[1] Miki Aoyagi and SumioWatanabe. Stochastic complexities of reduced rank regression
in Bayesian estimation. Neural Netw., 18(7):924{933, 2005.
[2] V. I. Arnol'd, S. M. Gusen-Zade, and A. N. Varchenko. Singularities of dierentiable
maps. Vol. II, volume 83 of Monographs in Mathematics. Birkhauser Boston, Inc.,
Boston, MA, 1988.
[3] Jacqueline Bertrand, Pierre Bertrand, and Jean-Philippe Ovarlez. The mellin transform.
In Alexander D. Poularikas, editor, Transforms and applications handbook, The
Electrical Engineering Handbook Series, chapter 12, pages xii+898. CRC Press, Boca
Raton, FL, third edition, 2010.
REFERENCES 49
[4] Edward Bierstone and Pierre D. Milman. Resolution of singularities. In Several
complex variables, volume 37 of Math. Sci. Res. Inst. Publ., pages 43{78. Cambridge
Univ. Press, Cambridge, 1999.
[5] Carles Bivia-Ausina. Nondegenerate ideals in formal power series rings. Rocky Mountain
J. Math., 34(2):495{511, 2004.
[6] Manuel Blickle and Robert Lazarsfeld. An informal introduction to multiplier ideals.
In Trends in commutative algebra, volume 51 of Math. Sci. Res. Inst. Publ., pages
87{114. Cambridge Univ. Press, Cambridge, 2004.
[7] Ana Mara Bravo, Santiago Encinas, and Orlando Villamayor U. A simplied proof of
desingularization and applications. Rev. Mat. Iberoamericana, 21(2):349{458, 2005.
[8] Mathias Drton and Martyn Plummer. A bayesian information criterion for singular
models. Journal of the Royal Statistical Society: Series B, 79:1{38, 2017.
[9] Mathias Drton, Bernd Sturmfels, and Seth Sullivant. Lectures on algebraic statistics,
volume 39 of Oberwolfach Seminars. Birkhauser Verlag, Basel, 2009.
[10] David Eisenbud. Commutative algebra, volume 150 of Graduate Texts in Mathematics.
Springer-Verlag, New York, 1995. With a view toward algebraic geometry.
[11] Michael J. Evans, Zvi Gilula, and Irwin Guttman. Latent class analysis of two-way
contingency tables by Bayesian methods. Biometrika, 76(3):557{563, 1989.
[12] William Fulton. Introduction to toric varieties, volume 131 of Annals of Mathematics
Studies. Princeton University Press, Princeton, NJ, 1993.
[13] Michael Greenblatt. An elementary coordinate-dependent local resolution of singularities
and applications. J. Funct. Anal., 255(8):1957{1994, 2008.
[14] Michael Greenblatt. Resolution of singularities, asymptotic expansions of integrals
and related phenomena. J. Anal. Math., 111:221{245, 2010.
[15] Heisuke Hironaka. Resolution of singularities of an algebraic variety over a eld of
characteristic zero. I, II. Ann. of Math. (2), 79:109{326, 1964.
[16] J. A. Howald. Multiplier ideals of monomial ideals. Trans. Amer. Math. Soc.,
353(7):2665{2671, 2001.
[17] Janos Kollar. Singularities of pairs. In Algebraic geometry|Santa Cruz 1995, volume
62 of Proc. Sympos. Pure Math., pages 221{287. Amer. Math. Soc., Providence,
RI, 1997.
[18] Janos Kollar. Lectures on resolution of singularities, volume 166 of Annals of Mathematics
Studies. Princeton University Press, Princeton, NJ, 2007.
50
[19] Robert Lazarsfeld. Positivity in algebraic geometry. I, volume 48 of A Series of
Modern Surveys in Mathematics. Springer-Verlag, Berlin, 2004. Classical setting:
line bundles and linear series.
[20] Shaowei Lin, Bernd Sturmfels, and Zhiqiang Xu. Marginal likelihood integrals for
mixtures of independence models. J. Mach. Learn. Res., 10:1611{1631, 2009.
[21] Dmitry Rusakov and Dan Geiger. Asymptotic model selection for naive Bayesian
networks. J. Mach. Learn. Res., 6:1{35, 2005.
[22] Marcelo J. Saia. The integral closure of ideals and the Newton ltration. J. Algebraic
Geom., 5(1):1{11, 1996.
[23] Morihiko Saito. On real log canonical thresholds. arXiv:0707.2308, 2007.
[24] Alexander N Varchenko. Newton polyhedra and estimation of oscillating integrals.
Functional analysis and its applications, 10(3):175{196, 1976.
[25] V. A. Vasil'ev. Asymptotic behavior of exponential integrals in the complex domain.
Funktsional. Anal. i Prilozhen., 13(4):1{12, 96, 1979.
[26] Sumio Watanabe. Algebraic analysis for nonidentiable learning machines. Neural
Comput., 13(4):899{933, 2001.
[27] Sumio Watanabe. Algebraic geometry and statistical learning theory, volume 25 of
Cambridge Monographs on Applied and Computational Mathematics. Cambridge University
Press, Cambridge, 2009.
[28] Keisuke Yamazaki and Sumio Watanabe. Singularities in mixture models and upper
bounds of stochastic complexity. Neural Netw., 16(7):1029{1038, 2003.
[29] Keisuke Yamazaki and Sumio Watanabe. Newton diagram and stochastic complexity
in mixture of binomial distributions. In Algorithmic learning theory. 15th international
conference, ALT 2004, Padova, Italy, October 2{5, 2004. Proceedings., pages
350{364. Berlin: Springer, 2004.
Thank you for copying data from http://www.arastirmax.com