1. Pat Langley School of Computing and Informatics Arizona State University Tempe, Arizona Institute for the Study of Learning and Expertise Palo Alto, California Challenges for the Computational Discovery of Scientific Knowledge Thanks to K. Arrigo, D. Billman, M. Bravo, S. Borrett, W. Bridewell, S. Dzeroski, and L. Todorovski for their contributions to this research, which is funded by a grant from the National Science Foundation.

2. Drawbacks of Scientific Data Mining  generates models in forms inappropriate to most sciences  makes incorrect assumptions about the available inputs  focuses on convenient algorithmic issues, not scientists’ needs Because it borrows from work on commercial applications, most work on scientific data mining: We need to redirect attention toward a broader range of discovery tasks that actually arise in scientific fields. Data-mining researchers would benefit from looking at the older literature on computational scientific discovery.

3. Claim 1: Scientific Notations NPPc =  month max (E  ·  IPAR, 0) E = 0.56 · T1 · T2 · W T1 = 0.8 + 0.02 · Topt – 0.0005 · Topt 2 T2 = 1.18 / [(1 + e 0.2 · (Topt – Tempc – 10) ) · (1 + e 0.3 · (Tempc – Topt – 10) )] W = 0.5 + 0.5 · EET / PET PET = 1.6 · (10 · Tempc / AHI) A · PET-TW-M if Tempc > 0 PET = 0 if Tempc < 0 A = 0.00000068 · AHI 3 – 0.000077 · AHI 2 + 0.018 · AHI + 0.49 IPAR = 0.5 · FPAR-FAS · Monthly-Solar · Sol-Conver FPAR-FAS = min [(SR-FAS – 1.08) / SR (UMD-VEG), 0.95] SR-FAS = (Mon-FAS-NDVI + 1000) / (Mon-FAS-NDVI – 1000) DFR NBLANBLR RRPhoto PBS Health - + + + - - - psbA1 psbA2 cpcB + + - - Light + Traditional data-mining notations are not easily understood by or communicated to domain scientists. Most sciences state and communicate models in formalisms they have used for decades. We need more work on discovering scientific knowledge cast in communicable forms (Dzeroski & Todorovski, 2007). Ecosystem model Gene regulation model

4. Claim 2: Background Knowledge Scientists often have initial knowledge that should influence the discovery process. Ignoring this knowledge can produce models that scientists reject as nonsensical (Pazzani et al., 2001). ModelRevision Initial model DFR NBLANBLR RRPhoto PBS Health - + + + - - - psbA1 psbA2 cpcB + + - - Light + Observations Revised model × DFR NBLANBLR RRPhoto PBS Health - - + + - - psbA1 psbA2 cpcB + - + Light + ×

5. Claim 3: Small Data Sets Most data-mining work assumes that large data sets are available. But in many scientific domains, data are rare and hard to obtain. Discovering scientific knowledge from small data sets raises an entirely different set of challenges (Lee et al., 1998). We need more research on this important aspect of discovery. Ecosystem model Gene regulation model Number of variables Number of equations Number of parameters Number of samples 8 11  20 303 Number of variables Number of initial links Number of initial links Number of possible links Number of possible links Number of samples Number of samples 911  70 20

6. Claim 4: Scientific Explanation Most work on data mining finds models that, although accurate, merely describe the observations. However, scientists often want models that explain their data using familiar concepts. Explanatory models can include theoretical entities and processes that link back to domain knowledge (Langley et al., 2002). Ecosystem model Gene regulation model NPPc IPAR PET T1T2We_max E EET Tempc Topt NDVI SOLAR AHI A PETTWM SR FPAR VEG DFR NBLANBLR RRPhoto PBS Health - + + + - - - psbA1 psbA2 cpcB + + - - Light +

7. Claim 5: Interactive Discovery Most data-mining work focused on entirely automated algorithms. But most scientists want computational aids rather than systems that would replace them. We need more work on interactive discovery (Bridewell et al., 2007). ModelRevision Initial model DFR NBLANBLR RRPhoto PBS Health - + + + - - - psbA1 psbA2 cpcB + + - - Light + Observations Revised model × DFR NBLANBLR RRPhoto PBS Health - - + + - - psbA1 psbA2 cpcB + - + Light + × Domain user

8. The P ROMETHEUS System (Bridewell et al., 2007)