An overview of basic probability theory and theory of estimation; Bayesian statistics; maximum a posteriori (MAP) estimation; conjugate priors; Exponential family; posterior asymptotics; linear statistical models; multiple linear regression: inference technique for the general linear model, generalised linear models: inference procedures, special case of generalised linear models leading to logistic regression and log linear models; introduction to non-linear modelling; sampling methods: basic sampling algorithms, rejection sampling, adaptive rejection sampling, sampling and the EM algorith

Kernel Methods: reproducing kernel Hilbert space concepts, kernel algorithms, multiple kernels, graph kernels; multitasking, deep learning architectures; spectral clustering ; model based clustering, independent component analysis; sequential data: Hidden Markhov models; factor analysis; graphical models; reinforcement learning; Gaussian processes; motiff discovery; graph-based semisupervised learning; natural language processing algorithms.

Programming with Python: Introduction to Python, data types, file operations, object oriented programming. Programming with R: Introduction to R, string operations, data visualization.

Machine learning basics: capacity, overfitting and underfitting, hyperparameters and validation sets, bias & variance; PAC model; Rademacher complexity; growth function; VC-dimension; fundamental concepts of artificial neural networks; single layer perceptron classifier; multi-layer feed forward networks; single layer feed-back networks; associative memories; introductory concepts of reinforcement learning, Markhov decision process.

Introduction to fundamental linear algebra problems and their importance, computational difficulties using theoretical linear algebra techniques, review of core linear algebra concepts; introduction to matrix calculus; floating point representation; conditioning of problems and stability of algorithms; singular value decomposition and regularization theory.

Introduction to data mining concepts; linear methods for regression; classification methods: k- nearest neighbourclassifiers, decision tree, logistic regression, naive Bayes, Gaussian discriminant analysis; model evaluation & selection;unsupervised learning: association rules; apriori algorithm, FP tree, cluster analysis, self organizing maps, google page ranking; dimensionality reduction methods: supervised feature selection, principal component analysis; ensemble learning: bagging, boosting, AdaBoost; outlier mining; imbalance problem; multi class classification; evolutionary computat

Optimization: need for unconstrained methods in solving constrained problems, necessary conditions of unconstrained optimization, structure methods, quadratic models, methods of line search, steepest descent method; quasi-Newton methods: DFP, BFGS, conjugate-direction methods: methods for sums of squares and nonlinear equations; linear programming: simplex methods, duality in linear programming, transportation problem; nonlinear programming: Lagrange multiplier, KKT conditions, convex programing