Live Session 2 Applied Linear Algebra in AI and ML by Prof.Swanand Khare | IIT Kharagpur -NPTEL
Applied Linear Algebra in AI and ML by Prof.Swanand Khare | IIT Kharagpur | NPTEL | Week 2 Live Session ABOUT THE COURSE: Linear algebra, optimization techniques and statistical methods together form essential tools for most of the algorithms in artificial intelligence and machine learning. In this course, we propose to build some background in these mathematical foundations and prepare students to take on advanced study or research in the field of AI and ML. The objective of this course is to familiarize students with the important concepts and computational techniques in linear algebra useful for AI and ML applications. The unique objective of this course and the distinguishing point from the existing courses on the similar topics is the illustration of application of these concepts to many problems in AI and ML. Some of the key topics to be covered in this course are listed below: least squares solution, parameter estimation problems, concept of cost function and relation to parameter estimation, constrained least squares, multi-objective least squares, applications to portfolio optimization, sparse solutions to underdetermined systems of linear equations, applications to dictionary learning, eigenvalue eigenvector decomposition of square matrices, spectral theorem for symmetric matrices, SVD, multicollinearity problem and applications to principal component analysis (PCA) and dimensionality reduction, power method, application to Google page ranking algorithm, inverse eigenvalue problem, construction of Markov chains from the given stationary distribution, low rank approximation and structured low rank approximation problem (SLRA), Autoregressive model order selection using Hankel SLRA, approximate GCD computation and application to image de- blurring, tensors and CP tensor decomposition, tensor decomposition based sparse learning in deep networks, matrix completion problems, application to collaborative filtering
Applied Linear Algebra in AI and ML by Prof.Swanand Khare | IIT Kharagpur | NPTEL | Week 2 Live Session ABOUT THE COURSE: Linear algebra, optimization techniques and statistical methods together form essential tools for most of the algorithms in artificial intelligence and machine learning. In this course, we propose to build some background in these mathematical foundations and prepare students to take on advanced study or research in the field of AI and ML. The objective of this course is to familiarize students with the important concepts and computational techniques in linear algebra useful for AI and ML applications. The unique objective of this course and the distinguishing point from the existing courses on the similar topics is the illustration of application of these concepts to many problems in AI and ML. Some of the key topics to be covered in this course are listed below: least squares solution, parameter estimation problems, concept of cost function and relation to parameter estimation, constrained least squares, multi-objective least squares, applications to portfolio optimization, sparse solutions to underdetermined systems of linear equations, applications to dictionary learning, eigenvalue eigenvector decomposition of square matrices, spectral theorem for symmetric matrices, SVD, multicollinearity problem and applications to principal component analysis (PCA) and dimensionality reduction, power method, application to Google page ranking algorithm, inverse eigenvalue problem, construction of Markov chains from the given stationary distribution, low rank approximation and structured low rank approximation problem (SLRA), Autoregressive model order selection using Hankel SLRA, approximate GCD computation and application to image de- blurring, tensors and CP tensor decomposition, tensor decomposition based sparse learning in deep networks, matrix completion problems, application to collaborative filtering