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Foundations of Data Analysis (MA4800)

For detailed information about the course, please consult the moodle page.

Organization

  • Lectures (4 SWS)
  • Tutorial Sessions (2 SWS)
    • Dr. Mi-Song Dupuy, Mondays, 4:00 - 5:30 PM
    • Dr. Mi-Song Dupuy, Wednesdays, 10:00 - 11:30 AM
    • Tim Fuchs, Wednesdays, 2:00 - 3:30 PM

Literature

  • A. Bandeira, Ten Lectures and Forty-Two Open Problems in the Mathematics of Data Science, http://www.cims.nyu.edu/~bandeira/TenLecturesFortyTwoProblems.pdf
  • G. Bennett, Probability inequalities for the sum of independent random variables, J. Amer. Statist. Assoc. 57 (1962), 33-45.
  • H. Chernoff, A measure of asymptotic efficiency of tests of a hypothesis based on the sum of observations, Ann. Math. Statist. 23 (1952), 49-507.
  • G. Grimmett and D. Stirzaker, Probability and Random Processes, third ed., Oxford University Press, New York, 2001.
  • W. Hackbusch, Tensor Spaces and Numerical Tensor Calculus, Berlin: Springer, 2012 (English).
  • R. A. Horn and Ch. R. Johnson, Matrix Analysis, 2nd ed., Cambridge University Press, 2013 (English).
  • J. Hopcroft and R. Kannan, Computer Science Theory for the Information Age, https://www.cs.cmu.edu/~venkatg/teaching/CStheory-infoage/book-chapter-4.pdf, 2012.
  • T. Hagerup and C. Rüb, A guided tour of Chernoff bounds, Inform. Process. Lett. 33 (1990), No. 6, 305-308.
  • I.T. Jolliffe, Principal Component Analysis, 2nd ed., Springer, 2002 (English).
  • G. Kemper, Lineare Algebra für Informatik, Lecture Notes, 2017
  • M. Mazeika, The singular value decomposition and low rank approximation, http://math.uchicago.edu/~may/REU2016/REUPapers/Mazeika.pdf, 2016.
  • C. McDiarmid, Concentration, Probabilistic methods for algorithmic discrete mathematics, Algorithms Combin., Vol. 16, Springer, 1998, 195-248.
  • L. Mirsky, Symmetric gauge functions and unitarily invariant norms, The Quarterly Journal of Mathematics 11 (1960), No. 1, 50.
  • S. Ross, Introduction to Probability Models, nineth ed., Academic Press, 2006.
  • S. Varadhan, Large Deviations and Applications, École d'Été de Probabilités de Saint-Flour XV-XVII, 1985-87, Lecture Notes in Math., Vol. 1362, Springer, 1988, 1-49.
  • R. Vershynin, High dimensional probability, https://www.math.uci.edu/~rvershyn/papers/HDP-book/HDP-book.html, 2017.
  • H. Weyl , Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Differentialgleichungen (mit einer Anwendung auf die Theorie der Hohlraumstrahlung)., Math. Ann. 71 (1912), 441-479 (German).