Pat Langley Institute for the Study of Learning and Expertise Palo Alto, California and

1. Computational Discovery of Communicable Scientific Knowledge Pat Langley Institute for the Study of Learning and Expertise Palo Alto, California and Center for the Study of Language and Information Stanford University, Stanford, California http://www.isle.org/~langley langley@isle.org Thanks to S. Bay, V. Brooks, S. Klooster, A. Pohorille, C. Potter, K. Saito, J. Shrager, M. Schwabacher, and A. Torregrosa.

2. Motivations for Computational Discovery Humans strive to discover new knowledge from experience so that they can: better predict and control future events understand both previous and future events communicate that understanding to others Computational techniques should let us automate and/or assist this discovery process. Recent research on computer-aided discovery has focused on some of these issues but downplayed others.

3. The Data Mining Paradigm One computational discovery paradigm, known as datamining or KDD, can be best characterized as: emphasizing the availability of vast amounts of data; drawing on heuristic search methods to find regularities in these data; using formalisms like decision trees, association rules, and Bayes nets to describe those regularities. Thus, most KDD researchers favor their own formalisms over those used by scientists and engineers. As a result, their discoveries are seldom very communicable to members of those communities.

4. Myths About Understandability Within the data mining paradigm, one quite popular myth is that: However, Kononenko found that doctors felt that naïve Bayesian classifiers were easier to interpret than decision trees. Conclusion: Any formalism’s understandability depends on the interpreter’s familiarity with that formalism. decision trees and rules are inherently understandable because logical formalisms are easier to interpret than other notations.

5. Myths About Understandability Another popular myth in the data mining community is that: However, Saito and Nakano (1997) have shown that one can use such methods to discover explicit numeric equations. Conclusion: Understandability depends on the resulting formalism, not on the search method used to discover knowledge. connectionist methods produce results that are opaque because the set of weights they learn cannot be easily interpreted.

6. Computational Scientific Discovery An older paradigm, computational scientific discovery, can be characterized as: drawing on heuristic search to find regularities in scientific data, either historical or novel; using formalisms like numeric laws, structural models, and reaction pathways to describe regularities. Thus, researchers in this framework favor representations used by scientists and engineers. As a result, their systems’ discoveries are more communicable to members of those communities.

7. 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 Bacon.1–Bacon.5 Abacus, Coper Fahrehneit, E*, Tetrad, IDSN Hume, ARC DST, GPN LaGrange SDS SSF, RF5, LaGramge AM Glauber NGlauber IDSQ, Live RL, Progol HR Dendral Dalton, Stahl Stahlp, Revolver Gell-Mann BR-3, Mendel Pauli BR-4 IE Coast, Phineas, AbE, Kekada Mechem, CDP Astra, GPM Numeric laws Qualitative laws Structural models Process models Time Line for Research on Computational Scientific Discovery Legend

8. Successes of Computational Scientific Discovery Over the past decade, systems of this type have helped discover new knowledge in many scientific fields: • stellar taxonomies from infrared spectra (Cheeseman et al., 1989) • qualitative chemical factors in mutagenesis (King et al., 1996) • quantitative laws of metallic behavior (Sleeman et al., 1997) • qualitative conjectures in number theory (Colton et al., 2000) • temporal laws of ecological behavior (Todorovski et al., 2000) • reaction pathways in catalytic chemistry (Valdes-Perez, 1994, 1997) Each of these has led to publications in the refereed literature of the relevant scientific field (see Langley, 2000).

9. The Developer’s Role in Computational Discovery problem formulation representation engineering algorithm manipulation data manipulation algorithm invocation filtering and interpretation

10. We aim to extend previous approaches to computational scientific discovery by: Themes of the Research generating explanations that involve hidden objects/variables revising existing models rather than starting from scratch drawing on domain knowledge to constrain the search process developing interactive discovery tools for use by scientists As in earlier work, the notation for discovered knowledge will be the same as that used by domain scientists. Two promising fields in which to pursue this research agenda are Earth science and molecular biology.

11. Some Interesting Questions in Earth Science • What environmental variables determine the production of carbon and the generation of various gases? • What functional forms relate these predictive variables to the ones they influence? • How do extreme values of these variables affect behavior of the ecosystem? • Are the Earth ecosystem parameters constant or have values changed in recent years?

12. The Task of Ecological Model Revision Given: A model of Earth’s ecosystem (CASA) stated as equations that involve observable and hidden variables. Given: Inferred values for global parameters and intrinsic properties associated with discrete variables (e.g., ground cover). Given: Observations about numeric variables (rainfall, sunlight, temperature, NPPc) as they change over space and time. Find: A revised ecosystem model with altered equations and/or parametric values that fits the data better.

13. The NPPc Portion of CASA NPPc = Smonthmax (E·IPAR, 0) E = 0.56 · T1 · T2 · W T1 = 0.8 + 0.02 · Topt – 0.0005 · Topt2 T2 = 1.18 / [(1 + e0.2 · (Topt – Tempc – 10) ) · (1 + e0.3 · (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 · AHI3 – 0.000077 · AHI2 + 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)

14. The NPPc Portion of CASA NPPc E IPAR e_max W T2 T1 SOLAR FPAR A PET EET Topt SR AHI PETTWM Tempc NDVI VEG

15. One way to improve the NPPc model’s fit to observed data is to: Improving the NPPc Portion of CASA 1. Transform the model into a multilayer neural network that makes the same predictions. 2. Identify portions of the model that are candidates for revision. 3. Use an error-driven connectionist learning algorithm to revise those portions of the model. 4. Transform the revised multilayer network back into numeric equations using the improved components. This approach is similar to Towell’s (1991) method for revising qualitative models.

16. Saito and Nakano (2000) describe RF6, a discovery system that: The RF6 Discovery Algorithm 1. Creates a multilayer neural network that links predictive with predicted variables using additive and product units. 2. Invokes the BPQ algorithm to search through the weight space defined by this network. 3. Transforms the resulting network into a polynomial equation of the form y = S ciP x jd ij . They have shown this approach can discover an impressive class of numeric equations from noisy data.

17. Three Facets of Model Revision We have adapted RF6 to revise an existing quantitative model in three distinct ways: • Altering the value of parameters in a specified equation; • Changing the associated values for an intrinsic property; and • Replacing the equation for a term with another expression. Rather than initializing weights randomly, the system starts with weights based on parameters in the original model. We have applied this strategy to revise six different portions of the NPPc submodel.

18. Altering Parameters in the NPPc Model Initial model: T2 = 1.18 / [(1 + e 0.2 · (Topt – Tempc – 10) ) · (1 + e 0.3 · (Tempc – Topt – 10) )] Cross-validated RMSE = 467.910 Behavior: Gaussian-like function of temperature difference. Revised model: T2 = 1.80 / [(1 + e 0.05 · (Topt – Tempc – 10.8) ) · (1 + e 0.3 · (Tempc – Topt – 90.33) )] Cross-validated RMSE = 461.466 [ one percent reduction ] Behavior: nearly flat function in actual range of temperature difference. Conclusion: The T2 temperature stress term contributes little to the overall predictive ability of the NPPc submodel.

19. The NPPc submodel includes one intrinsic property, SR, associated with the variable for vegetation type, UMD-VEG. The corresponding RF6 network includes one hidden node for SR and one dummy input variable for each vegetation type. Veg type A B C D E F G H I J K Initial 3.06 4.35 4.35 4.05 5.09 3.06 4.05 4.05 4.05 5.09 4.05 Revised 2.57 4.77 2.20 3.99 3.70 3.46 2.34 0.34 2.72 3.46 1.60 RMSE = 467.910 for the original model; RMSE = 448.376 for the revised model, an improvement of four percent. Observation: Nearly all intrinsic values are lower in the revised model. Revising Intrinsic Values in the Model

20. Initial model: E = 0.56 · T1 · T2 · W Cross-validated RMSE = 467.910 Behavior: Each stress term decreases the photosynthetic efficiency E. Revised model: E = 0.521 · T10.00 · T2 0.03 · W 0.00 Cross-validated RMSE = 446.270 [ five percent reduction ] Behavior: T1 and W have no effect on E and T2 has only a minor effect . Conclusion: The stress terms are not useful to the NPPc model, most likely because of recent improvements in NDVI measures. Revising Equations in the NPPc Model

21. Future Work on Ecological Model Revision • Apply the revision method to other parts of NPPc submodel and other static parts of CASA model. • Extend the revision method to improve parts of CASA that involve difference equations. • Develop software for visualizing both spatial and temporal anomalies, as well as relating them to the model. • Implement an interactive system that lets scientists direct high-level search for improved ecosystem models.

22. One way to visualize a model involves plotting its rules spatially. Visualizing an Improved Model Our Earth science collaborators found this useful, as regions often correspond to recognizable ecological zones.

23. Some Interesting Biological Questions • How do organisms acclimate to increased temperature or ultraviolet radiation? • Why do we observe bleaching of plant cells under high light conditions? • What differences in biological processes exist between a mutant organism and the original? • What are the effects on an organism’s biological processes when one of its important genes is removed?

24. Modeling Microarrary Results on Photosynthesis Given: Qualitative knowledge about reactions and regulations for Cyanobacteria in a high light situation. Given: Knowledge about the genes in Cyanobacteria relevant to the photosynthetic process. Given: Observed expression levels, over time, of the organism’s genes in the presence of high ultraviolet light. Find: A revised model with altered reactions and regulations that explains the expression levels and bleaching.

25. A Model of Photosynthesis Regulation How do plants modify their photosynthetic apparatus in high light? + - NBLR NBLA PBS + - DFR psbA1 Health + - - + - + RR psbA2 Photo + - Light cpcB

26. Collecting Data on Photosynthetic Processes www.affymetrix.com/ Microarray Trace /wwwscience.murdoch.edu.au/teach Continuous Culture (Chemostat) Stress (e.g., High Light) Adaptation Period Sampling mRNA/cDNA Health of Culture Equlibrium Period www.affymetrix.com/ Time

27. Microarray Data on Photosynthetic Regulation

28. Revising a Model of Gene Regulation Our approach carries out heuristic search through the model space, guided by candidates’ abilities to explain the data: Starting state: Initial model proposed by the biologist Operators: Add a link, delete a link, determine sign on a link Control: Greedy search for N steps to determine link structure; Exhaustive search to determine best signs on links Evaluation: Agreement with predicted relations among partial correlations, similar to those used in Tetrad To reduce variance, the system repeats this process using bootstrap sampling and only makes changes that occur in 75% of the models.

29. Initial model Revision 1.1 Revision 1.2 Revision 1.3 Revision 1.4 Revision 2.1 Revision 2.2 Revision 2.3 Revision 2.4 Revision 3.1 Revision 3.2 Revision 3.3 Revision 3.4 Greedy Search Through a Space of Models

30. A Revised Model of Photosynthesis Regulation Changes to the model improve its match to the expression data. + - NBLR NBLA PBS + + DFR psbA1 Health + - - - × × RR psbA2 Photo + - Light cpcB Similar changes adapt the model to expression data from mutants.

31. Future Work on Biological Modeling • Add more knowledge about biochemical pathways and use to interpret other microarray data (e.g., rat metabolism, cancer). • Introduce taxonomic knowledge to limit the search process and improve final models. • Expand modeling formalism to support biological mechanisms in addition to abstract processes. • Implement an interactive system that lets scientists direct high-level search for improved biological process models.

32. In summary, unlike work in the data mining paradigm, our research on computational discovery: Concluding Remarks attempts to move beyond description and prediction to both explanation and understanding; uses domain knowledge to initialize search and to characterize differences from revised model; presents the new knowledge in some communicable notation that is familiar to domain experts. This approach seems especially appropriate for manipulating and understanding complex scientific and engineering data.

33. In Memoriam Earlier this year, computational scientific discovery lost two of its founding fathers: Both contributed to the field in many ways: posing new problems, inventing methods, training students, and organizing meetings. Moreover, both were interdisciplinary researchers who contributed to computer science, psychology, philosophy, and statistics. Herb Simon and Jan Zytkow were excellent role models that we should aim to emulate. Herbert A. Simon (1916 – 2001) Jan M. Zytkow (1945 – 2001)

34. A Closing Quotation We would like to imagine that the great discoverers, the scientists whose behavior we are trying to understand, would be pleased with this interpretation of their activity as normal (albeit high-quality) human thinking. . . But science is concerned with the way the world is, not with how we would like it to be. So we must continue to try new experiments, to be guided by new evidence, in a heuristic search that is never finished but always fascinating. Herbert A. Simon, Envoi to Scientific Discovery, 1987.

36. We can easily plot an improved model’s errors in spatial terms. Visualizing Errors in the Model Such displays can help suggest causes for prediction errors and thus ways to further improve the model.

37. Our approach to computational scientific discovery borrows ideas from earlier work on: Related Research on Discovery equation discovery (Langley et al. 1983; Zytkow et al, 1990; Washio & Motoda, 1998; Todorovski & Dzeroski, 1997); revision of qualitative models (Ourston & Mooney, 1990; Towell, 1991); revision of quantitative models (Glymour et al., 1987; Chown & Dietterich, 2000). However, our work combines these ideas in novel ways to produce a discovery system with new functionality.