The class will be taught in French or English, depending on attendance (all slides and class notes are in English).
sanitary situation, all classes will be online, with the following
tentative plan. Detailed class notes will be made available
2 days before each class, while connection details sent to the
registered participants the night before (I will use GotoMeeting).
student is expected to read the class notes before the class.
During class, I will go over them, provide additional details and
answer questions. Classes will be held on Friday between
8.30am and 11.30am.
||Learning with infinite data (population setting)
-Decision theory (loss, risk, optimal predictors)
-Decomposition of excess risk into approximation and estimation errors
-No free lunch theorems
-Basic notions of concentration inequalities (MacDiarmid, Hoeffding, Bernstein)
||Liner Least-squares regression
-Guarantees in the fixed design settings (simple in closed-form)
-Ridge regression: dimension independent bounds
-Guarantees in the random design settings
-Lower bound of performance
|October 2||Empirical risk minimization
-Convexification of the risk
-Estimation error: finite number of hypotheses and covering numbers
||Optimization for machine learning
-Stochastic gradient descent
-Generalization bounds through stochastic gradient descent
|October 23||Local averaging techniques
-Kernels and representer theorems
-Analysis of well-specified models
-Sharp analysis of ridge regression
-Single hidden layer neural networks
- Estimation error
- Approximation properties and universality
-Generalization/optimization properties of infinitely wide neural networks
written in-class exam, and (very) simple coding assignments (to
illustrate convergence results, to be sent to
email@example.com). For all classes, the
coding assignment is to reproduce the experiments shown in the lecture
notes and send only the figures to the address above.