Linear algebra concepts are key for understanding and creating machine learning algorithms, especially as applied to deep learning and neural networks. This course reviews linear algebra with applications to statistics, image processing and optimization–and above all a full explanation of the structure of Neural Networks.
Curriculum
scheda docente
materiale didattico
Matrix-matrix multiplication; column & row space; rank
The four fundamental subspaces of linear algebra
Fundamentals of Matrix factorizations:
A=LU rows & columns point of view
A=LU elimination & factorization; permutations
A=RU=VU; Orthogonal matrices
Eigensystems and Linear ODE
Intro to PSym; the energy function
Gradient and Hessian
Singular Value Decomposition
Eckart-Young; derivative of a matrix norm
Principal Component Analysis
Generalized evectors;
Norms
Least Squares
Convexity & Newton’s method
Newton & L-M method; Recap of non-linear regression
Lagrange multipliers
Machine Learning:
Gradient Descend; exact line search; GD in action; GD with Matlab
Learning & Loss; Intro to Deep Neural Network; DNN with Matlab
Loss functions: Quadratic VS Cross entropy
Stocastics Gradient Descend (SGD) & Kaczmarcz; SGD convergence rates & ADAM
Matlab interface for DNN
Construction of DNN: the key steps
Backpropagation and the Chain Rule
Machine Learning examples with Wolfram Mathematica
Convolutional NN + Mathematica examples of 1D convolution
Convolution and 2D filters + Mathematica examples of 2D convolution
Matlab Live Script, Network Designer, Pretrained Net
G. Strang,
Linear Algebra and Learning from Data,
Wellesley-Cambridge Press
Mutuazione: 20410875 FM530 - METODI MATEMATICI PER IL MACHINE LEARNING in Scienze Computazionali LM-40 TERESI LUCIANO, REUVERS Robin Johannes Petrus
Programma
Highlights of Linear Algebra:Matrix-matrix multiplication; column & row space; rank
The four fundamental subspaces of linear algebra
Fundamentals of Matrix factorizations:
A=LU rows & columns point of view
A=LU elimination & factorization; permutations
A=RU=VU; Orthogonal matrices
Eigensystems and Linear ODE
Intro to PSym; the energy function
Gradient and Hessian
Singular Value Decomposition
Eckart-Young; derivative of a matrix norm
Principal Component Analysis
Generalized evectors;
Norms
Least Squares
Convexity & Newton’s method
Newton & L-M method; Recap of non-linear regression
Lagrange multipliers
Machine Learning:
Gradient Descend; exact line search; GD in action; GD with Matlab
Learning & Loss; Intro to Deep Neural Network; DNN with Matlab
Loss functions: Quadratic VS Cross entropy
Stocastics Gradient Descend (SGD) & Kaczmarcz; SGD convergence rates & ADAM
Matlab interface for DNN
Construction of DNN: the key steps
Backpropagation and the Chain Rule
Machine Learning examples with Wolfram Mathematica
Convolutional NN + Mathematica examples of 1D convolution
Convolution and 2D filters + Mathematica examples of 2D convolution
Matlab Live Script, Network Designer, Pretrained Net
Testi Adottati
Lecture notesG. Strang,
Linear Algebra and Learning from Data,
Wellesley-Cambridge Press
Modalità Erogazione
Theory and practicals with computers; practicals have a noteworthy role in these lecturModalità Valutazione
Project to be defined with the instructor: the students are required to produce a written report containing the description of a select problem and a discussion about the numerical experiments.
scheda docente
materiale didattico
Mutuazione: 20410875 FM530 - METODI MATEMATICI PER IL MACHINE LEARNING in Scienze Computazionali LM-40 TERESI LUCIANO, REUVERS Robin Johannes Petrus
scheda docente
materiale didattico
Matrix-matrix multiplication; column & row space; rank
The four fundamental subspaces of linear algebra
Fundamentals of Matrix factorizations:
A=LU rows & columns point of view
A=LU elimination & factorization; permutations
A=RU=VU; Orthogonal matrices
Eigensystems and Linear ODE
Intro to PSym; the energy function
Gradient and Hessian
Singular Value Decomposition
Eckart-Young; derivative of a matrix norm
Principal Component Analysis
Generalized evectors;
Norms
Least Squares
Convexity & Newton’s method
Newton & L-M method; Recap of non-linear regression
Lagrange multipliers
Machine Learning:
Gradient Descend; exact line search; GD in action; GD with Matlab
Learning & Loss; Intro to Deep Neural Network; DNN with Matlab
Loss functions: Quadratic VS Cross entropy
Stocastics Gradient Descend (SGD) & Kaczmarcz; SGD convergence rates & ADAM
Matlab interface for DNN
Construction of DNN: the key steps
Backpropagation and the Chain Rule
Machine Learning examples with Wolfram Mathematica
Convolutional NN + Mathematica examples of 1D convolution
Convolution and 2D filters + Mathematica examples of 2D convolution
Matlab Live Script, Network Designer, Pretrained Net
G. Strang,
Linear Algebra and Learning from Data,
Wellesley-Cambridge Press
Mutuazione: 20410875 FM530 - METODI MATEMATICI PER IL MACHINE LEARNING in Scienze Computazionali LM-40 TERESI LUCIANO, REUVERS Robin Johannes Petrus
Programma
Highlights of Linear Algebra:Matrix-matrix multiplication; column & row space; rank
The four fundamental subspaces of linear algebra
Fundamentals of Matrix factorizations:
A=LU rows & columns point of view
A=LU elimination & factorization; permutations
A=RU=VU; Orthogonal matrices
Eigensystems and Linear ODE
Intro to PSym; the energy function
Gradient and Hessian
Singular Value Decomposition
Eckart-Young; derivative of a matrix norm
Principal Component Analysis
Generalized evectors;
Norms
Least Squares
Convexity & Newton’s method
Newton & L-M method; Recap of non-linear regression
Lagrange multipliers
Machine Learning:
Gradient Descend; exact line search; GD in action; GD with Matlab
Learning & Loss; Intro to Deep Neural Network; DNN with Matlab
Loss functions: Quadratic VS Cross entropy
Stocastics Gradient Descend (SGD) & Kaczmarcz; SGD convergence rates & ADAM
Matlab interface for DNN
Construction of DNN: the key steps
Backpropagation and the Chain Rule
Machine Learning examples with Wolfram Mathematica
Convolutional NN + Mathematica examples of 1D convolution
Convolution and 2D filters + Mathematica examples of 2D convolution
Matlab Live Script, Network Designer, Pretrained Net
Testi Adottati
Lecture notesG. Strang,
Linear Algebra and Learning from Data,
Wellesley-Cambridge Press
Modalità Erogazione
Theory and practicals with computers; practicals have a noteworthy role in these lecturModalità Valutazione
Project to be defined with the instructor: the students are required to produce a written report containing the description of a select problem and a discussion about the numerical experiments.
scheda docente
materiale didattico
Mutuazione: 20410875 FM530 - METODI MATEMATICI PER IL MACHINE LEARNING in Scienze Computazionali LM-40 TERESI LUCIANO, REUVERS Robin Johannes Petrus