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Machine Learning

Interpretable Architecture Neural Networks for Function Visualization

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Pages 1258-1271 | Received 21 Jun 2022, Accepted 15 Mar 2023, Published online: 02 May 2023

References

  • Agarwal, R., Melnick, L., Frosst, N., Zhang, X., Lengerich, B., Caruana, R., and Hinton, G. E. (2021), “Neural Additive Models: Interpretable Machine Learning with Neural Nets,” Advances in Neural Information Processing Systems, 34, 4699–4711.
  • An, J., and Owen, A. (2001), “Quasi-Regression,” Journal of Complexity, 17, 588–607. DOI: 10.1006/jcom.2001.0588.
  • Apley, D. W., and Zhu, J. (2020), “Visualizing the Effects of Predictor Variables in Black Box Supervised Learning Models,” Journal of the Royal Statistical Society, Series B, 82, 1059–1086. DOI: 10.1111/rssb.12377.
  • Becker, R. A., Cleveland, W. S., and Shyu, M.-J. (1996), “The Visual Design and Control of Trellis Display,” Journal of Computational and Graphical Statistics, 5, 123–155. DOI: 10.2307/1390777.
  • Becker, R. A., Cleveland, W. S., Shyu, M.-J., and Kaluzny, S. P. (1994), “Trellis Displays: User’s Guide,” Statistics Research Report, 10.
  • Breiman, L. (2001), “Random Forests,” Machine Learning, 45, 5–32. DOI: 10.1023/A:1010933404324.
  • Buitinck, L., Louppe, G., Blondel, M., Pedregosa, F., Mueller, A., Grisel, O., Niculae, V., Prettenhofer, P., Gramfort, A., Grobler, J., Layton, R., VanderPlas, J., Joly, A., Holt, B., and Varoquaux, G. (2013), “API Design for Machine Learning Software: Experiences from the Scikit-Learn Project,” in ECML PKDD Workshop: Languages for Data Mining and Machine Learning, pp. 108–122.
  • Cleveland, W. S., and McGill, R. (1984), “Graphical Perception: Theory, Experimentation, and Application to the Development of Graphical Methods,” Journal of the American Statistical Association, 79, 531–554. DOI: 10.1080/01621459.1984.10478080.
  • Cybenko, G. (1989), “Approximation by Superpositions of a Sigmoidal Function,” Mathematics of Control, Signals and Systems, 2, 303–314. DOI: 10.1007/BF02551274.
  • Fisher, A., Rudin, C., and Dominici, F. (2019), “All Models are Wrong, but Many are Useful: Learning a Variable’s Importance by Studying an Entire Class of Prediction Models Simultaneously,” Journal of Machine Learning Research, 20, 1–81.
  • Friedman, J. H. (2001), “Greedy Function Approximation: A Gradient Boosting Machine,” Annals of Statistics, 29, 1189–1232.
  • Gerber, S., Bremer, P.-T., Pascucci, V., and Whitaker, R. (2010), “Visual Exploration of High Dimensional Scalar Functions,” IEEE Transactions on Visualization and Computer Graphics, 16, 1271–1280. DOI: 10.1109/TVCG.2010.213.
  • Goldstein, A., Kapelner, A., Bleich, J., and Pitkin, E. (2015), “Peeking Inside the Black Box: Visualizing Statistical Learning with Plots of Individual Conditional Expectation,” Journal of Computational and Graphical Statistics, 24, 44–65. DOI: 10.1080/10618600.2014.907095.
  • Harper, W. V., and Gupta, S. K. (1983), “Sensitivity/Uncertainty Analysis of a Borehole Scenario Comparing Latin Hypercube Sampling and Deterministic Sensitivity Approaches,” Office of Nuclear Waste Isolation, Battelle Memorial Institute Columbus, Ohio.
  • Harvey, W., Rübel, O., Pascucci, V., Bremer, P.-T., and Wang, Y. (2012), “Enhanced Topology-Sensitive Clustering by Reeb Graph Shattering,” in Topological Methods in Data Analysis and Visualization II, eds. R. Peikert, H. Hauser, H. Carr, and R. Fuchs, pp. 77–90, Berlin: Springer.
  • Herman, J., and Usher, W. (2017), “SALib: An Open-Source Python Library for Sensitivity Analysis,” The Journal of Open Source Software, 2, 1–2. DOI: 10.21105/joss.00097.
  • Hornik, K. (1991), “Approximation Capabilities of Multilayer Feedforward Networks,” Neural Networks, 4, 251–257. DOI: 10.1016/0893-6080(91)90009-T.
  • Hornik, K., Stinchcombe, M., and White, H. (1989), “Multilayer Feedforward Networks are Universal Approximators,” Neural Networks, 2, 359–366. DOI: 10.1016/0893-6080(89)90020-8.
  • Johnson, M. E., Moore, L. M., and Ylvisaker, D. (1990), “Minimax and Maximin Distance Designs,” Journal of Statistical Planning and Inference, 26, 131–148. DOI: 10.1016/0378-3758(90)90122-B.
  • Kennedy, M. C., and O’Hagan, A. (2000), “Predicting the Output from a Complex Computer Code When Fast Approximations are Available,” Biometrika, 87, 1–13. DOI: 10.1093/biomet/87.1.1.
  • Kennedy, M. C., and O’Hagan, A. (2001), “Bayesian Calibration of Computer Models,” Journal of the Royal Statistical Society, Series B, 63, 425–464. DOI: 10.1111/1467-9868.00294.
  • König, G., Molnar, C., Bischl, B., and Grosse-Wentrup, M. (2021), “Relative Feature Importance,” in 2020 25th International Conference on Pattern Recognition (ICPR), pp. 9318–9325. IEEE. DOI: 10.1109/ICPR48806.2021.9413090.
  • Lundberg, S. M., and Lee, S.-I. (2017), “A Unified Approach to Interpreting Model Predictions,” in Proceedings of the 31st International Conference on Neural Information Processing Systems, pp. 4768–4777.
  • Maljovec, D., Wang, B., Pascucci, V., Bremer, P.-T., Pernice, M., Mandelli, D., and Nourgaliev, R. (2013), “Exploration of High-Dimensional Scalar Function for Nuclear Reactor Safety Analysis and Visualization,” in International Conference on Mathematics and Computational Methods Applied to Nuclear Science & Engineering. Citeseer.
  • McKay, M. D., Beckman, R. J., and Conover, W. J. (2000), “A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code,” Technometrics, 42, 55–61. DOI: 10.1080/00401706.2000.10485979.
  • Morgan-Wall, T. (2022), “rayshader: Create Maps and Visualize Data in 2D and 3D,” available at https://www.rayshader.com, https://github.com/tylermorganwall/rayshader, https://www.rayshader.com/.
  • Morris, M. D., Mitchell, T. J., and Ylvisaker, D. (1993), “Bayesian Design and Analysis of Computer Experiments: Use of Derivatives in Surface Prediction,” Technometrics, 35, 243–255. DOI: 10.1080/00401706.1993.10485320.
  • Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M., Prettenhofer, P., Weiss, R., Dubourg, V., Vanderplas, J., Passos, A., Cournapeau, D., Brucher, M., Perrot, M., and Duchesnay, E. (2011), “Scikit-Learn: Machine Learning in Python,” Journal of Machine Learning Research, 12, 2825–2830.
  • Robinson, T. J., Borror, C. M., and Myers, R. H. (2004), “Robust Parameter Design: A Review,” Quality and Reliability Engineering International, 20, 81–101. DOI: 10.1002/qre.602.
  • Sacks, J., Welch, W. J., Mitchell, T. J., and Wynn, H. P. (1989), “Design and Analysis of Computer Experiments,” Statistical Science, 4, 409–423. DOI: 10.1214/ss/1177012413.
  • Surjanovic, S., and Bingham, D. (2013), “Virtual Library of Simulation Experiments: Test Functions and Datasets,” available at http://www.sfu.ca/∼ssurjano. Retrieved January 4, 2022.
  • Taguchi, G. (1986), “Introduction to Quality Engineering: Designing Quality into Products and Processes,” Technical Report.

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