Semester | Mand. | Option | Filières |
x | E | ||
H | x | ||
MA1, MA3 | x | ||
MA1, MA3 | x | C | |
MA1, MA3 | x | D | |
MA1, MA3 | x | E | |
MA1 | x | ||
MA1 | x | B | |
MA3 | x |
Lecture | 3 weekly |
Practical work | 3 weekly |
Study plan | Semester | Mand. | Option | Filières |
Data Science 2022-23 | MA1 | x | ||
Data Science 2022-23 | MA3 | x | ||
EDEE - Electrical Engineering 2022-23 | x | E | ||
EL MNIS 2022-23 | MA3 | x | ||
Génie électrique et électronique 2022-23 | MA1 | x | E | |
Génie électrique et électronique 2022-23 | MA3 | x | E | |
Management, technologie et entrepreneuriat 2022-23 | MA1 | x | C | |
Management, technologie et entrepreneuriat 2022-23 | MA3 | x | C | |
Mineur : Neuro-X 2022-23 | H | x | ||
Neuro-X 2022-23 | MA1 | x | ||
Science et ingénierie computationelles 2022-23 | MA1 | x | D | |
Science et ingénierie computationelles 2022-23 | MA3 | x | D | |
Science et ingénierie quantiques 2022-23 | MA1 | x | B | |
Statistique 2022-23 | MA1 | x |
Cursus | Sem. | Type |
---|---|---|
Computational science and Engineering | MA1, MA3 | Opt. |
Data Science | MA1, MA3 | Opt. |
Electrical Engineering | Opt. | |
Electrical and Electronical Engineering | MA1, MA3 | Opt. |
MNIS | MA3 | Opt. |
Managmt, tech et entr. | MA1, MA3 | Opt. |
Neuro-X minor | H | Opt. |
Neuro-X | MA1 | Opt. |
Quantum Science and Engineering | MA1 | Opt. |
Statistics | MA1 | Opt. |
The course consists of the following lectures (2h each)
Lecture 1: Introduction. The role of models and data. Maximum-likelihood formulations. Error decomposition for estimation and prediction.
Lecture 2: Generalized linear models. Logistic regression.
Lecture 3: Linear algebra reminders. Computation of Gradients. Reading convergence plots.
Lecture 4: The role of computation. Challenges to optimization algorithms. Optimality measures. Structures in optimization. Gradient descent. Convergence rate of gradient descent for smooth functions.
Lecture 5: Optimality of convergence rates. Lower bounds. Accelerated gradient descent. Concept of total complexity. Stochastic gradient descent.
Lecture 6: Concise signal models. Compressive sensing. Sample complexity bounds for estimation and prediction. Challenges to optimization algorithms for non-smooth optimization. Subgradient method.
Lecture 7: Introduction to proximal-operators. Proximal gradient methods. Linear minimization oracles. Conditional gradient method for constrained optimization.
Lecture 8: Time-data trade-offs. Variance reduction for improving trade-offs.
Lecture 9: Introduction to deep learning. Generalization through uniform convergence bounds. Rademacher complexity.
Lecture 10: Double descent curves and over-parameterization. Implicit regularization. Generalization bounds using stability.
Lecture 11: Escaping saddle points. Adaptive gradient methods.
Lecture 12: Adversarial machine learning and generative adversarial networks (GANs). Wasserstein GAN. Difficulty of minimax optimization. Pitfalls of gradient descent-ascent approach.
Lecture 13: Primal-dual optimization-I: Fundamentals of minimax problems. Fenchel conjugates. Duality.
Lecture 14: Primal-dual optimization-II: Extra gradient method. Chambolle-Pock algorithm. Stochastic primal-dual methods.
Lecture 15: Primal-dual III: Lagrangian gradient methods. Lagrangian conditional gradient methods.
Machine Learning. Signal Processing. Optimization. Statististical Analysis. Linear and non-linear models. Algorithms. Data and computational trade-offs.
Previous coursework in calculus, linear algebra, and probability is required. Familiarity with optimization is useful.
Familiarity with python, and basic knowledge of one deep learning framework (Pytorch, TensorFlow, JAX) is needed.
optionnel
optionnel
Cours
Lecture
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
TP
Practical work
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Ecrit
Written
Session hiver
Session winter
HIV
HIV
optionnel
optionnel
Cours
Lecture
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
TP
Practical work
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Ecrit
Written
Session hiver
Session winter
HIV
HIV
optionnel
optionnel
Cours
Lecture
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
TP
Practical work
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Ecrit
Written
Session hiver
Session winter
HIV
HIV
optionnel
optionnel
Cours
Lecture
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
TP
Practical work
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Ecrit
Written
Session hiver
Session winter
HIV
HIV
optionnel
optionnel
Cours
Lecture
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
TP
Practical work
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Ecrit
Written
Session hiver
Session winter
HIV
HIV
optionnel
optionnel
Cours
Lecture
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
TP
Practical work
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Ecrit
Written
Session hiver
Session winter
HIV
HIV
optionnel
optionnel
Cours
Lecture
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
TP
Practical work
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Ecrit
Written
Session hiver
Session winter
HIV
HIV
optionnel
optionnel
Cours
Lecture
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
TP
Practical work
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Ecrit
Written
Session hiver
Session winter
HIV
HIV
optionnel
optionnel
Cours
Lecture
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
TP
Practical work
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Ecrit
Written
Session hiver
Session winter
HIV
HIV
optionnel
optionnel
Cours
Lecture
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
TP
Practical work
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Ecrit
Written
Session hiver
Session winter
HIV
HIV
optionnel
optionnel
Cours
Lecture
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
TP
Practical work
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Ecrit
Written
Session hiver
Session winter
HIV
HIV
optionnel
optionnel
Cours
Lecture
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
TP
Practical work
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Ecrit
Written
Session hiver
Session winter
HIV
HIV
optionnel
optionnel
Cours
Lecture
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
TP
Practical work
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Ecrit
Written
Session hiver
Session winter
HIV
HIV
optionnel
optionnel
Cours
Lecture
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
TP
Practical work
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Ecrit
Written
Session hiver
Session winter
HIV
HIV
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BOOLEAN_Symbol
BaliseJS_debut
\x5beta\x5d
BaliseJS_fin
Balise_debut
[eta]
Balise_fin
FO_debut
[inline]=η
FO_fin
HTML_debut
η
HTML_fin
JS_debut
\x26#951;
JS_fin
CODE72092805
BOOLEAN_Symbol
BaliseJS_debut
\x5bETA\x5d
BaliseJS_fin
Balise_debut
[ETA]
Balise_fin
FO_debut
[inline]=Η
FO_fin
HTML_debut
Η
HTML_fin
JS_debut
\x26#919;
JS_fin
BALISE_SOULIGNER
BOOLEAN_Symbol
BaliseJS_debut
\x5bu\x5d
BaliseJS_fin
\x5b\x2fu\x5d
Balise_debut
[u]
Balise_fin
[/u]
FO_debut
text-decoration=underline
FO_fin
text-decoration=none
HTML_debut
<u>
HTML_fin
</u>
JS_debut
\x3cu\x3e
JS_fin
\x3c\x2fu\x3e
CODE72092388
BOOLEAN_Symbol
BaliseJS_debut
\x5bpsi\x5d
BaliseJS_fin
Balise_debut
[psi]
Balise_fin
FO_debut
[inline]=ψ
FO_fin
HTML_debut
ψ
HTML_fin
JS_debut
\x26#968;
JS_fin
CODE72092541
BOOLEAN_Symbol
BaliseJS_debut
\x5bPSI\x5d
BaliseJS_fin
Balise_debut
[PSI]
Balise_fin
FO_debut
[inline]=Ψ
FO_fin
HTML_debut
Ψ
HTML_fin
JS_debut
\x26#936;
JS_fin
CODE140502511
BOOLEAN_Symbol
1
BaliseJS_debut
\x5brho\x5d
BaliseJS_fin
Balise_debut
[rho]
Balise_fin
FO_debut
[inline]=ρ
FO_fin
HTML_debut
ρ
HTML_fin
JS_debut
\x26#961;
JS_fin
CODE140504636
BOOLEAN_Symbol
1
BaliseJS_debut
\x5bRHO\x5d
BaliseJS_fin
Balise_debut
[RHO]
Balise_fin
FO_debut
[inline]=Ρ
FO_fin
HTML_debut
Ρ
HTML_fin
JS_debut
\x26#929;
JS_fin
CODE148292791
BOOLEAN_Symbol
BaliseJS_debut
\x5bepsilon\x5d
BaliseJS_fin
Balise_debut
[epsilon]
Balise_fin
FO_debut
[inline]=ε
FO_fin
HTML_debut
ε
HTML_fin
JS_debut
\x26#949;
JS_fin
CODE169976220
BOOLEAN_Symbol
BaliseJS_debut
\x5blig\x5d
BaliseJS_fin
Balise_debut
[lig]
Balise_fin
FO_debut
[inline]=›  
FO_fin
HTML_debut
›  
HTML_fin
JS_debut
\x26#x203A;\x26#160;\x26#160;
JS_fin
CODE148292899
BOOLEAN_Symbol
BaliseJS_debut
\x5bEPSILON\x5d
BaliseJS_fin
Balise_debut
[EPSILON]
Balise_fin
FO_debut
[inline]=Ε
FO_fin
HTML_debut
Ε
HTML_fin
JS_debut
\x26#917;
JS_fin
BALISETXT_SAUT
BOOLEAN_Symbol
BaliseJS_debut
\x5bbr\x2f\x5d
BaliseJS_fin
Balise_debut
[br/]
Balise_fin
FO_debut
FO_fin
HTML_debut
<br/>
HTML_fin
JS_debut
\x3cbr\x2f\x3e
JS_fin