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Computational Mathematics for Learning and Data Analysis 2017-2018
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Corso di Laurea Magistrale in Informatica (LM-18)
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CM17
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Course Material
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Introduction to the course
Introduction to the course
Slides: introduction to the course (Antonio Frangioni)
Click
0-introduction.pdf
link to view the file.
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Topology and Calculus background
Info on the linear algebra part + how to install Matlab
Matrix products
Matrix products (annotated)
Orthogonality and positive definiteness
Orthogonality and positive definiteness (annotated)
Singular value decomposition
SIngular value decomposition (annotated)
Matrix norms
Matrix norms (annotated)
Unconstrained Optimality and Convexity
Practical uses of the SVD
Practical uses of the SVD (annotated)
Unconstrained Optimization I
QR factorization
QR factorization (annotated)
Applications of linear least squares problems.
Applications of linear least squares problems (annotated)
Linear least squares: properties and normal equations
Linear least squares: properties and normal equations (annotated)
Pseudoinverse of a matrix (annotated)
Pseudoinverse of a matrix
Linear least squares: QR factorization
Linear least squares: QR factorization (annotated)
Unconstrained Optimization II
Linear least squares: solution with the SVD, rank-deficient problems and regularization
Linear least squares: solution with the SVD, rank-deficient problems and regularization (annotated)
Conditioning
Conditioning (annotated)
Conditioning of LS problems
Conditioning of LS problems (annotated)
Numerical stability
Numerical stability (annotated)
Stability of LS problems
Stability of LS problems (annotated)
Stability and residual (annotated)
Stability and residual (includes slides that were missing during the lectures)
Unconstrained Optimization III
Constrained Optimality and Duality
LU factorization
LU factorization (annotated)
Cholesky factorization
Arnoldi process
Arnoldi process (annotated)
Constrained Optimization
Arnoldi and eigenvalue computation
Arnoldi and eigenvalue computation (annotated)
GMRES
GMRES (annotated)
Conjugate gradient for linear systems
Conjugate gradient for linear systems (annotated)
Examples of large-scale linear systems
Examples of large-scale linear systems (annotated)
Background 1 (Antonio Frangioni)
Background 2 (Antonio Frangioni)
Background 3 (Antonio Frangioni)
Unconstrained Optimality Conditions (Antonio Frangioni)
Convexity 1 (Antonio Frangioni)
Background on matrix algebra (Federico Poloni, 2017-09-22)
Singular value decomposition (Federico Poloni, 2017-09-29)
Orthogonal matrices and positive definiteness (Federico Poloni, 2017-09-27)
Examples of applications of SVD (Federico Poloni, 2017-10-05)
Convexity 3 (Antonio Frangioni)
Gradient 4 Quadratic - Theory (Antonio Frangioni)
Gradient 4 Quadratic - MATLAB (Antonio Frangioni)
Gradient 4 Nonlinear - Exact LS (Antonio Frangioni)
Gradient 4 Nonlinear - Inexact LS (Antonio Frangioni)
Gradient 4 Nonlinear - MATLAB (Antonio Frangioni)
Gradient 4 Nonlinear - Fixed Stepsize (Antonio Frangioni)
Introduction to Newton's method (Antonio Frangioni)
Newton's Method - Hessian Modification (Antonio Frangioni)
Quasi-Newton Method - DFG and BFGS (Antonio Frangioni)
Householder reflectors and QR factorization(FP 2017-10-13)
Examples of LS problems (FP 2017-10-19) (file with problems)
Least squares problems (FP 2017-10-20)
LS problems, SVD and regularization (FP 2017-10-27)
Conditioning and sensitivity (FP 2017-11-09)
Numerical stability (FP 2017-11-10)
Limited-memory BFGS and Conjugate Gradient (Antonio Frangioni)
Heavy Ball and Accelerated Gradient (Antonio Frangioni)
Subgradient Methods - Motivation and Introduction (Antonio Frangioni)
Subgradient Methods - Advanced (Antonio Frangioni)
Cutting-Plane Methods (Antonio Frangioni)
Introduction to Constrained Optimization (Antonio Frangioni)
Karush-Khun-Tucker conditions (Antonio Frangioni)
Lagrangian Duality (Antonio Frangioni)
Conic and Fenchel Duality (Antonio Frangioni)
Equality Constrained Quadratic Programs and the Projected Gradient Method (Antonio Frangioni)
The Active Set Method for Quadratic Programs (Antonio Frangioni)
The Frank-Wolfe Method (Antonio Frangioni)
The Dual-Ascent Method (Antonio Frangioni)
Barrier Methods - Theory (Antonio Frangioni)
Barrier Methods - Practice (Antonio Frangioni)
GMRES; Lanczos procedure (FP 2017-12-07)
Conjugate gradient; experiments on positive definite linear systems (FP, 2017-12-15)
Termination and use of Arnoldi (FP, 2017-12-01)
LU factorization and sparsity (FP, 2017-11-17)
Arnoldi algorithm (FP, 2017-11-24)
LDL and Cholesky factorizations (FP, 2017-11-23)
Lecture notes (seminars & exercises)
SVD examples (eigenfaces and text mining)
Steepest descent method for quadratic functions
Test Functions
Gradient Method for General Nonlinear functions
Newton's Method
Quasi-Newton Method (BFGS)
Nonlinear Conjugate Gradient
Heavy Ball Gradient
Accelerated Gradient Method
SubGradient Method
Proximal Bundle Method
Generator of BCQP
Solver of BCQP
Projected Gradient for BCQP
Active Set for BCQP
Frank-Wolfe for BCQP
Dual-Ascent for BCQP
Interior-Point for BCQP
Projects on topics overlapping with the Machine Learning course
Projects on self-contained topics
Project pairings
Topology and Calculus background ►