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Informatique et Mathématiques appliquées

# Data Science: Algebrical & Statistical Fundamentals - WMMBESDD

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• #### Number of hours

• Lectures : 24.0
• Tutorials : -
• Laboratory works : 6.0
• Projects : -
• Internship : -
• Written tests : -
ECTS : 2.0
• Officials : Thomas BURGER

### Goals

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

Content

• 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.

Prerequisites

• fundamental concepts of linear algebra
• Euclidean space
• Scalar product
• Basic operations on matrices
• Positive semi-described matrixes
• Hermitian forms
• Matrix diagonalization and eigenvalues
• fundamental concepts of probability
• Expectation, variance
• Joint and conditional probabilities, Bayes formula
• Usual laws (Bernoulli, uniform, normal)
• Estimation of the parameters using maximum likelihood
• 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

Tests

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N2=E2

N1=E1
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Calendar

The course exists in the following branches:

• Curriculum - Big-Data Post-Graduate Program - Semester 9
see the course schedule for 2020-2021

Course ID : WMMBESDD
Course language(s):

You can find this course among all other courses.

Bibliography

Principes et méthodes statistiques
https://www-ljk.imag.fr/membres/Olivier.Gaudoin/PMS.pdf

Notes de cours de probabilités
http://membres-timc.imag.fr/Olivier.Francois/Poly_Cours_Proba.pdf

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Date of update March 10, 2020

École nationale supérieure d'informatique et de mathématiques appliquées
681, rue de la passerelle - Domaine universitaire - BP 72
38402 SAINT MARTIN D'HERES