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Graphical Methods

EDI-Graphic: A Tool To Study Parameter Discrimination and Confirm Identifiability in Black-Box Models, and to Select Data-Generating Machines

Pages 126-137 | Received 18 Dec 2022, Accepted 14 Apr 2023, Published online: 12 Jun 2023

References

  • Birgé, L. (2006), “Model Selection via Testing: An Alternative to Penalized Maximum Likelihood Estimators,” Annales de l’Institut Henri Poincaré, 42, 273–325.
  • Breiman, L. (2001), “Statistical Modeling: The Two Cultures,” Statistical Science, 16, 199–231. DOI: 10.1214/ss/1009213726.
  • Breiman, L. (2002), “Looking Inside the Black Box,” available at https://www.stat.berkeley.edu/users/breiman/wald2002-2.pdf
  • Csörgo, M., and Horvath, L. (1997), Limit Theorems in Change-Point Analysis, New York: Wiley.
  • Dempster, A. P., and Schatzoff, M. (1965), “Expected Significance Level as a Sensibility Index for Test Statistics,” Journal of the American Statistical Association, 60, 420–436. DOI: 10.1080/01621459.1965.10480802.
  • Fukumizu, K. (2003), “Likelihood Ratio of Non-identifiable Models and Multilayer Neural Networks,” Annals of Statistics, 31, 833–851.
  • Fukumizu, K., and Amari, S. (2000), “Local Minima and Plateaus in Hierarchical Structures of Multilayer Perceptions,” Neural Networks, 13, 317–327. DOI: 10.1016/s0893-6080(00)00009-5.
  • Glazer, A., Lindenbaoum, M., and Markovitch, S. (2012), “Learning High-Density Regions for a Generalized Kolmogorov-Smirnov Test in High-Dimensional Data,” Advances in Neural Information Processing Systems, 1, 728–736.
  • Hartigan, J. A. (1985), “A Failure of Likelihood Asymptotics for Normal Mixtures,” Proceedings of the Berkeley Conference in Honor of Jerzy Neyman and Jack Kiefer (Vol. 2), eds. L. M. Le Camand and R. A. Olshen, pp. 807–810, Belmont, CA: Wadsworth.
  • Haynes, M. A., MacGillivray, H. L., and Mengersen, K. L. (1997), “Robustness of Ranking and Selection Rules using Generalized g-and-k Distributions,” Journal of Statistical Planning and Inference, 65, 45–66. DOI: 10.1016/S0378-3758(97)00050-5.
  • Hyvärinen, A., and Morioka, H. (2016), “Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICA,” in Advances in Neural Information Processing Systems, pp. 3765–3773.
  • Hyvärinen, A., Sasaki, H., and Turner, R. E. (2018), “Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning,” Arxiv Preprint Arxiv:1805.08651.
  • LeCam, L. M. (1973), “Convergence of Estimates Under Dimensionality Restrictions,” Annals of Statistics, 1, 38–53.
  • LeCam, L. M., and Yang, G. L. (1990), Asymptotics in Statistics. Some Basic Concepts, New York: Springer.
  • Peacock, J. A. (1983), “Two-Dimensional Goodness-of-Fit Testing in Astronomy,” Monthly Notices Royal Astronomy Society, 202, 615–627. DOI: 10.1093/mnras/202.3.615.
  • Polonik, W. (1999), “Concentration and Goodness-of-Fit in Higher Dimensions: (Asymptotically) Distribution-Free Methods,” Annals of Statistics, 27, 1210–1229.
  • Ramberg, J. S., Tadikamalla, P. R., Dudewicz, E. J., and Mykytka, E. F. (1979), “A Probability Distribution and Its Uses in Fitting Data,” Technometrics, 21, 201–214. DOI: 10.1080/00401706.1979.10489750.
  • Ran, Z.-Y., and Hu, B.-G. (2014), “Determining Parameter Identifiability from the Optimization Theory Framework: A Kullback-Leibler Divergence Approach,” Neurocomputing, 142, 307–317. DOI: 10.1016/j.neucom.2014.03.055.
  • Ran, Z.-Y., and Hu, B.-G. (2017), “Parameter Identifiability in Statistical Machine Learning: A Review,” Neural Computation, 29, 1151–1203.
  • Rayner, G. D., and MacGillivray, H. L. (2002), “Numerical Maximum Likelihood Estimation for the g-and-k and Generalized g-and-h Distributions,” Statistics and Computing, 12, 57–75.
  • Roeder, G., Metz, L., and Kingma, D. P. (2021), “On Linear Identifiability of Learned Representations,” in Proceedings of the 38th International Conference on Machine Learning, PMLR 139. arXiv:2007.00810v3 [stat.ML] 8 Jul 2020
  • Rothenberg, T. J. (1971), “Identification in Parametric Models,” Econometrica, 39, 577–591. DOI: 10.2307/1913267.
  • Sackrowitz, H., and Samuel-Cahn, E. (1999), “p-Values as Random Variables-Expected p-Values,” American Statistician, 53, 326–331. DOI: 10.2307/2686051.
  • Stein, C. (1964), “Inadmissibility of the Usual Estimator for the Variance of a Normal Distribution with Unknown Mean,” Annals of the Institute of Statistical Mathematics, 16, 155–160. DOI: 10.1007/BF02868569.
  • Tukey, J. W. (1962), “The Future of Data Analysis,” Annals of Mathematical Statistics, 33, 1–67. DOI: 10.1214/aoms/1177704711.
  • Tukey, J. W. (1977), “Modern Techniques in Data Analysis,” NSF-sponsored Regional Research Conference at Southeastern Massachusetts University, North Dartmouth, MA.
  • Veres, S.(1987), “Asymptotic Distributions of Likelihood Ratios for Overparameterized ARMA Processes,” Journal of Time Series Analysis, 8, 345–357. DOI: 10.1111/j.1467-9892.1987.tb00446.x.
  • Watanabe, S. (2001), “Algebraic Analysis of Nonidentifiable Learning Machines,” Neural Computation, 13, 899–933. DOI: 10.1162/089976601300014402.
  • Yan, Y., and Genton, M. G. (2019), “The Tukey g-and-h Distribution,” Significance, 2019, 12–13. DOI: 10.1111/j.1740-9713.2019.01273.x.
  • Yatracos, Y. G. (2020), “Learning with Matching in Data-Generating Experiments,” DOI: 10.13140/RG.2.2.30964.58245.
  • Yatracos, Y. G. (2021), “Fiducial Matching for the Approximate Posterior: F-ABC.” DOI: 10.13140/RG.2.2.20775.06568.
  • Yatracos, Y. G. (2022), “Limitations of the Wasserstein MDE for Univariate Data,” Statistics and Computing, 32, 95. DOI: 10.1007/s11222-022-10146-7.