Overview of Pattern classification and regression : Introduction to Statistical Pattern Recognition – Overview of Pattern Classifiers
Bayesian decision making and Bayes Classifier : The Bayes Classifier for minimizing Risk – Estimating Bayes Error; Minimax and Neymann-Pearson classifiers
Parametric Estimation of Densities : Implementing Bayes Classifier; Estimation of Class Conditional Densities – Maximum Likelihood estimation of different densities – Bayesian estimation of parameters of density functions, MAP estimates – Bayesian Estimation examples; the exponential family of densities and ML estimates – Sufficient Statistics; Recursive formulation of ML and Bayesian estimates
Mixture Densities and EM Algorithm : Mixture Densities, ML estimation and EM algorithm – Convergence of EM algorithm; overview of Nonparametric density estimation
Nonparametric density estimation : Convergence of EM algorithm; overview of Nonparametric density estimation – Nonparametric estimation, Parzen Windows, nearest neighbour methods
Linear models for classification and regression : Linear Discriminant Functions; Perceptron — Learning Algorithm and convergence proof – Linear Least Squares Regression; LMS algorithm – AdaLinE and LMS algorithm; General nonliner least-squares regression – Logistic Regression; Statistics of least squares method; Regularized Least Squares – Fisher Linear Discriminant – Linear Discriminant functions for multi-class case; multi-class logistic regression
Overview of statistical learning theory, Empirical Risk Minimization and VC-Dimension : Learning and Generalization; PAC learning framework – Overview of Statistical Learning Theory; Empirical Risk Minimization – Consistency of Empirical Risk Minimization – Consistency of Empirical Risk Minimization; VC-Dimension – Complexity of Learning problems and VC-Dimension – VC-Dimension Examples; VC-Dimension of hyperplanes
Artificial Neural Networks for Classification and regression : Overview of Artificial Neural Networks – Multilayer Feedforward Neural networks with Sigmoidal activation functions; – Backpropagation Algorithm; Representational abilities of feedforward networks – Feedforward networks for Classification and Regression; Backpropagation in Practice – Radial Basis Function Networks; Gaussian RBF networks – Learning Weights in RBF networks; K-means clustering algorithm
Support Vector Machines and Kernel based methods : Support Vector Machines — Introduction, obtaining the optimal hyperplane – SVM formulation with slack variables; nonlinear SVM classifiers – Kernel Functions for nonlinear SVMs; Mercer and positive definite Kernels – Support Vector Regression and ε-insensitive Loss function, examples of SVM learning – Overview of SMO and other algorithms for SVM; ν-SVM and ν-SVR; SVM as a risk minimizer – Positive Definite Kernels; RKHS; Representer Theorem
Feature Selection, Model assessment and cross-validation : Feature Selection and Dimensionality Reduction; Principal Component Analysis – No Free Lunch Theorem; Model selection and model estimation; Bias-variance trade-off – Assessing Learnt classifiers; Cross Validation;
Boosting and Classifier ensembles : Bootstrap, Bagging and Boosting; Classifier Ensembles; AdaBoost – Risk minimization view of AdaBoost
This Course is provided by IISc Bangalore as part of NPTEL online courses.
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