Data Science: Algebrical & Statistical Fundamentals - WMMBESDD

Goal(s)

Acquire a general knowledge of data science sufficient to be able to interact with specialists in statistical learning theory.

Content(s)

• Reminders of linear algebra,
• Minimization of the empirical risk,
• Introduction to the statistical theory of learning,
• Specificities of learning in a "Big Data" context: curse and blessing of the dimension,
• Variety learning,
• Parsimony and penalty,
• Large-scale inference: hypothesis testing and i.i.d. data simulation,
• Control of the rate of false discoveries and correction of multiple tests.

• fundamental concepts of linear algebra
  • Euclidean space
  • Scalar product
  • Basic operations on matrices
  • Positive semi-described matrixes
  • Hermitian forms
  • Matrix diagonalization and eigenvalues

• Indicative bibliography :
  • Fabien Margairaz. Algèbre linéaire I & II: Notes de cours de l’EPFL. https://docplayer.fr/23918385-Algebre-lineaire-i-ii.html
  • Wikipédia

• fundamental concepts of probability
  • Expectation, variance
  • Joint and conditional probabilities, Bayes formula
  • Usual laws (Bernoulli, uniform, normal)
  • Estimation of the parameters using maximum likelihood

• Indicative bibliography :
  • Olivier François. Notes de cours de Probabilités Appliquées. Les 40 premières pages. http://membres-timc.imag.fr/Olivier.Francois/Poly_Cours_Proba.pdf

• basic concepts of statistics
  • Descriptive statistics : Statistical population, Central tendency and dispersion estimators, Common representations (histogram, bar chart, etc.)
  • Elementary notions of hypothesis testing: Samples, Null hypothesis, alternative hypothesis, type I and II risks, Student Test

• Indicative bibliography:
  • Olivier Gaudoin. Principes et Méthodes Statistiques : Notes de cours, Ensimag 2A. Chapitres I,II, V (3 premières sections)
    https://www-ljk.imag.fr/membres/Olivier.Gaudoin/PMS.pdf