This information is indicative and can be subject to change.
Statistical learning
Teacher: Alain Celisse
E-mail: alain.celisse@univ-paris1.fr
ECTS: 2.5
Evaluation: Project consisting in analyzing data by means of Python libraries
Previsional Place and time:
Prerequisites: Background in applied mathematics, probability theory and main concepts of statistics.
Aim of the course: Reviewing the main learning strategies classically applied when trying to extract valuable information form a dataset. The lectures detail the mathematical background for all the reviewed learning strategies in order to avoid misleading conclusions.
Syllabus:
1. Linear regression and model selection:
(a) Statistical model
(b) Penalized criteria: AIC/BIC
(c) Cross-validation
2. Classification:
(a) Logistic regression
(b) Discriminant Analysis: linear and quadratic
(c) kNN classifier
3. Clustering by Gaussian mixture models:
(a) Gaussian mixture models
(b) EM algorithm
4. Visualisation/dimension reduction:
(a) Principal Component Analysis
(b) Spectral Clustering
5. Convex optimization and machine learning:
(a) Convex optimization
(b) KKT conditions and Duality gap
(c) Gradient Descent
(d) Stochastic Gradient Descent
6. Introduction to Deep Neural Networks:
(a) Multi-layer perceptron
(b) Back-propagation et SGD
(c) Main architectures: MLP, CNN and Autoencoders
References:
Statistical learning
Teacher: Alain Celisse
E-mail: alain.celisse@univ-paris1.fr
ECTS: 2.5
Evaluation: Project consisting in analyzing data by means of Python libraries
Previsional Place and time:
Prerequisites: Background in applied mathematics, probability theory and main concepts of statistics.
Aim of the course: Reviewing the main learning strategies classically applied when trying to extract valuable information form a dataset. The lectures detail the mathematical background for all the reviewed learning strategies in order to avoid misleading conclusions.
Syllabus:
1. Linear regression and model selection:
(a) Statistical model
(b) Penalized criteria: AIC/BIC
(c) Cross-validation
2. Classification:
(a) Logistic regression
(b) Discriminant Analysis: linear and quadratic
(c) kNN classifier
3. Clustering by Gaussian mixture models:
(a) Gaussian mixture models
(b) EM algorithm
4. Visualisation/dimension reduction:
(a) Principal Component Analysis
(b) Spectral Clustering
5. Convex optimization and machine learning:
(a) Convex optimization
(b) KKT conditions and Duality gap
(c) Gradient Descent
(d) Stochastic Gradient Descent
6. Introduction to Deep Neural Networks:
(a) Multi-layer perceptron
(b) Back-propagation et SGD
(c) Main architectures: MLP, CNN and Autoencoders
References:
