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High Dimensional and Deep Learning


The main theme of the course is learning methods, especially deep neutral networks, for processing high dimensional data, such as signals or images. We will cover the following topics : 

  • Neutral networks and introduction to deep learning : definition of neutral networks, activation functions, multilayer perceptron, backpropagation algorithms, optimization algorithms, regularisation.
  • Convolutional neutral networks : convolutional layer, pooling, dropout, convoltional network architectures (resNet, Inception), transfert learning and fine tuning, applications for image or signal classification.
  • Encoder-decoder, Variational auto-encoder, Generative adversarial networks.
  • Functional decomposition on splines, Fourier or wavelets bases : cubic splines, penalized least squares criterion, Fourier basis, wavelet bases, applications to nonparametric regression, linear estimators and nonlinear estimators by thresholding, links withthe LASSO method.
  • Anomaly detection for functional data : One Class SVM, Random Forest, Isolation Forest, Local Outlier Factor. Applications to anomaly detection in functional data.



  • Lectures : 15H
  • Practical works : 25H applications on real data sets with the softwares R and Python’s libraries Scikit Learn and Kears-Tensorflow.


At the end of this module, the student will have understood and be able to explain (main concepts):

  • Using deep learnig methods for classification in high dimension
  • Calssification of signal and images
  • Estimation of the prediction error
  • Dimension reduction by projections onto orthonormal bases
  • Anomaly detection
  • Application of deep learning methods on real data sets 


The student will be able to:

  •  Fit a deep neutral network for signal or image classification
  • Implement deep learning methods in high dimension on real data sets with the softwares R or Python's libraries.

Needed prerequisite

Probability and statistics
Elements of statistical modelling [I4MMMS71]

Form of assessment

The evaluation of outcome prior learning is made as a continuous training during the semester. According ot the teaching, the assessment will be different: as a written exam, an oral exam, a record, a written report, peers review...