Spatial data representation – discrete Euclidean plane/ geometric domain/ discritisation of arcs – spatial object domain: vector data models: spaghetti, arc – node , DCEL – field based model: tasseled representation, triangulation, voronoi, Delaunay triangulation – geometric algorithms, topological  and set based algorithms – network analysis, traveling salesperson algorithm – spatial analysis: interpolation methods, deterministic, stochastic, geostatistics, spatial autocorrelation, semi-variogram, kriging, types of kriging – uncertainty and its assessment.

Kernel Methods:  Introduction to metric space, vector space, normed space, inner product space; RKHS; Learning theory;  SVM for classification & regression; implementation techniques of SVM;   kernel ridge regression;  kernel density estimation;  kernel PCA; kernel online learning.Random forest, Genetic algorithms, ant colony optimization

Spectral Clustering; model based clustering, Expectation Maximization; Independent Component Analysis; Hidden Markhov models;  Factor Analysis; introduction to Graphical models & Sampling Methods.

Big data analytics: Introduction to spark 2.0 & tensor flow, tools to assess the quality of big data analytics. Mini project on a topic related with data modeling.

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.