Objectives

The objective of this course is to provide students the basic knowledge of mathematical tools that they will often encountered in machine learning and data science. The emphasis will be more on the « practical » understanding of the algorithms rather than the detailed analysis of the rather sophisticated mathematical tools beyond the scene.

 

Syllabus

  • Multivariable functions, gradients, Jacobian matrix, Hessian
  • Unconstrained  optimization algorithms
    • Gradient descent
    • Line-searching algorithm
    • Speeding-up gradient descent (Newton algorithm, conjugate gradient)
  • Constrained optimization
    •  Duality, Lagrange multipliers.
    • Constrained optimization algorithm
  • Numerical linear algebra
    • matrix, vector spaces, determinants,
    • solutions of systems of linear equations, direct methods,
    • error analysis, structured matrix, iterative methods
    • Eigenvalue decomposition,
    • Singular value decomposition. 

Langue du cours : Anglais