I’ve noticed that there are rapidly growing interests and attentions in data mining and machine learning among astronomers but the level of execution is yet rudimentary or partial because there has been no comprehensive tutorial style literature or book for them. I recently introduced a machine learning book written by an engineer. Although it’s a very good book, it didn’t convey the foundation of machine learning built by statisticians. In the quest of searching another good book so as to satisfy the astronomers’ pursuit of (machine) learning methodology with the proper amount of statistical theories, the first great book came along is The Elements of Statistical Learning. It was chosen for this writing not only because of its fame and its famous authors (Hastie, Tibshirani, and Friedman) but because of my personal story. In addition, the 2nd edition, which contains most up-to-date and state-of-the-art information, was released recently.

First, the book website:

The Elements of Statistical Learning by Hastie, Tibshirani, and Friedman

You’ll find examples, R codes, relevant publications, and plots used in the text books.

Second, I want to tell how I learned about this book before its first edition was published. Everyone has a small moment of meeting very famous people. Mine is shaking hands with President Clinton, in 2000. I still remember the moment vividly because I really wanted to tell him that ice cream was dripping on his nice suit but the top of the line guards blocked my attempt of speaking/pointing icecream dripping with a finger afterward the hand shaking. No matter what context is, shaking hands with one of the greatest presidents is a memorable thing. Yet it was not my cherishing moment because of icecreaming dripping and scary bodyguards. My most cherishing moment of meeting famous people is the half an hour conversation with late Prof. Leo Breinman (click for my two postings about him), author of probability textbook, creator of CART, and the most forefront pioneer in machine learning.

The conclusion of that conversation was a book soon to be published after explaining him my ideas of applying statistics to astronomical data and his advices to each problems. I was not capable to understand every statistics so that his answer about this new coming book at that time was the most relevant and apt one.

This conversation happened during the 3rd Statistical Challenges in Modern Astronomy (SCMA). Not long passed since I began my graduate study in statistics but had an opportunity to assist the conference organizer, my advisor Dr. Babu and to do some chores during the conference. By accident, I read the book by Murtagh about multivariate data analysis, so I wanted to speak to him. Except that, I have no desire to speak renown speakers and attendees. Frankly, I didn’t have any idea who’s who at the conference and a few years later, I realized that the conference dragged many famous people and the density of such people was higher than any conference I attended. Who would have imagine that I could have a personal conversation with Prof. Breiman, at that time. I have seen enough that many famous professors train people during conferences. Getting a chance for chatting some seconds are really hard and tall/strong people push someone small like me away always.

The story goes like this: a sunny perfect early summer afternoon, he was taking a break for a cigar and I finished my errands for the session. Not much to do until the end of session, I decided to take some fresh air and I spotted him enjoying his cigar. Only the worst was that I didn’t know he was the person of CART and the founder of statistical machine learning. Only from his talk from the previous session, I learned he was a statistician, who did data mining on galaxies. So, I asked him if I can join him and ask some questions related to some ideas that I have. One topic I wanted to talk about classification of SN light curves, by that time from astronomical text books, there are Type I & II, and Type I has subcategories, Ia, Ib, and Ic. Later, I heard that there is Type III. But the challenge is observations didn’t happen with equal intervals. There were more data mining topics and the conversation went a while. In the end, he recommended me a book which will be published soon.

Having such a story, a privilege of talking to late Prof. Breiman through an very unique meeting, SCMA, before knowing the fame of the book, this book became one of my favorites. The book, indeed, become popular, around that time, almost only book discussing statistical learning; therefore, it was an excellent textbook for introducing statistics to engineerers and machine learning to statisticians. In the mean time, statistical learning enjoyed popularity in many disciplines that have data sets and urging for learning with the aid of machine. Now books and journals on machine learning, data mining, and knowledge discovery (KDD) became prosperous. I was so delighted to see the 2nd edition in the market to bridge the gap over the years.

I thank him for sharing his cigar time, probably his short free but precious time for contemplation, with me. I thank his patience of spending time with such an ignorant girl with a foreign english accent. And I thank him for introducing a book which will became a bible in the statistical learning community within a couple of years (I felt proud of myself that I access the book before people know about it). Perhaps, astronomers cannot have many joys from this book that I experienced from how I encounter the book, who introduced the book, whether the book was used in a course, how often book is referred, etc. But I assure that it’ll narrow the gap in the notions how astronomers think about data mining (preprocessing, pipelining, and bulding catalogs) and how statisticians treat data mining. The newly released 2nd edition would help narrowing the gap further and assist astronomers to coin brilliant learning algorithms specific for astronomical data. [The END]

—————————– Here, I patch my scribbles about the book.

What distinguish this book from other machine learning books is that not only authors are big figures in statistics but also fundamentals of statistics and probability are discussed in all chapters. Most of machine learning books only introduce elementary statistics and probability in chapter 2, and no basics in statistics is discussed in later chapters. Generally, empirical procedures, computer algorithms, and their results without presenting basic theories in statistics are presented.

You might want to check the book’s website for data sets if you want to try some ideas described there
The Elements of Statistical Learning
In addition to its historical footprint in the field of statistical learning, I’m sure that some astronomers want to check out topics in the book. It’ll help to replace some data analysis methods in astronomy celebrating their centennials sooner or later with state of the art methods to cope with modern data.

This new edition reflects some evolutions in statistical learning whereas the first edition has been an excellent harbinger of the field. Pages quoted from the 2nd edition.

[p.28] Suppose in fact that our data arose from a statistical model $Y=f(X)+e$ where the random error e has E(e)=0 and is independent of X. Note that for this model, f(x)=E(Y|X=x) and in fact the conditional distribution Pr(Y|X) depends on X only through the conditional mean f(x).
The additive error model is a useful approximation to the truth. For most systems the input-output pairs (X,Y) will not have deterministic relationship Y=f(X). Generally there will be other unmeasured variables that also contribute to Y, including measurement error. The additive model assumes that we can capture all these departures from a deterministic relationship via the error e.

How statisticians envision “model” and “measurement errors” quite different from astronomers’ “model” and “measurement errors” although in terms of “additive error model” they are matching due to the properties of Gaussian/normal distribution. Still, the dilemma of hen or eggs exists prior to any statistical analysis.

[p.30] Although somewhat less glamorous than the learning paradigm, treating supervised learning as a problem in function approximation encourages the geometrical concepts of Euclidean spaces and mathematical concepts of probabilistic inference to be applied to the problem. This is the approach taken in this book.

Strongly recommend to read chapter 3, Linear Methods for Regression: In astronomy, there are so many important coefficients from regression models, from Hubble constant to absorption correction (temperature and magnitude conversion is another example. It seems that these relations can be only explained via OLS (ordinary least square) with the homogeneous error assumption. Yet, books on regressions and linear models are not generally thin. As much diversity exists in datasets, more amount of methodology, theory and assumption exists in order to reflect that diversity. One might like to study the statistical properties of these indicators based on mixture and hierarchical modeling. Some inference, say population proportion can be drawn to verify some hypotheses in cosmology in an indirect way. Understanding what regression analysis and assumptions and how statistician efforts made these methods more robust and interpretable, and reflecting reality would change forcing E(Y|X)=aX+b models onto data showing correlations (not causality).

• Space Weather Research Lab at NJIT
• SEEDS — Solar Eruptive Event Detection System at George Mason University.
• CACTUS A software package for ‘Computer Aided CME Tracking
• SRON in the Netherlands

These seem quite informative and I believe more statisticians and data scientists (signal and image processing, machine learning, computer vision, and data mining) easily collaborate with solar physicists. All the complexity, as a matter of fact, comes from data processing to be fed in to (machine, statistical) learning algorithms and defining the objectives of learning. Once settled, one can easily apply numerous methods in the field to these time varying solar images.

I’m writing this short posting because I finally found those interesting articles that I collected for my previous post on Space Weather. After finding them and scanning through, I realized that methodology-wise they only made baby steps. You’ll see a limited number key words are repeated although there is a humongous society of scientists and engineers in the knowledge discovery and data mining.

Note that the objectives of these studies are quite similar. They described machine learning for the purpose of automatizing the procedure of detecting features of interest of the Sun and possible forecasting relevant phenomena that affects our own atmosphere due to associated solar activities.

1. Automated Prediction of CMEs Using Machine Learning of CME – Flare Associations by Qahwaji et al. (2008) in Solar Phy. vol 248, pp.471-483.
2. Automatic Short-Term Solar Flare Prediction using Machine Learning and Sunspot Associations by Qahwaji and Colak (2007) in Solar Phy. vol. 241, pp. 195-211
   

   Space weather is defined by the U.S. National Space Weather Probram (NSWP) as “conditions on the Sun and in the solar wind, magnetosphere, ionosphere, and thermosphere that can influence the performance and reliability of space-borne and ground-based technological systems and can endanger human life or health”

   Personally thinking, the section of “jackknife” needs to be replaced with “cross-validation.”

3. Automatic Detection and Classification of Coronal Mass Ejections by Qu et al. (2006) in Solar Phy. vol. 237, pp.419-431.
4. Automatic Solar Filament Detection Using image Processing Techniques by Qu et al. (2005) in Solar Phy., vol. 228, pp. 119-135
5. Automatic Solar Flare Tracking Using Image-Processing Techniques by Qu, et al. (2004) in Solar Phy. vol. 222, pp. 137-149
6. Automatic Solar Flare Detection Using MLP, RBF, and SVM by Qu et al. (2003) in Solar Phy. vol. 217, pp.157-172. pp. 157-172

I’d like add a survey paper on another type of learning methods beyond Support Vector Machine (SVM) used in almost all articles above. Luckily, this survey paper happened to address my concern about the “practices of background subtraction” in high energy astrophysics.

A Survey of Manifold-Based Learning methods by Huo, Ni, Smith
[Excerpt] What is Manifold-Based Learning?
It is an emerging and promising approach in nonparametric dimension reduction. The article reviewed principle component analysis, multidimensional scaling (MDS), generative topological mapping (GTM), locally linear embedding (LLE), ISOMAP, Laplacian eigenmaps, Hessian eigenmaps, and local tangent space alignment (LTSA) Apart from these revisits and comparison, this survey paper is useful to understand the danger of background subtraction. Homogeneity does not mean constant background to be subtracted, often cause negative source observation.

More collaborations among multiple disciplines are desired in this relatively new field. For me, it is one of the best data and information scientific fields of the 21st century and any progress will be beneficial to human kind.

1. I must acknowledge him for his kindness and patience. He was my wikipedia to questions while I was studying the Sun.

[arXiv:math.ST:0907.4728]
A survey of cross validation procedures for model selection by Sylvain Arlot

Nonetheless, I’ll not review the paper itself except some quotes:

-CV is a popular strategy for model selection, and algorithm selection.
-Compared to the resubstitution error, CV avoids overfitting because the training sample is independent from the validation sample.
-A noticed in the early 30s by Larson (1931), training an algorithm and evaluating its statistical performance on the same data yields an overoptimistic results.

There are books on statistical resampling methods covering more general topics, not limited to model selection. Instead, I decide to do a little search how CV is used in astronomy. These are the ADS search results. More publications than I expected.

• Kernel regression for determining photometric redshifts from Sloan broad-band photometry [arXiv:0706.2704]
  Wang, D.; Zhang, Y. X.; Liu, C.; Zhao, Y. H.
  Monthly Notices of the Royal Astronomical Society, Volume 382, Issue 4, pp. 1601-1606 (2007)
• STECKMAP: STEllar Content and Kinematics from high resolution galactic spectra via Maximum A Posteriori [arXiv:0507002]
  Ocvirk, P.; Pichon, C.; Lançon, A.; Thiébaut, E.
  Monthly Notices of the Royal Astronomical Society, Volume 365, Issue 1, pp. 74-84 (2006)
• STECMAP: STEllar Content from high-resolution galactic spectra via Maximum A Posteriori [arXiv:0505209]
  Ocvirk, P.; Pichon, C.; Lançon, A.; Thiébaut, E.
  Monthly Notices of the Royal Astronomical Society, Volume 365, Issue 1, pp. 46-73 (2006)
• Automated Detection of Classical Novae with Neural Networks [arXiv:0604236]
  Feeney, S. M et al.
  The Astronomical Journal, Volume 130, Issue 1, pp. 84-94 (2005)
• Estimation of regularization parameters in multiple-image deblurring[arxiv:0405545]
  Vio, R.et al.
  Astronomy and Astrophysics, v.423, p.1179-1186 (2004)
• Machine learning and image analysis for morphological galaxy classification
  de la Calleja, Jorge and Fuentes, Olac
  Monthly Notices of the Royal Astronomical Society, Volume 349, Issue 4, pp. 87-93 (2004)
• Ensembles of Classifiers for Morphological Galaxy Classification
  Bazell, D.; Aha, David W.
  The Astrophysical Journal, Volume 548, Issue 1, pp. 219-223.(2001)
• Bayesian image reconstruction with space-variant noise suppression
  Nunez, J.; Llacer, J.
  Astronomy and Astrophysics Supplement, v.131, p.167-180 (1998)
• Estimating the sun’s rotation from solar oscillations by regularisation
  Thompson, A. M.
  Astronomy and Astrophysics (ISSN 0004-6361), vol. 265, no. 1, p. 289-295. (1992)

One can easily grasp that many adopted CV under the machine learning context. The application of CV, and bootstrapping is not limited to machine learning. As Arlot’s title, CV is used for model selection. When it come to model selection in high energy astrophysics, not CV but reduced chi^2 measures and fitted curve eye balling are the standard procedure. Hopefully, a renovated model selection procedure via CV or other statistically robust strategy soon challenge the reduced chi^2 and eye balling. On the other hand, I doubt that it’ll come soon. Remember, eyes are the best classifier so it won’t be a easy task.

With my limited knowledge, I cannot lay out all important aspects in solar physics, climate changes (not limited to our lower atmosphere but covering the space between the sun and the earth) due to solar activities, and the most important issues of recent years related to space weather. Only I can emphasize that compared to earth climate/atmosphere or meteorology, contribution from statisticians to space weather is almost none existing. I’ve witnessed frequently that crude eyeballing instead of statistics in analyzing data and quantifying images occurs in Solar Physics. Luckily, a few articles discussing statistics are found and my discussion is rather focused on these papers while leaving a room for solar physicists to chip in how space weather is dealt statistically for collaborating with statisticians.

By the way, I have no intention of degrading “eyeballing” in data analysis by astronomers. Statistical methods under EDA, exploratory data analysis whose counterpart is CDA, confirmatory data analysis, or statistical inference, is basically “eyeballing” with technical jargon and basics from probability theory. EDA is important to doubt every step in astronomers’ chi-square methods. Without those diagnostics and visualization, choosing right statistical strategies is almost impossible with real data sets. I used “crude” because instead of using “edge detection” algorithms, edges are drawn by hand via eyeballing. Also, my another disclaimer is that there are brilliant image processing/computer vision strategies developed by astronomers, which I’m not going to present. I’m focusing on small areas in statistics related to space weather and its forecasting.

Statistical Assessment of Photospheric Magnetic Features in Imminent Solar Flare Predictions by Song et al. (2009) SoPh. v. 254, p.101.

Their forte is “logistic regression” a statistical model that is not often used in astronomy. It is seen when modeling binary responses (or categorical responses like head or tail; agree, neutral, or disgree) and bunch of predictors, i.e. classification with multiple features or variables (astronomers might like to replace these lexicons with parameters). Also, the issue of variable selection is discussed like L_{gnl} to be the most powerful predictor. Their training set was carefully discussed from the solar physical perspective. Against their claim that they used “logistic regression” to predict solar flares for the first time, there was another paper a few years back discussing “logistic regression” to predict geomagnetic storms or coronal mass ejections. This statement can be wrong if flares and CMEs are exclusive events.

The Challenge of Predicting the Occurrence of Intense Storms by Srivastava (2006) J.Astrophys. Astr. v.27, pp.237-242

Probability of the storm occurrence is response in logistic regression model, of which predictors are CME related variables including latitude and longitude of the origin of CME, and interplanetary inputs like shock speeds, ram pressure, and solar wind related measures. Cross-validation was performed. A comment that the initial speed of a CME might be the most reliable predictor is given but no extensive discussion of variable selection/model selection.

Personally speaking, both publications^[1] can be more statistically rigorous to discuss various challenges in logistic regression from the statistical learning/classification perspective and from the model/variable selection aspect to define more well behaving and statistically rigorous classifiers.

Often times we plan our days according to the weather forecast (although we grumble weather forecasts are not right, almost everyone relies on numbers and predictions from weather people). Although it may not be 100% reliable, those forecasts make our lives easier. Also, more reliable models are under developing. On the other hand, forecasting space weather with the help of statistics is yet unthinkable. However, scientists and engineers understand that the reliable space weather models help planning space missions and controlling satellites into safety mode. At least I know is that with the presence of flare or CME forecasting models, fewer scientists/engineers need to wake up in the middle of night, because of, otherwise unforeseen storms from the sun.

1. I thought I collected more papers under “statistics” and “space weather,” not just these two. A few more probably are buried somewhere. It’s hard to believe such rich field is not touched by statisticians. I’d appreciate very much your kind forwarding those relevant papers. I’ll gradually add them.

From A Survey of the Statistical Theory of Shape by David G. Kendall, Statistical Science, Vol. 4, No. 2 (May, 1989), pp. 87-99.
It is well known that no classical test for two dimensional stochastic point processes can match the performance of the human eye and brain in detecting the presence of improbably large holes in the realized pattern of points. This fact has generated a great deal of research in the last few years, especially in connection with the large “voids” and long “strings” that the eye sees (or declares that it sees) in maps of the Shane and Wirtanen catalogue of positions of galaxies. Astronomers are interested in (i)whether these phenomena are sufficiently extreme to require explanation, and if so (ii) whether any of the various “model” universes now in vsgue can be said to display them to just the same degree.

Survey and population studies generally invite large data sets. Any discussion about individual objects from that survey is an indication that those objects are outliers with respect to the objects in the catalog, created from survey and population studies. These outliers are the objects deserving strong spotlights, in contrast to the notion that outliers are useless. Other than studies about outliers, survey and population studies generally involve machine learning and pattern recognition, or supervised learning and unsupervised learning, or classification and clustering, or statistical learning. Whatever jargon you choose to use, the book overviews most popular machine learning methods extensively with examples, nice illustrations, and concise math. Upon understanding characteristics of the catalog such as dimensions, sample size, independent variable, dependent variable, missing values, sampling (volume limited, magnitude limited, incompleteness), measurement errors, scatter plots, and so on, as a second step to summarize the large data as a whole, the book could offer proper approaches based on your data analysis objective in a statistical sense – in terms of summarizing data.

Click here to access the book website for various resources including a few book chapters, retailer links, examples, and solutions. One of reviews you can check.

A lesson from reading arxiv/astro-ph during the past year is that astronomers must become interdisciplinary particularly those in surveys and creating catalogs. From the information retrieval viewpoint, some rudimentary education about pattern recognition and machine learning is a must as I personally think basic statistics and probability theory should be offered to young astronomers (like astrostatistics summer school at Penn State). While attending graduate school, I saw non stat majors taking statistics classes, except students from astronomy or physics. To confirm this hypothesis, I took computational physics to learn how astronomers and physicists handle data with uncertainty. Although it was one of my favorite classes, the course was quite off from statistics. (Game theory was the most statistically relevant subject.) Hence, I think not many astronomy departments offer practical statistics courses or machine learning and therefore, recommending good and modern textbooks related to (statistical) data analysis can be beneficial to self teaching astronomers. I hope my reasoning is in the right track.

I’m glad to see this week presented a paper that I had dreamed of many years ago in addition to other interesting papers. Nowadays, I’m more and more realizing that astronomical machine learning is not simple as what we see from machine learning and statistical computation literature, which typically adopted data sets from the data repository whose characteristics are well known over the many years (for example, the famous iris data; there are toy data sets and mock catalogs, no shortage of data sets of public characteristics). As the long list of authors indicates, machine learning on astronomical massive data sets are never meant to be a little girl’s dream. With a bit of my sentiment, I offer the list of this week:

• [astro-ph:0804.4068] S. Pires et al.
  FASTLens (FAst STatistics for weak Lensing) : Fast method for Weak Lensing Statistics and map making
• [astro-ph:0804.4142] M.Kowalski et al.
  Improved Cosmological Constraints from New, Old and Combined Supernova Datasets
• [astro-ph:0804.4219] M. Bazarghan and R. Gupta
  Automated Classification of Sloan Digital Sky Survey (SDSS) Stellar Spectra using Artificial Neural Networks
• [gr-qc:0804.4144]E. L. Robinson, J. D. Romano, A. Vecchio
  Search for a stochastic gravitational-wave signal in the second round of the Mock LISA Data challenges
• [astro-ph:0804.4483]C. Lintott et al.
  Galaxy Zoo : Morphologies derived from visual inspection of galaxies from the Sloan Digital Sky Survey
• [astro-ph:0804.4692] M. J. Martinez Gonzalez et al.
  PCA detection and denoising of Zeeman signatures in stellar polarised spectra
• [astro-ph:0805.0101] J. Ireland et al.
  Multiresolution analysis of active region magnetic structure and its correlation with the Mt. Wilson classification and flaring activity

A relevant post related machine learning on galaxy morphology from the slog is found at svm and galaxy morphological classification

< Added: 3rd week May 2008>[astro-ph:0805.2612] S. P. Bamford et al.
Galaxy Zoo: the independence of morphology and colour