IIT Madras MLF Lectures: Machine Learning Foundations
BSCS200493 lectures12 weeks
Weeks
- Week 19 lecturesWhat is machine learning? | intro to machine learning & its applications · Data, models & machine learning task · Supervised learning: regression · Supervised learning: classification · Unsupervised learning: dimensionality reduction · Unsupervised learning: density estimation · To machine learning or not to machine learning · Illustration with a real world dataset · Dimensionality reduction & density estimation with applications
- Week 27 lecturesSets & functions · Univariate calculus: continuity & differentiability · Univariate calculus: derivatives & linear approximations · Univariate calculus: applications & advanced rules · Multivariate calculus: lines & planes in higher dimensional space · Multivariate calculus: linear approximation & applications · Tutorial
- Week 38 lecturesFour fundamental subspaces · Orthogonal vectors & subspaces · Projections · Least squares & projections onto a subspace · Example of least squares · Four fundamental vector subspaces · Row space computation using reduced row echelon form & solution to ax = b · Orthogonality, projections & least squares method
- Week 47 lecturesLinear & polynomial regression · Eigenvalues & Eigenvectors · Diagonalization of a matrix · Solving fibonacci sequence using diagonalization · Orthogonality diagonalizable matrices · Polynomial regression · Tutorial on eigenvalues & eigenvectors
- Week 56 lecturesComplex matrices · Hermitian matrices · Unitary matrices · Diagonalization of hermitian matrices | part 1 · Diagonalization of hermitian matrices | part 2 · Some problems to think & solve
- Week 67 lecturesSingular value decomposition · Example of singular value decomposition (SVD) · Positive definiteness · Positive definite matrices · Real world application of SVD · Geometric interpretation of SVD · Positive definite functions & matrices
- Week 76 lecturesPrincipal component analysis(PCA) · Principal component analysis (contd.) · PCA as maximizing variance · PCA in higher dimensions · Tutorial | principal component analysis · Tutorial
- Week 88 lecturesPillars of machine learning · Introduction to optimization · Solving an unconstrained optimization problem | part 1 · Solving an unconstrained optimization problem | part 2 · Basic algorithm for unconstrained optimization: gradient descent · Gradient descent & taylor series · Gradient descent for multivariate functions · Taylor series in higher dimensions
- Week 98 lecturesConstrained optimization | part -1 · Constrained optimization | part -2 · Method of lagrange multiplier, projected gradient descent · Introduction to convexity · Properties of convex sets · Convex functions · Properties of convex functions · Constrained optimization, lagrange multpliers, convex sets & convex functions
- Week 106 lecturesProperties of convex functions · Applications of optimization in machine learning · Revisiting constrained optimization · Relation between primal & dual problem, karush-kuhn-tucker(KKT) conditions · Karush-kuhn-tucker (KKT) conditions continued · Linear programming, KKT conditions, relationship between primal & dual problem
- Week 118 lecturesContinuous random variables · Conditional pdf · Expectation · Multiple random variables · Independent random variables · Transformed random variables · Uniform, exponential, normal · Examples on continuous random variables
- Week 125 lecturesBivariate & multivariate normal · Estimation of parameters using machine learning · Gaussian mixture models & expectation maximization · Laws of large numbers: markov, chebyshev, hoeffding, central limit · Solved examples