The course introduces important numerical techniques currently applied in Data Science and Machine (Deep) Learning. It builds on (numerical) linear algebra and numerical optimization, and it is organized into four units:
1. Optimization basics
2. Least-squares problems
3. Optimization for deep learning
4. Matrix data and latent factor models.
The main topics covered will be:
1. Unconstrained optimization, optimality conditions. Basic algorithms for unconstrained optimization (gradient descent, conjugate gradient). Newton's method. Quasi-Newton methods. Line search strategies. Introduction to constrained optimization. Optimality conditions (KKT).
2. Least-squares problems. Gauss-Newton and Levenberg-Marquardt methods. Tikhonov and Lasso regularization.
3. Numerical optimization for machine learning and deep learning. Support vector machines (SVM). Unconstrained minimization problem arising in the training of DNNs. Stochastic gradient descent. Stochastic second-order methods (L-BFGS).
4. Latent Semantic Analysis and collaborative filtering. SVD. Eckart-Young-Mirsky theorem. NMF. Overview of methods for computing NMF. CUR matrix decomposition.
Lecturer: Prof. Angeles Martinez Calomardo
Contact info:
e-mail: amartinez@units.it
Office address: Room 228, 2nd floor, H2/bis Building.
1. Optimization basics
2. Least-squares problems
3. Optimization for deep learning
4. Matrix data and latent factor models.
The main topics covered will be:
1. Unconstrained optimization, optimality conditions. Basic algorithms for unconstrained optimization (gradient descent, conjugate gradient). Newton's method. Quasi-Newton methods. Line search strategies. Introduction to constrained optimization. Optimality conditions (KKT).
2. Least-squares problems. Gauss-Newton and Levenberg-Marquardt methods. Tikhonov and Lasso regularization.
3. Numerical optimization for machine learning and deep learning. Support vector machines (SVM). Unconstrained minimization problem arising in the training of DNNs. Stochastic gradient descent. Stochastic second-order methods (L-BFGS).
4. Latent Semantic Analysis and collaborative filtering. SVD. Eckart-Young-Mirsky theorem. NMF. Overview of methods for computing NMF. CUR matrix decomposition.
Lecturer: Prof. Angeles Martinez Calomardo
Contact info:
e-mail: amartinez@units.it
Office address: Room 228, 2nd floor, H2/bis Building.
- Teacher: ANGELES MARTINEZ CALOMARDO