will come from MultiFit methods, but coadds still have an important role to play. − The use of MultiFit methods isn’t limited to shape measurement, but shape measurement represents the biggest challenge from an algorithmic and computational perspective. − In one summer, with a small team, we’ve mostly reimplemented a state-of- the-art MultiFit shape measurement code, and developed modifications that have the potential to improve the computational performance enough to fit within LSST’s computational budget allow more complex models to be used without a catastrophic increase computation time − Even if the state-of-the-art in 2020 doesn’t look much like lensfit, the combination of an expert development team and a conservative roadmap will ensure we can adapt it to work for LSST.

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29 CORE DATA PROCESSING SOFTWARE PLAN REVIEW | SEATTLE, WA | SEPTEMBER 19-20, 2013 Summary: Responding to the Charge We believe that MultiFit approach to multi-epoch object characterization algorithmically sound and justified. − We believe MultiFit is more algorithmically sound than a purely coadd-based approach, and justified from the perspective that we don’t want to rely on the hope that a purely-coadd based approach will be sufficient. We believe the choice of MultiFit as the default shape measurement algorithm is reasonable given the current state of the art. − Bayesian forward modeling represents the current state of the art, in the form of lensfit, and we have identified ways in which it can be improved from a scientific standpoint to meet LSST requirements. − Bayesian forward modeling is also the most computationally demanding approach to shape measurement, ensuring our cost estimates are conservative. We have a credible plan for code optimizations that will ensure it is computationally feasible for LSST.

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