1909.11714.pdf

Astro2020 State of the Profession

Consideration White Paper

Realizing the potential of astrostatistics and

astroinformatics

September 27, 2019

Principal Author:

Name:

Gwendolyn Eadie

,

,

,

,

Email: eadieg@uw.edu

Co-authors:

Thomas Loredo

,

, Ashish A. Mahabal

,

,

,

, Aneta Siemiginowska

,

, Eric Feigelson

,

Eric B. Ford

,

, S.G. Djorgovski

,

, Matthew Graham

,

,

eljko Ivezi

,

, Kirk Borne

,

Jessi Cisewski-Kehe

,

,

, J. E. G. Peek

,

, Chad Schafer

,

, Padma A.

Yanamandra-Fisher

,

, C. Alex Young

,

Cornell University, Cornell Center for Astrophysics and Planetary Science (CCAPS) & Department of

Statistical Sciences, Ithaca, NY 14853, USA

Division of Physics, Mathematics, & Astronomy, California Institute of Technology, Pasadena, CA

91125, USA

Center for Astrophysics

Harvard & Smithsonian, Cambridge, MA 02138, USA

eScience Institute, University of Washington, Seattle, WA 98195, USA

DIRAC Institute, Department of Astronomy, University of Washington, Seattle, WA 98195, USA

Department of Astronomy, University of Washington, Seattle, WA 98195, USA

Penn State University, University Park, PA 16802, USA

Booz Allen Hamilton, Annapolis Junction, MD, USA

Department of Statistics & Data Science, Yale University, New Haven, CT 06511, USA

Department of Physics & Astronomy, Johns Hopkins University, Baltimore, MD 21218, USA

Space Telescope Science Institute, Baltimore, MD 21218, USA

Department of Statistics & Data Science Carnegie Mellon University, Pittsburgh, PA, USA

Founder, The PACA Project, Space Science Institute, Boulder, CO 80301, USA

NASA Goddard Space Flight Center, Greenbelt, MD 20771 USA

American Astronomical Society Working Group on Astroinformatics and Astrostatistics

American Astronomical Society Working Group on Time-Domain Astronomy

American Statistical Association Astrostatistics Interest Group

International Astronomical Union Commission B3 on Astroinformatics & Astrostatistics

LSST’s Informatics and Statistics Science Collaboration (ISSC)

International AstroInformatics Association

arXiv:1909.11714v1 [astro-ph.IM] 25 Sep 2019

1 The growing impact of astrostatistics and astroinformatics

Astrostatistics and astroinformatics (A&A) comprise interdisciplinary research combining

astronomy with one or more of the information sciences, including statistics, machine learning,

data mining, computer science, information engineering, and related fields. For the Astro2010

decadal survey, nearly 100 astronomers and information scientists submitted two State of the

Profession Position Papers (Borne

et al.

, 2009; Loredo

et al.

, 2009) highlighting the potential of

the then-emerging areas of astrostatistics and astroinformatics to make transformative

contributions to astronomy, if only support for research and education in those areas could be

enhanced. In the decade since, the size and impact of A&A has grown dramatically, despite only

modest changes in formal support of these areas.

In the time since Astro2010, the community of A&A researchers has grown tremendously in size.

Scholarly societies and large astronomy projects have responded with the creation of several

A&A groups, with a combined membership of several hundred astronomers and information

scientists: LSST’s Informatics and Statistics Science Collaboration (ISSC, 2009, 72 members),

the International Astrostatistics Association

(IAA, 2012, 601 members), the American

Astronomical Society Working Group in Astroinformatics and Astrostatistics

, (WGAA; 2012,

116 members) the American Astronomical Society Working Group on Time Domain Astronomy

(2014), the American Statistical Association Astrostatistics Interest Group

(2014, 111 members),

the IEEE Astrominer Task Force (2014), the International Astronomical Union Commission B3

on Astroinformatics & Astrostatistics

(2015, 239 members), and the International

AstroInformatics Association

(2019, 182 members).

Various teams from within the A&A community have submitted multiple Science White Papers

addressing recent and future A&A science impacts in various areas of astronomy, and APC White

Papers addressing specific A&A considerations such as the needs of petascale A&A research, and

education and collaboration support issues.

This White Paper is authored by leaders of the A&A groups listed above, and reflects broad A&A

support considerations discussed across their memberships. It briefly

highlights the strong and

growing impact of A&A, identifies key issues hampering the growth of this new field, and

offers recommendations for improved support of both research and education in A&A.

This

WP is not comprehensive; it does not address a number of astroinformatics issues, especially in

the arenas of data systems, cyberinfrastructure, Virtual Observatory, etc..

At the turn of the century, SDSS — the first large-scale, public, digital sky survey — dramatically

increased interest in statistics as well as machine learning and other computational sciences.

Indeed, SDSS is cited as an early example of the so-called Fourth Paradigm of science —

data-intensive science

, colloquially called “big data science” (Hey

et al.

, 2009; Bell

et al.

, 2009).

Many astronomical data sources embody the classic “three Vs” —

volume, variety and velocity

—

http://iaa.mi.oa-brera.inaf.it/IAA/home.html

https://aas.org/comms/working-group-astroinformatics-and-astrostatistics-wgaa

https://aas.org/comms/working-group-time-domain-astronomy-wgtda

https://community.amstat.org/astrostats/home

https://www.iau.org/science/scientific_bodies/commissions/B3/

http://astroinformatics.info/

distinguishing data-intensive science, particularly with recent wide-field surveys, optical/infrared

integral field units, and radio interferometric instruments from earlier smaller and narrowly

focused astronomy problems. Time domain survey astronomy has emerged as a major endeavor

as wide-field telescopes, both large and small, are dedicated to repeated photometric

measurements of celestial populations, producing particularly large datasets. Extracting sound

science from complex data often requires advanced statistical and computational methods, even at

relatively smaller volumes. Challenging A&A research problems arise across the full spectrum of

dataset scales. To highlight broader data science challenges, researchers have added other “Vs” to

the list of big-data Vs, most notably

veracity

, referring to the need to quantify uncertainty in

data-based inferences, whether based on big datasets or modest ones.

Figure 1:

Research papers using the emerg-

ing methodology published in AAS Jour-

nals since 2000. The number of papers/yr is

log10 scale. Methodology is marked in col-

ors: Bayesian - purple, Machine Learning -

yellow, Gaussian Processes - red, Random

Forests - grey, Deep Learning - green.

Recent

data challenges

provide excellent examples

of the value of considering diverse methodologies

for complex problems, and highlight the need

to seek interdisciplinary collaboration. A decade ago,

the Gravitational LEnsing Accuracy Testing (GREAT)

weak lensing shear measurement competitions,

GREAT08 and GREAT10 (including galaxy and

star/PSF shape measurement challenges, Bridle

et al.

2010; Kitching

et al.

2012, 2013), were announced

Annals of Applied Statistics

. They drew submissions

from dozens of teams, many submitting results

from multiple methods, with several teams comprising

non-astronomers. The GREAT08 prize went to a

pair of computer scientists; the GREAT10 galaxy prize

went to a pair of astronomers new to weak lensing,

with organizers describing it as

“a major success in its

effort to generate new ideas and attract new people into

the field.”

The more recent 2018 Photometric LSST

Astronomical Time-Series Classification Challenge

(PLAsTiCC, Kessler

et al.

2019) took advantage of

newer crowd-sourcing tools (via the Kaggle platform),

and attracted over 1000 submissions. Among the top five performing teams, only a single

participant was an astronomer.

The rise of advanced methodologies is recent and incredibly rapid with significant response by

the research community. Basic bibliometric statistics, displayed in Fig. 1, show that the use of

many modern approaches and methods — e.g., Bayesian statistics, machine learning, Gaussian

processes, random forests, and deep learning — is growing exponentially. The

Appendix

describes

selected themes of emerging, advanced A&A research, highlighting the breadth of methods and

applications, and the rapid growth of interest in adapting state-of-the art data science methods to

astronomy. During the 2013–19 period, the number of jobs emphasizing data analysis

methodology offered to Ph.D. astronomers (both post-doc and faculty positions) approximately

https://mapr.com/blog/top-10-big-data-challenges-serious-look-10-big-data-vs/

doubled

. The Astrostatistics Facebook group

has over 4000 members with new members

joining daily. The community interest reflects the need for new methodology, and also for

communication and training, as the standard training of astronomers lags behind.

The growth of interest in A&A research stands in contrast to serious deficiencies in support of the

A&A education and research enterprise. The following section highlights three key gaps between

needs and available resources for realizing the potential of A&A to meet current and emerging

science challenges. The final section offers specific recommendations to close these gaps.

2 Key Issues: Education, funding, and quality control

Recent developments in methodology were not widely anticipated and have proceeded rapidly.

This has resulted in unfamiliar challenges and imbalances for the educational, funding, and

quality control structures of the field. In the following subsections, we describe in detail the

challenges and imbalances in each of these three areas. From here, it is clear that actions are

needed by different segments of the community — universities, observatories and institutes,

funding agencies, and leadership organizations like the National Academy of Sciences — and we

outline some recommendations in Section 3.

2.1 The education gap

Astronomers are well-trained in mathematics relating to physical processes in order to do

astrophysics, but not in applied mathematics, statistics, and computer science relating to

extraction of reliable information from complex, noisy datasets. They are typically conversant

with computer programming and processing on a moderate scale, but many are not prepared for

the world of Big Data with challenges in data storage, access, and efficient analysis on high

performance multicore computers, and modern software development practices.

The problem arises in the curriculum of physical scientists: courses in modern statistics, applied

mathematics, and computer science are not in the required curriculum. For computation, this

deficiency has been recently documented among astronomers: a survey of

≈

1100

astronomers

found that 90% write software but only 8% received substantial training in software development

(Momcheva and Tollerud, 2015). Informal on-the-job training is adequate for some purposes, but

limits reproducibility, results in inefficient duplication, and can lead to mediocrity, or even

unnecessary failure, for more challenging problems. The methodology needed for astronomy and

astrophysics is so diverse that specialized coursework in the usage of statistical software

environments and computer resources is essential for the astronomical research enterprise.

This deficit in the education of astronomers has been repeatedly noted: recent NASA

and

National Academy of Sciences

reports emphasize the need for professional training beyond

https://asaip.psu.edu/resources/jobs

https://www.facebook.com/groups/astro.r/

Big Data @ STScI: Enhancing STScI’s Astronomical Data Science Capabilities over the Next Five Years (2016),

http://archive.stsci.edu/reports/BigDataSDTReport_Final.pdf

Optimizing the U.S. Ground-Based Optical and Infrared Astronomy System (2015), National Academy Press

https://www.nap.edu/

long-standing formal education in the physical sciences. Some progress has been made.

Textbooks on statistical methodology and data analysis (with computer codes) for astrophysics

are available and taught in some universities (e.g., Feigelson and Babu, 2012; Ivezi

et al.

, 2014;

Bailer-Jones, 2017; Hilbe

et al.

, 2017)

. Informal Summer Schools, Hack Days, and tutorials

have proliferated. However, except perhaps for disorganized Facebook-based discussion forums,

these resources are touching relatively few astronomers (perhaps 10%).

University curricula are not renovating fast enough to match the needs of methodological

education for future space scientists, and professional development resources are insufficiently

funded or organized to meet the needs of the research community.

2.2 The funding gap

Grants to universities and other institutions specifically designed to improve methodology for

astronomical research are very scarce. NASA closed its only grant program in this area in 2011

Applied Information Science Research Program (AISRP). This program was critical, for example,

to the development of the worldwide Virtual Observatory (Szalay, 2014), and funded many

smaller-scale A&A efforts, including development of SAOImage-DS9 and work on new

statistical and machine learning algorithms by individual investigators and multi-university

collaborations (the NASA

Astrophysics Research, Analysis & Enabling Technology 2011 Review

Panel

evaluated the AISRP program in more detail

). NSF has had short-lived interdisciplinary

grant programs to promote mathematical developments for astronomy, and has supported

astrostatistics at SAMSI programs. While astronomers do have access to agency-wide programs

in cyberscience such as the Computational and Data-Enabled Science and Engineering (CDS&E)

and various cyber infrastructure programs, the success rate of such proposals may be

de facto

limited by level of buy-in from NSF’s Division of Astronomical Sciences.

Other scientific fields do not have these structural problems. Biostatistics is taught in most

universities and has been heavily funded by NIH for decades with many large grant programs

Statistics and informatics for Earth sciences have been well-funded by the NSF and NASA

coordinated by the inter-agency Big Earth Data Initiative, with results presented in several dozen

poster sessions at annual AGU meetings.

see

https://asaip.psu.edu/resources/recent-books/methodology-books-for-astronomy

See the July 2011 section of the NAC Astrophysics Subcommittee site.

For illustration, the following NIH grant programs are available in cancer research (

statfund.cancer.gov/

funding

): Big Data to Knowledge; Development of Informatics Technology; Informatics Technology for Cancer

Research; Bridging the Gap between Cancer Mechanism and Population Science; Spatial Uncertainty: Data, Model-

ing, and Communication; Cancer Intervention and Surveillance Modeling Network; Short Courses on Mathematical,

Statistical, and Computation Tools for Studying Biological Systems; NIDCR Grants for Data Analysis and Statistical

Methodology applied to Genome-wide Data; NLM Express Analysis in Biomedical Informatics; Integrative Omics

Data Analysis for Biomedical Informatics; New Computational Methods for Understanding the Functional Role of

DNA Variants.

The following NSF grant programs are available in geosciences, in addition to agency-wide programs in math-

ematics and cyberscience: Collaboration in Mathematical Geosciences; EarthCube; Geoinformatics; Signals in the

Soil; Advanced Digitization of Biodiversity Collections. NASA operates the: Earth Observing System Data and

Information System; NASA Center for Climate Simulation

2.3 The quality gap

The culture of our research community and funding agencies is fully cognizant that major

advances are driven by improvements in instrumentation, and that these instruments require

software for operation and knowledge extraction. It is less well recognized that new instruments

give rise to science questions so diverse and complex that traditional data analysis procedures are

often inadequate. The knowledge and skills of the statistician, applied mathematician, and

algorithmic computer scientist need to be incorporated into programs that currently emphasize

engineering and physical science in order to fully achieve the scientific potential of instruments

and telescopes and the data they provide. These issues might be divided into two stages: (1) data

reduction through software pipelines (often developed within instrumentation groups, but ripe for

methodological improvements from the broader community); and (2) science analysis that is

performed by hundreds of scientists dispersed through U.S. universities and abroad. Both stages

benefit from modern statistical and computational methods; in some cases, the science result is

completely inaccessible without state-of-the-art methodology.

High standards for analysis methodology are not set consistently for publications, instrument

analysis pipelines, science analysis software developed by national observatories or space mission

science centers, or for software produced by extramural science programs. The result is uneven

quality in data and science analysis products; the methods used in astronomical software systems

for data processing and science analysis are often inappropriate and/or obsolete (e.g., see

Protassov

et al.

, 2002; Tak

et al.

, 2018). Limited peer review resources often make these kinds of

problems undetectable until after publication.

3 Strategic Plan

We have outlined an unusual situation for our profession: the historical unfamiliarity of research

based on advanced cross-disciplinary methodology, and the rapidity of its growth, have led to

imbalances that hinder research. Strides made in methodologies and computer science are often

not incorporated into astronomical research because we lack adequate educational, funding, and

quality control structures. In the last decade or so,

data science

has gained traction in both

industry and academia; privately funded data science centers have appeared in industry and data

science institutes have appeared in universities. While these centers and institutes have

contributed to the development of new methodologies in A&A, they are often not fully utilized by

astronomy departments at universities and do not provide enough focused support for astronomy.

Thus, a serious organizational commitment from the astronomy community at many levels is

needed.

The problems outlined in Section 2 can be substantially rectified if concerted effort is made by the

funding agencies, national observatories and mission centers, universities, and scholarly societies.

Large projects could not only fund software pipelines, but also cross-disciplinary study and

oversight so the pipelines and associated science analysis software incorporate modern statistical

and computational methods. National institutes could nurture internal teams devoted to

methodology and hire consultants to advise large hardware and research groups. Universities can

offer undergraduate and graduate courses in statistics, informatics, and the data sciences within

astronomy programs, assuring students interested in data-intensive research careers sufficient

curricular flexibility to become appropriately trained.

Cross-disciplinary interest groups that have emerged in scholarly societies can be energized with

funds to organize collaborative research efforts, conferences and workshops, and informal

education tutorials.

The obvious result of the lack of investment and commitment by the American astronomical

enterprise in astrostatistics and astroinformatics is the loss of astronomical results, particularly

relating to Big Data science from LSST and its predecessor instruments. During the past decade,

A&A has been established as an important research area in the astronomical community. The

importance of this research should be also recognized by agencies and universities, and supported

by appropriate changes in the funding and educational structures.

With these issues in mind, we offer the following recommendations. We estimate that the total

new cost for implementing our specific research and training recommendations is a few million

dollars annually, a small fraction of annual spending in astronomy. This small investment will

have a disproportionately large impact on A&A and on astronomy as a whole. Our team does not

have the resources and expertise to assess costs in detail; further, several recommendations involve

adjusting the balance of various resources (monetary and otherwise) across multiple stakeholders.

We propose that the Astro2020 survey recommend that the AAS or another appropriate body

establish a committee to review the support of A&A, using these recommendations as a starting

point.

The committee should be provided sufficient resources and access to stakeholders to enable

developing detailed and realistic recommendations for improved support of A&A.

3.1 Closing the education gap

3.1.1 Universities and National Observatories

•

Universities should revise the curriculum in undergraduate physical science to require

courses in applied statistics, mathematics, and computer science. At the graduate level,

specialized courses in computational methods and usage of statistical methods should be

incorporated into the astronomy and astrophysics curriculum. Specifically, students should

learn how to use modern astronomy computing environments, and how to harness modern

computing hardware efficiently.

•

Universities and national observatories should develop information science courses for

astronomers at the undergraduate and graduate levels.

•

Universities and national observatories should financially support summer schools and

cross-disciplinary workshops on advanced methods, both to train astronomical data science

researchers and to integrate this emerging area into mainstream astronomy.

•

Universities and national observatories should establish specialized permanent

appointments for data science in astronomy, as routinely as they now do for

observers/instrumentalists and theorists. Cross-appointment permanent positions (e.g., with

statistics departments, computer science departments, etc.) should also be considered.

3.1.2 NSF and NASA

•

NSF and NASA should establish mechanisms to support educators interested in developing,

curating, improving, maintaining, and/or disseminating astroinformatics materials that

accelerate and improve astroinformatics education in the community.

•

NSF and NASA should survey their existing programs, at the agency and center levels (e.g.

NASA centers), which support the A&A education of the community within these agencies.

This includes programs such as the Frontier Development Lab from NASA Ames, NASA

Goddard’s astropy summer schools, and the astroinformatics working groups at Goddard

(and other centers).

3.2 Closing the funding gap

3.2.1 Universities and National Observatories

•

University astronomy departments and National Observatories should work with internal

data science institutes and other departments (e.g. statistics, mathematics, computer

science) to offer competitive, interdisciplinary postdoctoral fellowships in A&A.

•

Universities should financially support multidisciplinary PhDs in astronomy (e.g., in A&A).

This would also encourage graduates to enter astronomy programs even if they are

interested in possibly pursuing a more general career in data science.

3.2.2 NSF and NASA

•

NSF should provide interdisciplinary grant support for research related to A&A.

•

NSF Division of Astronomical Sciences should pursue partnerships in support of medium

and large projects that have a significant astronomical data science component.

•

With community input, NASA should be urged to reorganize its support of data analysis

and information science research. There should be a focus on financial support for both

routine and advanced data analysis research that serves space-based astrophysics through

development, adaptation, validation and application of modern A&A methods.

•

Both NASA and NSF A&A research programs should implement explicitly multi-tiered

support, with different categories of research of various duration and levels of funding.

Long-term funding must be included, especially targeting young researchers.

•

NASA and NSF should encourage reviewers of postdoctoral fellowship applications to

recognize A&A, including both proposed A&A research and/or a track-record of

high-quality A&A in previous research publications.

•

NASA and NSF should instate a 3-year interdisciplinary fellowship program in

astronomical data sciences. This would encourage young scientists to pursue A&A careers,

and would bring recognition to these scientists and to the discipline.

•

NASA and NSF should also support astronomical data science research targeting

infrastructure

(e.g., data management and computational resource management research,

including development of astronomy-oriented parallel, grid, and cloud computing software

environments, and maintaining the critical software tools). Such support should be

separated from support from focused,

science-driven data science research

, either via

separate programs, or via explicitly identified proposal categories within a single program.

•

Similarly, NASA and NSF should support the development of significant public,

open-source software that provides important science-enabling technology, much like the

development of a new instrument. As with instruments, significant codebases need

maintenance, and funding channels need to support major updates of widely-used

codebases similar to how instrument maintenance is supported.

•

Agencies should develop or adapt funding opportunities enabling support of A&A data

challenges, like those mentioned in

1. Data challenges (e.g. PLAsTiCC) draw in

participants from communities outside of astronomy, and could lead to more

interdisciplinary collaboration and higher quality research.

•

We echo the recommendations made in the NASA Task Force on Big Data for SMD

Recommendation: SMD should establish a new division that would focus on cross-cutting

data science and computing projects and whose responsibilities would include establishing

the Data Science Applications Program which will promote bringing modern data science

methodologies into SMD’s data analysis worlds including the science operations of SMD’s

missions.

Recommendation: In staffing the Science Committee and the four thematic Science

Advisory Committees, SMD should ensure that at least one appointment on each of these

committees is reserved for an expert who is a routine user of high-performance computers

(NASA’s or others), is active in employing modern data science methodologies, and/or is

deeply involved in the science operations of large, complex scientific data archives.

Recommendation: NASA should make prioritized investments in computing and analysis

hardware, workflow software and education and training to substantially accelerate

modeling workflows. NASA should take the lead to make substantial increases in: ...

software modernization; resources to develop new data analysis paradigms; education and

training workshops, scientific conferences and journal special collections to effect a culture

acceptance of the importance of workflow development and management; . . . lossy data

compression and more advanced methods for signal detection.

3.3 Closing the quality gap

•

Journals should maintain high standards for analysis methodology and algorithms. This

may involve supporting a statistics/informatics editor (as is currently done by the AAS

journals), and modifying review processes to ensure that papers with significant A&A

https://science.nasa.gov/science-committee/subcommittees/

big-data-task-force

content are examined by reviewers with expertise in both the relevant astrophysics and the

relevant information science. Authors should be strongly encouraged (perhaps required, in

some circumstances) to make computational results reproducible, e.g., by publishing

software, repositories, and/or computational “notebooks” along with papers.

•

Astronomy curricula should include training in best practices in development of software,

e.g., by encouraging or requiring formal training in programming and development

practices from faculty actively engaged in astroinformatics education, computer science

departments, and/or from well-vetted training programs (e.g., Software Carpentry).

•

Support interdisciplinary collaborations that seek funding to include substantive

contributions from experts in specific algorithms and/or computational methods that could

advance their research goals.

•

Funding agencies should encourage production of open-source software; this development

model improves code quality in broad scientific applications.

4 Appendix: Emerging data science themes in astronomy

Here we briefly survey a selection of important data science areas where recent developments in

statistics and machine learning are beginning to make significant impacts in astronomy

. This

survey is by no means exhaustive, nor are the highlighted applications meant to be endorsements

of specific approaches. Rather, this survey is intended to display the broad scope of data science

research in astronomy and its potential for producing qualitative advances in our ability to distill

science from data. Few if any of the highlighted approaches are covered in the recent spate of

books on statistics and machine learning in astronomy, emphasizing the need for interdisciplinary

research and collaboration.

Nonlinear dimensionality reduction.

Many astronomical datasets “live” in a high-dimensional

space. An observed spectral energy distribution comprising measurements in dozens, hundreds,

or thousands of spectral bands may be considered to be a vector in a sample space with a

dimension for each band. An image with a million spatial pixels may be considered as a vector in

a million-dimensional sample space. Empirically, a collection of many cases of such data very

often lies on or near a low-dimensional manifold in the full sample space. Discovering such a

manifold can enable dramatic improvement in inference tasks such as classification or regression

(characterizing correlations). When that manifold is a hyperplane, it may be found using

techniques from linear algebra that are well-known to astronomers,

principal component analysis

(PCA) being the best-known example. But more often, the manifold will be a complex curve or

surface, and discovering it requires tools for

nonlinear dimensionality reduction

. This has been a

major research area in statistics and machine learning in the last decade, with several new

techniques making significant impacts in diverse areas of astronomy. Several of the most

successful approaches rely on analysis of the matrix of pairwise distances or similarities of the

data (

spectral clustering

spectral connectivity analysis

). Examples include use of diffusion

maps for supernova classification, locally-biased spectral graph analysis for describing SDSS

see also the Science White Paper submitted to the Astro2020 in March 2019 (Siemiginowska

et al.

, 2019)

galaxy spectra, t-Distributed Stochastic Neighbor Embedding (t-SNE) for classification of

supernovae and stellar spectra, and convolutional neural network based autoencoders for radio

galaxy classification (Richards

et al.

, 2011; Lawlor

et al.

, 2016; Lochner

et al.

, 2016; Reis

et al.

2018; Ma

et al.

, 2019).

Sparsity.

A similar but complementary kind of reduction in complexity can occur in the

parameter space used to describe the “true” signals underlying observed data. Signals are often

best described in a

transform

space, e.g., Fourier space for periodic time-domain signals, or

wavelet or shapelet spaces for images. Empirically, many natural signals have very sparse

representations in an appropriately selected transform space. E.g., although the Fourier transform

of a light curve with N time samples has O(N) Fourier coefficients, periodic light curves can be

described with many fewer than O(N) coefficients. Similarly, image compression exploits the

observation that natural images with N pixels are well-described with many fewer than O(N)

coefficients in, say, a discrete cosine transform (DCT) or wavelet basis. Information scientists are

devising new models and algorithms that exploit knowledge of sparsity to improve signal

recovery. A notable example is

compressed sensing

, a class of signal processing techniques that

exploits sparsity in a transform space to enable recovery of complex signals even when the

data

are relatively sparse (e.g., not fully covering Fourier space). Example applications in astronomy

include improving image recovery in radio interferometry, measuring cosmological image

distortions due to weak lensing, and inverting solar flare differential emission measure (DEM)

data. The method now appears in about 30 astronomy papers/yr. (Hastie

et al.

, 2015; Wiaux

et al.

2009; Leonard

et al.

, 2012; Carrillo

et al.

, 2014; Cheung

et al.

, 2015)

Deep learning.

Many flexible model architectures in statistics and machine learning are built by

composition of a large number of simple elements. Examples include basis expansions (e.g.,

linear combinations of Fourier or wavelet basis functions) and artificial neural nets (ANNs, linear

combinations of simple but nonlinearly tunable “activation functions”). Early theoretical work on

the approximation power of ANNs showed that the flexibility of such compositions could be

greatly enhanced by layering: for models with fixed “width” (the number of linearly combined

components), flexibility can be greatly enhanced by adding “depth” (using the outputs of

components of one layer as inputs to a new layer of superposed components). Since the early

2000s, advances in training algorithms for deep models, combined with wide availability of

massively parallel computing capability via GPUs and large training sets, have enabled deep

learning (DL) algorithms to leapfrog competitors in many industrial applications (e.g., speech and

image recognition and classification). A key aspect of these algorithms has been inclusion of

dimension-reducing layers, e.g., via tunable convolution or subsampling operations. These enable

DL models to discover rich

hierarchical feature representations

of data, e.g., describing an image

in terms of edges with different orientations at the lowest level, groups of edges comprising more

complex features at the next level, and so on. It has long been appreciated that feature selection is

crucial to the performance of machine learning algorithms; DL models can partly automate

feature selection. DL is being applied to diverse learning tasks in many areas of astronomy, e.g.,

classification of galaxy images and stellar spectra, image deblending, photometric redshift

estimation, classification of variables and transients, and source discovery in multimessenger

astronomy (Goodfellow

et al.

, 2016; Hoyle, 2016; Mahabal

et al.

, 2017; Pasquet

et al.

, 2019;

Allen

et al.

, 2019; Boucaud

et al.

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