Syllabus for
Master of Science (Data Science)
Academic Year  (2021)

Data Science is popular in all academia, business sectors, and research and development to make effective decision in day to day activities. MSc in Data Science is a two year programme with four semesters. This programme aims to provide opportunity to all candidates to master the skill sets specific to data science with research bent. The curriculum supports the students to obtain adequate knowledge in theory of data science with hands on experience in relevant domains and tools. Candidate gains exposure to research models and industry standard applications in data science through guest lectures, seminars, projects, internships, etc.

CIA - 50%

ESE - 50%

Data Science is popular in all academia, business sectors, and research and development to make effective decision in day to day activities. MSc in Data Science is a two year programme with four semesters. This programme aims to provide opportunity to all candidates to master the skill sets specific to data science with research bent. The curriculum supports the students to obtain adequate knowledge in theory of data science with hands on experience in relevant domains and tools. Candidate gains exposure to research models and industry standard applications in data science through guest lectures, seminars, projects, internships, etc. 

Programme Outcome/Programme Learning Goals/Programme Learning Outcome:

PO2: Identify analyze and design solutions for data science problems using fundamental principles of mathematics, Statistics, computing sciences, and relevant domain disciplines.

PO3: Demonstrate the skills in handling data science programming tools towards problem solving and solution analysis for domain specific problems.

PO4: Produce innovative IT solutions and services based on global needs and trends.

PO5: Utilize the data science theories for societal and environmental concerns.

PO6: Understand and commit to professional ethics and cyber regulations, responsibilities, and norms of professional computing practices.

PO7: Use research-based knowledge and research methods including design of experiments, analysis and interpretation of data, and synthesis of the research-based knowledge and research methods including design of information to provide valid conclusions.

PO8: Function effectively as an individual and as a member or leader in diverse teams and in multidisciplinary environments.

PO9: Understand the role of statistical approaches and apply the same to solve the real life problems in the fields of data science.

CIA & ESE

Linear Algebra plays a fundamental role in the theory of Data Science. This course aims at introducing the basic notions of vector spaces, Linear Algebra and the use of Linear Algebra in applications to Data Science.

Vector Spaces: Rⁿ and Cⁿ, lists, Fⁿ and digression on Fields, Definition of Vector spaces, Subspaces, sums of Subspaces, Direct Sums, Span and Linear Independence, bases, dimension.

DefinitionofLinearMaps-AlgebraicOperationson L(V,W) - Null spaces and Injectivity-RangeandSurjectivity-FundamentalTheoremsofLinearMaps-Representing aLinearMapbyaMatrix-InvertibleLinearMaps-IsomorphicVectorspaces-LinearMap as Matrix Multiplication - Operators - Products of Vector Spaces - Product of Direct Sum - Quotients of Vector spaces.

Eigenvalues and Eigenvectors - Eigenvectors and Upper Triangular matrices - Eigenspaces and Diagonal Matrices - Inner Products and Norms - Linear functionals on Inner Product spaces.

 Matrix Norms – Least square problem - Singular value decomposition- Householder Transformation and QR decomposition- Non Negative Matrix Factorization – bidiagonalization.

Handwritten digits recognition using simple algorithm - Classification of handwritten digits using SVD bases and Tangent distance - Text Mining using Latent semantic index, Clustering, Non-negative Matrix Factorization and LGK bidiagonalization.

2. Eldén Lars, Matrix methods in data mining and pattern recognition, Society for Industrial and Applied Mathematics, 2007.

2. J. V. Kepner and J. R. Gilbert, Graph algorithms in the language of linear algebra, Society for Industrial and Applied Mathematics, 2011.

3. D. A. Simovici, Linear algebra tools for data mining, World Scientific Publishing, 2012.

4. P. N. Klein, Coding the matrix: linear algebra through applications to computer science, Newtonian Press, 2015.

ESE - 50%

Linear Algebra plays a fundamental role in the theory of Data Science. This course aims at introducing the basic notions of vector spaces, Linear Algebra and the use of Linear Algebra in applications to Data Science

Vector Spaces: Rⁿ and Cⁿ, lists, Fⁿ and digression on Fields, Definition of Vector spaces, Subspaces, sums of Subspaces, Direct Sums, Span and Linear Independence, bases, dimension

Definition of LinearMaps-AlgebraicOperationson L(V,W) - Null spaces and Injectivity-RangeandSurjectivity-FundamentalTheoremsofLinearMaps-Representing aLinearMapbyaMatrix-InvertibleLinearMaps-IsomorphicVectorspaces-LinearMap as Matrix Multiplication - Operators - Products of Vector Spaces - Product of Direct Sum - Quotients of Vector spaces

Eigenvalues and Eigenvectors - Eigenvectors and Upper Triangular matrices - Eigenspaces and Diagonal Matrices - Inner Products and Norms - Linear functionals on Inner Product spaces.

Matrix Norms – Least square problem - Singular value decomposition- Householder Transformation and QR decomposition- Non Negative Matrix Factorization – bidiagonalization.

Handwritten digits recognition using simple algorithm - Classification of handwritten digits using SVD bases and Tangent distance - Text Mining using Latent semantic index, Clustering, Non-negative Matrix Factorization and LGK bidiagonalization

2. Eldén Lars, Matrix methods in data mining and pattern recognition, Society for Industrial and Applied Mathematics, 2007.

2. J. V. Kepner and J. R. Gilbert, Graph algorithms in the language of linear algebra, Society for Industrial and Applied Mathematics, 2011.

3. D. A. Simovici, Linear algebra tools for data mining, World Scientific Publishing, 2012.

4. P. N. Klein, Coding the matrix: linear algebra through applications to computer science, Newtonian Press,2015

CIA II : 25%

CIA III : 10%

ATTENDANCE : 5%

ESE : 50%

Probability and probability distributions play an essential role in modeling data from the real-world phenomenon. This course will equip students with thorough knowledge in probability and various probability distributions and model real-life data sets with an appropriate probability distribution

Data – types of variables: numeric vs categorical - measures of central tendency – measures of dispersion - random experiment - sample space and random events – probability - probability axioms - finite sample space with equally likely outcomes - conditional probability - independent events - Baye’s theorem

Random variable – data as observed values of a random variable - expectation – moments & moment generating function - mean and variance in terms of moments - discrete sample space and discrete random variable – Bernoulli experiment and Binary variable: Bernoulli and binomial distributions – Count data: Poisson distribution – overdispersion in count data: negative binomial distribution – dependent Bernoulli  trails: hypergeometric distribution.

Continuous sample space - Interval data - continuous random variable – uniform distribution - normal distribution (Gaussian distribution) – modeling lifetime data: exponential distribution, gamma distribution, Weibull distribution.

Joint distribution of vector random variables – joint moments – covariance – correlation - the correlation - independent random variables - conditional distribution – conditional expectation - sampling distributions: chi-square, t, F (central).

Chebychev’s inequality - weak law of large n u mbers (iid): examples - strong law of large numbers (statement only) - central limit theorems (iid case): examples.

2. An Introduction to Probability and Statistics, V.K Rohatgi and Saleh, 3rd Edition, 2015

2. Ross, Sheldon M. Introduction to probability models. 12th Edition, Academic Press, 2019. 

ESE: 50%

Course Objectives

 To enable the students to understand the properties and applications of various probability functions.

CO2: Infer the expectations for random variable functions and generating functions.

CO3: Demonstrate various discrete and continuous distributions and their usage

Algebra of sets - fields and sigma - fields, Inverse function -Measurable function – Probability measure on a sigma field – simple properties - Probability space - Random variables and Random vectors – Induced Probability space – Distribution functions –Decomposition of distribution functions.

Definitions and simple properties - Moment inequalities – Holder, Jenson Inequalities – Characteristic function – definition and properties – Inversion formula. Convergence of a sequence of random variables - convergence in distribution - convergence in probability almost sure convergence and convergence in quadratic mean - Weak and Complete convergence of distribution functions – Helly - Bray theorem.

Khintchin's weak law of large numbers, Kolmogorov strong law of large numbers (statement only) – Central Limit Theorem – Lindeberg – Levy theorem, Linderberg – Feller theorem (statement only), Liapounov theorem – Relation between Liapounov and Linderberg –Feller forms – Radon Nikodym theorem and derivative (without proof) – Conditional expectation – definition and simple properties.

Distribution of functions of random variables – Laplace, Cauchy, Inverse Gaussian, Lognormal, Logarithmic series and Power series distributions - Multinomial distribution - Bivariate Binomial – Bivariate Poisson – Bivariate Normal - Bivariate Exponential of Marshall and Olkin - Compound, truncated and mixture of distributions, Concept of convolution - Multivariate normal distribution (Definition and Concept only) - Sampling distributions: Non-central chi-square, t and F distributions and their properties.

Order statistics, their distributions and properties - Joint and marginal distributions of order statistics - Distribution of range and mid range -Extreme values and their asymptotic distributions (concepts only) - Empirical distribution function and its properties – Kolmogorov - Smirnov distributions – Life time distributions -Exponential and Weibull distributions - Mills ratio – Distributions classified by hazard rate.

2. V.K Rohatgi and Saleh, An Introduction to Probability and Statistics, 3^rd Edition, 2015.

2. H.A David and H.N Nagaraja, Order Statistics, John Wiley & Sons, 3^rd Edition, 2003.

ESE - 50%

To provide strong foundation for data science and application area related to information technology and understand the underlying core concepts and emerging technologies in data science

Definition – Big Data and Data Science Hype – Why data science – Getting Past the Hype – The Current Landscape – Who is Data Scientist? - Data Science Process Overview – Defining goals – Retrieving data – Data preparation – Data exploration – Data modeling – Presentation.

Problems when handling large data – General techniques for handling large data – Case study – Steps in big data – Distributing data storage and processing with Frameworks – Case study.

Machine learning – Modeling Process – Training model – Validating model – Predicting new observations –Supervised learning algorithms – Unsupervised learning algorithms.

Introduction – Deep Feedforward Networks – Regularization – Optimization of Deep Learning – Convolutional Networks – Recurrent and Recursive Nets – Applications of Deep Learning.

Introduction to data visualization – Data visualization options – Filters – MapReduce – Dashboard development tools – Creating an interactive dashboard with dc.js-summary.

Data Science Ethics – Doing good data science – Owners of the data - Valuing different aspects of privacy - Getting informed consent - The Five Cs – Diversity – Inclusion – Future Trends.

[2]. An Introduction to Statistical Learning: with Applications in R, Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani, Springer, 1st edition, 2013

[3]. Deep Learning, Ian Goodfellow, Yoshua Bengio, Aaron Courville, MIT Press, 1st edition, 2016

[4]. Ethics and Data Science, D J Patil, Hilary Mason, Mike Loukides, O’ Reilly, 1st edition, 2018

[2]. Doing Data Science, Straight Talk from the Frontline, Cathy O'Neil, Rachel Schutt, O’Reilly, 1st edition, 2013

[3]. Mining of Massive Datasets, Jure Leskovec, Anand Rajaraman, Jeffrey David Ullman, Cambridge University Press, 2nd edition, 2014

ESE : 50 %

Course Description:

To provide strong foundation for Data Science and related areas of application. The course includes with the fundamentals of data science, different techniques for handing big data and machine learning algorithms for supervised and unsupervised learning. The importance of handling data in an ethical manner and the ethical practices to be adopted while dealing the data is also  a part of the course.

Course Objectives:

Problems when handling large data – General techniques for handling large data – Case study – Steps in big data – Distributing data storage and processing with Frameworks – Case study.

T2. An Introduction to Statistical Learning: with Applications in R, Gareth James, Daniela Witten, Trevor Hastic, Robert Tibshirani, Springer, 1^st edition, 2013

T3. Deep learning, Ian Goodfellow, Yoshua Bengio, Aaron Courville, MIT Press, 1^st   Edition, 2016

T4. Ethics and Data Science, D J Patil, Hilary mason, Mike Loukides, O’ Reilly, 1^st Edition, 2018

R2.Doing Data Science, Straight talk from the Frontline, Cathy O’Neil, Rachel Schutt, O’ Reilly, 1^st Edition, 2013

R3. Mining of Massive Datasets, Jure Leskovee, Anand Rajaraman, Jeffrey David Ullman, Cambridge University Press, 2^nd edition, 2014

This course is intended to assist students in planning and carrying out research work.The students are exposed to the basic principles, procedures and techniques of implementing a research project.

To introduce the research concept and the various research methodologies is the main objective. It focuses on finding out the research gap from the literature and encourages lateral, strategic and creative thinking. This course also introduces computer technology and basic statistics required for research and reporting the research outcomes scientifically emphasizing on research ethics.

Defining research problem:Selecting the problem, Necessity of defining the problem ,Techniques involved in defining a problem- Ethics in Research.

Principles of experimental design,Working with Literature: Importance, finding literature, Using your resources, Managing the literature, Keep track of references,Using the literature, Literature review,On-line Searching: Database ,SCIFinder, Scopus, Science Direct ,Searching research articles , Citation Index ,Impact Factor ,H-index.

Measurement of Scaling: Quantitative, Qualitative, Classification of Measure scales, Data Collection, Data Preparation. 

Scientific Writing and Report Writing: Significance, Steps, Layout, Types, Mechanics and Precautions, Latex: Introduction, Text, Tables, Figures, Equations, Citations, Referencing, and Templates (IEEE style), Paper writing for international journals, Writing scientific report. 

[2] Zina O’Leary, The Essential Guide of Doing Research, New Delhi: PHI, 2005. 

[2] Kumar, Research Methodology: A Step by Step Guide for Beginners, 3rd. ed. Indian: PE, 2010. 

ESE - 50%

This course is intended to assist students in planning and carrying out research work.The students are exposed to the basic principles, procedures and techniques of implementing a research project. 

To introduce the research concept and the various research methodologies is the main objective. It focuses on finding out the research gap from the literature and encourages lateral, strategic and creative thinking. This course also introduces computer technology and basic statistics required for research and reporting the research outcomes scientifically emphasizing on research ethics.

CO2: Apply research methods and methodology including research design,data collection, data analysis, and interpretation.

CO3: Create scientific reports according to specified standards.

Defining research problem:Selecting the problem, Necessity of defining the problem ,Techniques involved in defining a problem- Ethics in Research.

Principles of experimental design,Working with Literature: Importance, finding literature, Using your resources, Managing the literature, Keep track of references,Using the literature, Literature review,On-line Searching: Database ,SCIFinder, Scopus, Science Direct, Searching research articles , Citation Index ,Impact Factor ,H-index.

Measurement of Scaling: Quantitative, Qualitative, Classification of Measure scales, Data Collection, Data Preparation.

Scientific Writing and Report Writing: Significance, Steps, Layout, Types, Mechanics and Precautions, Latex: Introduction, Text, Tables, Figures, Equations, Citations, Referencing, and Templates (IEEE style), Paper writing for international journals, Writing scientific report.

[2] Zina O’Leary, The Essential Guide of Doing Research, New Delhi: PHI, 2005.

[2] Kumar, Research Methodology: A Step by Step Guide for Beginners, 3rd. ed. Indian: PE, 2010.

ESE- 50%

To enable the students to understand the fundamentals of statistics to apply descriptive measures and probability for data analysis.

Origin and development of Statistics, Scope, limitation and misuse of statistics. Types of data: primary, secondary, quantitative and qualitative data. Types of Measurements: nominal, ordinal, discrete and continuous data. Presentation of data by tables: construction of frequency distributions for discrete and continuous data, graphical representation of a frequency distribution by histogram and frequency polygon, cumulative frequency distributions

Measures of location or central tendency: Arthimetic mean, Median, Mode, Geometric mean, Harmonic mean. Partition values: Quartiles, Deciles and percentiles. Measures of dispersion: Mean deviation, Quartile deviation, Standard deviation, Coefficient of variation. Moments: measures of skewness, Kurtosis.

Correlation: Scatter plot, Karl Pearson coefficient of correlation, Spearman's rank correlation coefficient, multiple and partial correlations (for 3 variates only). Regression: Concept of errors, Principles of Least Square, Simple linear regression and its properties.

Random experiment, sample point and sample space, event, algebra of events. Definition of Probability: classical, empirical and axiomatic approaches to probability, properties of probability. Theorems on probability, conditional probability and independent events, Laws of total probability, Baye’s theorem and its applications

[2]. Gupta S.C and Kapoor V.K, Fundamentals of Mathematical Statistics, 11th edition, Sultan Chand & Sons, New Delhi, 2014.

[2]. Walpole R.E, Myers R.H, and Myers S.L, Probability and Statistics for Engineers and Scientists, Pearson, New Delhi, 2017.

[3]. Montgomery D.C and Runger G.C, Applied Statistics and Probability for Engineers, Wiley India, New Delhi, 2013.

[4]. Mood A.M, Graybill F.A and Boes D.C, Introduction to the Theory of Statistics, McGraw Hill, New Delhi, 2008.

ESE - 50%

To enable the students to understand the fundamental concepts of problem solving and programming structures.

Number Representation – Decimal, Binary, Octal, Hexadecimal and BCD numbers – Binary Arithmetic – Binary addition – Unsigned and Signed numbers – one’s and two’s complements of Binary numbers – Arithmetic operations with signed numbers - Number system conversions – Boolean Algebra – Logic gates – Design of Circuits – K - Map

Types of Problems – Problem solving with Computers – Difficulties with problem solving – problem solving concepts for the Computer – Constants and Variables – Rules for Naming and using variables – Data types – numeric data – character data – logical data – rules for data types – examples of data types – storing the data in computer - Functions – Operators – Expressions and Equations

Communicating with computer – organizing the solution – Analyzing the problem – developing the interactivity chart – developing the IPO chart – Writing the algorithms – drawing the flow charts – pseudocode – internal and external documentation – testing the solution – coding the solution – software development life cycle.

Introduction to programming structure – pointers for structuring a solution – modules and their functions – cohesion and coupling – problem solving with logic structure. Problem solving with decisions – the decision logic structure – straight through logic – positive logic – negative logic – logic conversion – decision tables – case logic structure -  examples.

[2] Peter Norton “Introduction to Computers”,6th Edition, Tata Mc Graw Hill, New Delhi,2006.

[3] Maureen Sprankle and Jim Hubbard, Problem-solving and programming concepts, PHI, 9th Edition, 2012

ESE: 50%

To enable the students to understand the fundamental concepts of problem solving and programming structures.

CO2: Apply different programming structure with suitable logic for computational problems. EM+S

Number Representation – Decimal, Binary, Octal, Hexadecimal and BCD numbers – Binary Arithmetic – Binary addition – Unsigned and Signed numbers – one’s and two’s complements of Binary numbers – Arithmetic operations with signed numbers - Number system conversions – Boolean Algebra – Logic gates – Design of Circuits – K - Map

Types of Problems – Problem solving with Computers – Difficulties with problem solving – problem solving concepts for the Computer – Constants and Variables – Rules for Naming and using variables – Data types – numeric data – character data – logical data – rules for data types – examples of data types – storing the data in computer - Functions – Operators – Expressions and Equations

Communicating with computer – organizing the solution – Analyzing the problem – developing the interactivity chart – developing the IPO chart – Writing the algorithms – drawing the flow charts – pseudocode – internal and external documentation – testing the solution – coding the solution – software development life cycle.

Introduction to programming structure – pointers for structuring a solution – modules and their functions – cohesion and coupling – problem solving with logic structure. Problem

solving with decisions – the decision logic structure – straight through logic – positive logic – negative logic – logic conversion – decision tables – case logic structure - examples.

[2]Peter Norton “Introduction to Computers”,6th Edition, Tata Mc Graw Hill, New Delhi,2006.

[3]Maureen Sprankle and Jim Hubbard, Problem solving and programming concepts, PHI, 9th Edition, 2012

ESE:50%

To Enable the students to excel in the Linux Platform

RHEL7.5,breaking root password, Understand and use essential tools for handling files, directories, command-line environments, and documentation - Configure local storage using partitions and logical volumes

Swapping, Extend LVM Partitions,LVM Snapshot - Manage users and groups, including use of a centralized directory for authentication

Kernel updations,yum and nmcli configuration, Scheduling jobs,at,crontab - Configure firewall settings using firewall config, firewall-cmd, or iptables , Configure key-based authentication for SSH ,Set enforcing and permissive modes for SELinux , List and identify SELinux file and process context ,Restore default file contexts

2.    https://access.redhat.com/documentation/en-US/Red_Hat_Enterprise_Linux/7/

ESE:50%

Origin and development of Statistics, Scope, limitation and misuse of statistics. Types of data: primary, secondary, quantitative and qualitative data. Types of Measurements: nominal, ordinal, discrete and continuous data. Presentation of data by tables: construction of frequency distributions for discrete and continuous data, graphical representation of a frequency distribution by histogram and frequency polygon, cumulative frequency distributions

Measures of location or central tendency: Arthimetic mean, Median, Mode, Geometric mean, Harmonic mean. Partition values: Quartiles, Deciles and percentiles. Measures of dispersion: Mean deviation, Quartile deviation, Standard deviation, Coefficient of variation. Moments: measures of skewness, Kurtosis

Correlation: Scatter plot, Karl Pearson coefficient of correlation, Spearman's rank correlation coefficient, multiple and partial correlations (for 3 variates only). Regression: Concept of errors, Principles of Least Square, Simple linear regression and its properties

Random experiment, sample point and sample space, event, algebra of events. Definition of Probability: classical, empirical and axiomatic approaches to probability, properties of probability. Theorems on probability, conditional probability and independent events, Laws of total probability, Baye’s theorem and its applications

[2]. Walpole R.E, Myers R.H, and Myers S.L, Probability and Statistics for Engineers and Scientists, Pearson, New Delhi, 2017.

[3]. Montgomery D.C and Runger G.C, Applied Statistics and Probability for Engineers, Wiley India, New Delhi, 2013.

[4]. Mood A.M, Graybill F.A and Boes D.C, Introduction to the Theory of Statistics, McGraw Hill, New Delhi, 2008.

ESE - 50%

The main objective of this course is to fundamental knowledge and practical experience with, database concepts. It includes the concepts and terminologies which facilitate the construction of relational databases, writing effective queries comprehend data warehouse and NoSQL databases and its types

 Concept & Overview of DBMS, Data Models, Database Languages, Database Administrator, Database Users, Three Schema architecture of DBMS. Basic concepts, Design Issues, Mapping Constraints, Keys, Entity-Relationship Diagram, Weak Entity Sets, Extended E-R features

 Lab Exercises

1. Data Definition,

2. Table Creation

3. Constraints

SQL and Integrity Constraints, Concept of DDL, DML, DCL. Basic Structure, Set operations, Aggregate Functions, Null Values, Domain Constraints, Referential Integrity Constraints, assertions, views, Nested Subqueries, Functional Dependency, Different anomalies in designing a Database, Normalization: using functional dependencies, Boyce-Codd Normal Form, 4NF

 Lab Exercises

1. Insert, Select, Update & Delete Commands

2. Nested Queries & Join Queries

3. Views

Defining Features, Data Warehouses and Data Marts, Architectural Types, Overview of the Components, Metadata in the Data warehouse, Data Design and Data Preparation: Principles of Dimensional Modeling, Dimensional Modeling Advanced Topics From Requirements To Data Design, The Star Schema, Star Schema Keys, Advantages of the Star Schema, Star Schema: Examples, Dimensional Modeling: Advanced Topics, Updates to the Dimension Tables, Miscellaneous Dimensions, The Snowflake Schema, Aggregate Fact Tables, Families Oo Stars

 Lab Exercises:

1. Importing source data structures

2. Design Target Data Structures

3. Create target multidimensional cube

Requirements, ETL Data Structures, Extracting, Cleaning and Conforming, Delivering Dimension Tables, Delivering Fact Tables, Real-Time ETL Systems

 Lab Exercises:

1. Perform the ETL process and transform into data map

2. Create the cube and process it

3. Generating Reports

4. Creating the Pivot table and pivot chart using some existing data

Introduction to NOSQL Systems, The CAP Theorem, Document-Based NOSQL Systems and MongoDB, NOSQL Key-Value Stores, Column-Based or Wide Column NOSQL Systems, Graph databases, Multimedia databases.

 Lab Exercises:

1. MongoDB Exercise - 1

2. MongoDB Exercise - 2

[2]. Thomas Cannolly and Carolyn Begg, “Database Systems, A Practical Approach to Design, Implementation and Management”, Third Edition, Pearson Education, 2007.

[3]. The Data Warehouse Toolkit: The Complete Guide to Dimensional Modeling, 2nd John Wiley & Sons, Inc. New York, USA, 2002

ESE: 50%

CO2: Understanding the process of OLAP system construction

CO3: Develop applications using Relational and NoSQL databases.

Concept & Overview of DBMS, Data Models, Database Languages, Database Administrator, Database Users, Three Schema architecture of DBMS. Basic concepts, Design Issues, Mapping Constraints, Keys, Entity-Relationship Diagram, Weak Entity Sets, Extended E-R features

 Lab Exercises

1. Data Definition,

2. Table Creation

3. Constraints

SQL and Integrity Constraints, Concept of DDL, DML, DCL. Basic Structure, Set operations, Aggregate Functions, Null Values, Domain Constraints, Referential Integrity Constraints, assertions, views, Nested Subqueries, Functional Dependency, Different anomalies in designing a Database, Normalization: using functional dependencies, Boyce-Codd Normal Form, 4NF

 Lab Exercises

1. Insert, Select, Update & Delete Commands

2. Nested Queries & Join Queries

3. Views

Defining Features, Data Warehouses and Data Marts, Architectural Types, Overview of the Components, Metadata in the Data warehouse, Data Design and Data Preparation: Principles of Dimensional Modeling, Dimensional Modeling Advanced Topics From Requirements To Data Design, The Star Schema, Star Schema Keys, Advantages of the Star Schema, Star Schema: Examples, Dimensional Modeling: Advanced Topics, Updates to the Dimension Tables, Miscellaneous Dimensions, The Snowflake Schema, Aggregate Fact Tables, Families Oo Stars

Lab Exercises:

1. Importing source data structures

2. Design Target Data Structures

3. Create target multidimensional cube

Introduction to NOSQL Systems, The CAP Theorem, Document-Based NOSQL Systems and MongoDB, NOSQL Key-Value Stores, Column-Based or Wide Column NOSQL Systems, Graph databases, Multimedia databases.

 Lab Exercises:

1. MongoDB Exercise - 1

2. MongoDB Exercise - 2

Statistical inference plays an important role in modeling data and decision-making from the real-world phenomenon. This course is designed to impart the knowledge of testing of hypothesis and estimation of parameters for real-life data sets.

Population and Statistics – Finite and Infinite population – Parameter and Statistics – Types of sampling - Sampling Distribution – Sampling Error - Standard Error – Test of significance –concept of hypothesis – types of hypothesis – Errors in hypothesis-testing – Critical region – level of significance - Power of the test – p-value.

Lab Exercise:

1. Calculation of sampling error and standard error

2. Calculation of probability of critical region using standard distributions

3. Calculation of power of the test using standard distributions.

Concept of large and small samples – Tests concerning a single population mean for known σ – equality of two means for known σ – Test for Single variance - Test for equality of two variance for normal population – Tests for single proportion – Tests of equality of two proportions for the normal population.

Lab Exercise:

4. Test of the single sample mean for known σ.

5. Test of equality of two means when known σ

6. Tests of single variance and equality of variance for large samples

7. Tests for single proportion and equality of two proportion for large samples.

Students t-distribution and its properties (without proofs) – Single sample mean test – Independent sample mean test – Paired sample mean test – Tests of proportion (based on t distribution) – F distribution and its properties (without proofs) – Tests of equality of two variances using F-test – Chi-square distribution and its properties (without proofs) – chisquare test for independence of attributes – Chi-square test for goodness of fit.

Lab Exercise:

8. Single sample mean test

9. Independent and Paired sample mean test

10. Tests of proportion of one and two samples based on t-distribution

11. Test of equality of two variances

12. Chi-square test for independence of attributes and goodness of fit.

Meaning and assumptions - Fixed, random and mixed effect models - Analysis of variance of one-way and two-way classified data with and without interaction effects – Multiple comparison tests: Tukey’s method - critical difference.

Lab Exercise:

13. Construction of one-way ANOVA

14. Construction of two-way ANOVA with interaction

15. Construction of two-way ANOVA without interaction

16. Multiple comparision test using Tukey’s method and critical difference methods

Concept of Nonparametric tests - Run test for randomness - Sign test and Wilcoxon Signed Rank Test for one and paired samples - Run test - Median test and Mann-Whitney-Wilcoxon tests for two samples.

Lab Exercise:

17. Test of one sample using Run and sign tests

18. Test of paried sample using Wilcoxon signed rank test

19. Test of two samples using Run test and Median test

20. Test for two samples using Mann-Whitney-Wilcoxon tests

2. Brian Caffo, Statistical Inference for Data Science, Learnpub, 2016. 

2. John V, Using R for Introductory Statistics, 2nd edition, CRC Press, Boca Raton, 2014.

3. Rajagopalan M and Dhanavanthan P, Statistical Inference, PHI Learning (P) Ltd, New Delhi, 2012.

4. Rohatgi V.K and Saleh E, An Introduction to Probability and Statistics, 3rd edition, JohnWiley & Sons Inc, New Jersey, 2015.

ESE:50%

This course is designed to introduce the concepts of theory of estimation and testing of hypothesis. This paper also deals with the concept of parametric tests for large and small samples. It also provides knowledge about non-parametric tests and its applications

CO2: Apply the idea of sampling distributions of different statistics in testing of hypotheses.

CO3: Infer the concept of nonparametric tests for single sample and two samples.

Neyman - Fisher Factorisation theorem - the existence and construction of minimal sufficient statistics - Minimal sufficient statistics and exponential family - sufficiency and completeness - sufficiency and invariance.

Lab Excercise 

1. Drawing random samples using random number tables.

2. Point estimation of parameters and obtaining estimates of standard errors.

Minimum variance unbiased estimation - locally minimum variance unbiased estimators - Rao Blackwell – theorem – Completeness: Lehmann Scheffe theorems - Necessary and sufficient condition for unbiased estimators - Cramer- Rao lower bound - Bhattacharya system of lower bounds in the 1-parameter regular case - Chapman -Robbins inequality

Lab Excercise 

1. Comparison of estimators by plotting mean square error.

2. Computing maximum likelihood estimates -1

3. Computing maximum likelihood estimates - 2

4. Computing moment estimates

Computational routines - strong consistency of maximum likelihood estimators - Asymptotic Efficiency of maximum likelihood estimators - Best Asymptotically Normal estimators - Method of moments - Bayes’ and minimax estimation: The structure of Bayes’ rules - Bayes’ estimators for quadratic and convex loss functions - minimax estimation - interval estimation.

Lab Exercise: 

1. Constructing confidence intervals based on large samples.

2. Constructing confidence intervals based on small samples.

3. Generating random samples from discrete distributions.

4. Generating random samples from continuous distributions.

Uniformly most powerful tests - the Neyman-Pearson fundamental Lemma - Distributions with monotone likelihood ratio - Problems - Generalization of the fundamental lemma, two sided hypotheses - testing the mean and variance of a normal distribution.

Lab Excercise :

1. Evaluation of probabilities of Type-I and Type-II errors and powers of tests.

2. MP test for parameters of binomial and Poisson distributions.

3. MP test for the mean of a normal distribution and power curve.

4. Tests for mean, equality of means when variance is (i) known, (ii) unknown under normality

(small and large samples)

Unbiased ness for hypotheses testing - similarity and completeness - UMP unbiased tests for multi-parameter exponential families - comparing two Poisson or Binomial populations - testing the parameters of a normal distribution (unbiased tests) - comparing the mean and variance of two normal distributions - Symmetry and invariance - maximal invariance - most powerful invariant tests.

Lab Excercise:

1. Tests for single proportion and equality of two proportions.

2. Tests for variance and equality of two variances under normality

3. Tests for correlation and regression coefficients.

SPRT procedures - likelihood ratio tests - locally most powerful tests - the concept of confidence sets - non parametric tests.

Lab Exercise :

1. Tests for the independence of attributes, analysis of categorical data and tests for the goodness of fit.(For uniform, binomial and Poisson distributions)

2. Nonparametric tests.

3. SPRT for binomial proportion and mean of a normal distribution.

[2]. An Introduction to Probability and Statistics, V.K Rohatgi and Saleh, 3rd Edition, 2015.

[2]. Linear Statistical Inference and its Applications, Rao C.R, Willy Publications, 2nd Edition, 2001.

ESE - 50%

The objective of this course is to provide comprehensive knowledge of python programming paradigms required for Data Science.

Structure of Python Program-Underlying mechanism of Module Execution-Branching and Looping-Problem Solving Using Branches and Loops-Functions - Lists and Mutability- Problem Solving Using Lists and Functions

Lab Exercises

1.      Demonstrate usage of branching and loopingstatements

2.      Demonstrate Recursivefunctions

3.      DemonstrateLists

Sequences, Mapping and Sets- Dictionaries- -Classes: Classes and Instances-Inheritance- Exceptional Handling-Introduction to Regular Expressions using “re” module.

Lab Exercises

1.      Demonstrate Tuples andSets

2.      DemonstrateDictionaries

3.      Demonstrate inheritance and exceptionalhandling

4.      Demonstrate use of“re”

Basics of NumPy-Computation on NumPy-Aggregations-Computation on Arrays- Comparisons, Masks and Boolean Arrays-Fancy Indexing-Sorting Arrays-Structured Data: NumPy’s Structured Array.

Lab Exercises

1.      DemonstrateAggregation

2.      Demonstrate Indexing andSorting

Introduction to Pandas Objects-Data indexing and Selection-Operating on Data in Pandas- Handling Missing Data-Hierarchical Indexing - Combining Data Sets

Lab Exercises

1.      Demonstrate handling of missingdata

2.      Demonstrate hierarchicalindexing

Aggregation and Grouping-Pivot Tables-Vectorized String Operations -Working with Time Series-High Performance Pandas- and query()

Lab Exercises

1.      Demonstrate usage of Pivottable

2.      Demonstrate use of andquery()

Basic functions of matplotlib-Simple Line Plot, Scatter Plot-Density and Contour Plots- Histograms, Binnings and Density-Customizing Plot Legends, Colour Bars-Three- Dimensional Plotting in Matplotlib.

Lab Exercises

1.      DemonstrateScatterPlot

2.      Demonstrate3Dplotting

[2].   Zhang.Y   ,An   Introduction   to    Python   and   Computer   Programming,   Springer Publications,2016

[2]. T.R.Padmanabhan, Programming with Python,SpringerPublications,2016

ESE: 50%

This course aims at laying down the foundational concepts of python programming. Starting with the fundamental programming using python, it escalates to the advanced programming concepts required for Data Science. It enables the students to organize, process and visualize data using the packages available in Python.

The objective of this course is to provide knowledge of python programming paradigms required for Data Science.

CO1: Understand and demonstrate the usage of built-in objects in Python

CO2:Analyze the significance of python program development environment and apply it to solve real world applications

CO3: Implement numerical programming, data handling and visualization through NumPy, Pandas and MatplotLib modules.

Structure of Python Program-Underlying mechanism of Module Execution-Branching and Looping-Problem Solving Using Branches and Loops-Functions - Lists and Mutability- Problem Solving Using Lists and Functions

Sequences, Mapping and Sets- Dictionaries- -Classes: Classes and Instances-Inheritance- Exceptional Handling-Introduction to Regular Expressions using “re” module.

Basics of NumPy-Computation on NumPy-Aggregations-Computation on Arrays- Comparisons, Masks and Boolean Arrays-Fancy Indexing-Sorting Arrays-Structured Data: NumPy’s Structured Array.

Introduction to Pandas Objects-Data indexing and Selection-Operating on Data in Pandas- Handling Missing Data-Hierarchical Indexing - Combining Data Sets

Aggregation and Grouping-Pivot Tables-Vectorized String Operations -Working with Time Series-High Performance Pandas- and query()

Basic functions of matplotlib-Simple Line Plot, Scatter Plot-Density and Contour Plots- Histograms, Binnings and Density-Customizing Plot Legends, Colour Bars-Three- Dimensional Plotting in Matplotlib

1. Jake VanderPlas ,Python Data Science Handbook - Essential Tools for Working with   Data, O’Reily Media,Inc, 2016

2. Zhang.Y ,An Introduction to Python and Computer Programming, Springer Publications,2016

1.   Joel Grus ,Data Science from Scratch First Principles with Python, O’Reilly Media,2016.
2.   T.R.Padmanabhan, Programming with Python,Springer Publications,2016
3. "CS41 - The Python Programming Language", Stanfordpython.com, 2019. [Online]. Available: https://stanfordpython.com/#overview. [Accessed: 20- Jun- 2019].
4.  "Python for Data Science", Cognitive Class, 2019. [Online]. Available: https://cognitiveclass.ai/courses/python-for-data-science/. [Accessed: 20- Jun- 2019].

This course aims at introducing data science related essential mathematics concepts such as fundamentals of topics on Calculus of several variables, Orthogonality, Convex optimization and Graph Theory.

Functions of Several Variables: Functions of two, three variables - Limits and continuity in HIgher Dimensions: Limits for functions of two variables, Functions of more than two variables - Partial Derivatives: partial derivative of functions of two variables, partial derivatives of functions of more than two variables, partial derivatives and continuity, second order partial derivatives - The Chain Rule: chain rule on functions of two, three variables, chain rule on functions defined on surfaces - Directional Derivative and Gradient vectors: Directional derivatives in a plane, Interpretation of directional derivative, calculation and gradients, Gradients and tangents to level curves.

Perpendicular vectors and Orthogonality - Inner Products and Projections onto lines - Projections of Rank one - Projections and Least Squares Approximations - Projection Matrices - Orthogonal Bases, Orthogonal Matrices and Gram-Schmidt orthogonalization

Affine and Convex Sets: Lines and Line segments, affine sets, affine dimension andrelative interior, convexsets, cones - Hyperplanes and half-spaces - Euclidean balls and ellipsoids- Norm balls and Norm cones - polyhedra - simplexes, Convex hull description of polyhedra - The positive semidefinitecone.

Graph Classes: Definition of a Graph and Graph terminology, isomorphism of graphs, Completegraphs, bipartite graphs, complete bipartite graphs-Vertex degree: adjacency and incidence, regular graphs - subgraphs, spanning subgraphs, induced subgraphs, removing or adding edges of a graph, removing vertices from graphs - Graph Operations: Graph Union, intersection, complement, self complement, Paths and Cycles, Connected graphs, Eulerian and HamiltonianGraphs.

Matrix Representation of Graphs, Adjacency matrices, Incidence Matrices, Trees and its properties, Bridges (cut-edges), spanning trees, weighted Graphs, minimal spanning tree problems, Shortest path problems, cut vertices, cuts, vertex and edge connectivity,  Graph Algorithms - Applications of Graph Theory

2.     G Strang, Linear Algebra and its Applications, 4th ed., Cengage, 2006. (Unit 2)

3.     S. P. Boyd and L.Vandenberghe, Convex optimization.Cambridge Univ. Pr., 2011.(Unit 3)

4.     J Clark, D A Holton, A first look at Graph Theory, Allied Publishers India, 1995. (Unit 4)

2.S. Sra, S. Nowozin, and S. J. Wright, Optimization for machine learning. MIT Press, 2012.

3.D. Jungnickel, Graphs, networks and algorithms. Springer, 2014.

4.D Samovici, Mathematical Analysis for Machine Learning and Data Mining, World Scientific Publishing Co. Pte. Ltd, 2018

5.P. N. Klein, Coding the matrix: linear algebra through applications to computer science. Newtonian Press, 2015.

6.K H Rosen, Discrete Mathematics and its applications, 7th ed., McGraw Hill, 2016

ESE :50%

 This course aims at introducing data science related essential mathematics concepts such as fundamentals of topics on Calculus of several variables, Orthogonality, Convex optimization and Graph Theory. 

 Functions of Several Variables: Functions of two, three variables - Limits and continuity in HIgher Dimensions: Limits for functions of two variables, Functions of more than two variables - Partial Derivatives: partial derivative of functions of two variables, partial derivatives of functions of more than two variables, partial derivatives and continuity, second order partial derivatives - The Chain Rule: chain rule on functions of two, three variables, chain rule on functions defined on surfaces - Directional Derivative and Gradient vectors: Directional derivatives in a plane, Interpretation of directional derivative, calculation and gradients, Gradients and tangents to level curves. 

 Perpendicular vectors and Orthogonality - Inner Products and Projections onto lines - Projections of Rank one - Projections and Least Squares Approximations - Projection Matrices - Orthogonal Bases, Orthogonal Matrices and Gram-Schmidt orthogonalization 

 Affine and Convex Sets: Lines and Line segments, affine sets, affine dimension andrelative interior, convexsets, cones - Hyperplanes and half-spaces - Euclidean balls and ellipsoids- Norm balls and Norm cones - polyhedra - simplexes, Convex hull description of polyhedra - The positive semidefinitecone. 

Graph Classes: Definition of a Graph and Graph terminology, isomorphism of graphs, Complete graphs, bipartite graphs, complete bipartite graphs- Vertex degree: adjacency and incidence, regular graphs - subgraphs, spanning subgraphs, induced subgraphs, removing or adding edges of a graph, removing vertices from graphs - Graph Operations: Graph Union, intersection, complement, self complement, Paths and Cycles, Connected graphs, Euclerian and Hamiltonian graphs.

Matrix Representation of Graphs, Adjacency matrices, Incidence Matrices, Trees and its properties, Bridges (cut-edges), spanning trees, weighted Graphs, minimal spanning tree problems, Shortest path problems, cut vertices, cuts, vertex and edge connectivity, Graph Algorithms - Applications of Graph Theory 

2. G Strang, Linear Algebra and its Applications, 4th ed., Cengage, 2006. 

3. S. P. Boyd and L.Vandenberghe, Convex optimization.Cambridge Univ. Pr., 2011.

CIA  II : 25%

CIA III : 10%

Attendance : 5%

ESE : 50%

This course aims to provide the grounding knowledge about the regression model building of simple and multiple regression.

Introduction to regression analysis: Modelling a response, overview and applications of regression analysis, major steps in regression analysis. Simple linear regression (Two variables): assumptions, estimation and properties of regression coefficients, significance and confidence intervals of regression coefficients, measuring the quality of the fit.

Multiple linear regression model: assumptions, ordinary least square estimation of regression coefficients, interpretation and properties of regression coefficient, significance and confidence intervals of regression coefficients.

Mean Square error criteria, R2 and  criteria for model selection; Need of the transformation of variables; Box-Cox transformation; Forward, Backward and Stepwise procedures.

Residual analysis, Departures from underlying assumptions, Effect of outliers, Collinearity, Non-constant variance and serial correlation, Departures from normality, Diagnostics and remedies.

Introduction to nonlinear regression, Least squares in the nonlinear case and estimation of parameters, Models for binary response variables, estimation and diagnosis methods for logistic and Poisson regressions. Prediction and residual analysis.

[2]. S. Chatterjee and AHadi, Regression Analysis by Example, 4^th Ed., John Wiley and Sons, Inc, 2006

[3].Seber, A.F. and Lee, A.J. (2003) Linear Regression Analysis, John Wiley, Relevant sections from chapters 3, 4, 5, 6, 7, 9, 10.

[2]. P. McCullagh, J.A. Nelder, Generalized Linear Models, Chapman & Hall, 1989.

ESE - 50%

Course Description - This course aims to provide the grounding knowledge about the regression model building of simple and multiple regression.

  Course Objectives :

• To build a foundation on the basic tools of regression analysis. 

• To apply econometric modelling on different types of data

• To learn how to identify the goodness of fit of some basic econometric models

• To diagnose common problems in linear regression modelling

CO2: Evaluate R-square criteria for model selection

CO3: Understand the forward, backward and stepwise methods for selecting the variables

CO4: Understand the importance of multicollinearity in regression modelling

CO5: Ability to use and understand generalizations of the linear model to binary and count data

Introduction to regression analysis: Modelling a response, overview and applications of regression analysis, major steps in regression analysis. Simple linear regression (Two variables): assumptions, estimation and properties of regression coefficients, significance and confidence intervals of regression coefficients, measuring the quality of the fit.

Mean Square error criteria, R2 and  criteria for model selection; Need of the transformation of variables; Box-Cox transformation; Forward, Backward and Stepwise procedures.

Residual analysis, Departures from underlying assumptions, Effect of outliers, Collinearity, Non-constant variance and serial correlation, Departures from normality, Diagnostics and remedies.

Introduction to nonlinear regression, Least squares in the nonlinear case and estimation of parameters, Models for binary response variables, estimation and diagnosis methods for logistic and Poisson regressions. Prediction and residual analysis.

a.     Wooldridge, J. M. (2015). Introductory econometrics: A modern approach. Cengage learning.

b.     Gujarati, D. N., Porter, D. C., & Gunasekar, S. (2012). Basic econometrics. Tata McGraw-Hill Education.

c. Studenmund, A. H. (2014). Using econometrics, a practical guide. Pearson

1. Iain Pardoe, Applied Regression Modelling, John Wiley and Sons, Inc, 2012.

2.  P. McCullagh, J.A. Nelder, Generalized Linear Models, Chapman & Hall, 1989.

3.   D.C Montgomery, E.A Peck and G.G Vining, Introduction to Linear Regression Analysis, John Wiley and Sons,Inc.NY, 2003.

4.  S. Chatterjee and AHadi, Regression Analysis by Example, 4th Ed., John Wiley and Sons, Inc, 2006

5. Seber, A.F. and Lee, A.J. (2003) Linear Regression Analysis, John Wiley, Relevant sections from chapters 3, 4, 5, 6, 7, 9, 10.

CIA II: 25%

CIA III: 10%

Attendance: 5%

ESE: 50%

 This course lays the foundation of Multivariate data analysis. The exposure provided to multivariate data structure, multinomial and multivariate normal distribution, estimation and testing of parameters, various data reduction methods would help the students in having a better understanding of research data, its presentation and analysis.

Basic concepts on multivariate variable. Multivariate normal distribution, Marginal and conditional distribution, Concept of random vector: Its expectation and Variance-Covariance matrix. Marginal and joint distributions. Conditional distributions and Independence of random vectors. Multinomial distribution. Sample mean vector and its distribution.

Sample mean vector and its distribution. Likelihood ratio tests: Tests of hypotheses about the mean vectors and covariance matrices for multivariate normal populations. Independence of sub vectors and sphericity test.

Multivariate analysis of variance (MANOVA) of one and two- way classified data. Multivariate analysis of covariance.  Wishart distribution, Hotelling’s T2 and Mahalanobis’ D2 statistics, Null distribution of Hotelling’s T2. Rao’s U statistics and its distribution.

Bayes, minimax, and Fisher’s criteria for discrimination between two multivariate normal populations. Sample discriminant function. Tests associated with discriminant functions. Probabilities of misclassification and their estimation. Discrimination for several multivariate normal populations

Principal components, sample principal components asymptotic properties. Canonical variables and canonical correlations: definition, estimation, computations. Test for significance of canonical correlations.

Factor analysis: Orthogonal factor model, factor loadings, estimation of factor loadings, factor scores.  Applications

[2]. Everitt B, Hothorn T, 2011. An Introduction to Applied Multivariate Analysis with R, Springer.

[3]. Barry J. Babin, Hair, Rolph E Anderson, and William C. Blac, 2013,  Multivariate Data Analysis, Pearson New International Edition, 

[2] Chatfield, C. and Collins, A.J. 1982. Introduction to Multivariate analysis. Prentice Hall

[3] Srivastava, M.S. and Khatri, C.G. 1979. An Introduction to Multivariate Statistics. North Holland

ESE - 50%

This course is designed to introduce the concepts of theory of estimation and testing of hypothesis. This paper also deals with the concept of parametric tests for large and small samples. It also provides knowledge about non-parametric tests and its applications.

Classification of Stochastic Processes, Markov Processes – Markov Chain - Countable State Markov Chain. Transition Probabilities, Transition Probability Matrix. Chapman - Kolmogorov's Equations, Calculation of n - step Transition Probability and its limit.

Classification of States, Recurrent and Transient States - Transient Markov Chain, Random Walk and Gambler's Ruin Problem. Continuous Time Markov Process:, Poisson Processes, Birth and Death Processes, Kolmogorov’s Differential Equations, Applications.

Branching Processes – Galton – Watson Branching Process - Properties of Generating Functions – Extinction Probabilities – Distribution of Total Number of Progeny. Concept of Weiner Process.

Renewal Processes – Renewal Process in Discrete and Continuous Time – Renewal Interval – Renewal Function and Renewal Density – Renewal Equation – Renewal theorems: Elementary Renewal Theorem. Probability Generating Function of Renewal Processes.

Stationary Processes: Discrete Parameter Stochastic Process – Application to Time Series. Auto-covariance and Auto-correlation functions and their properties. Moving Average, Autoregressive, Autoregressive Moving Average, Autoregressive Integrated Moving Average Processes. Basic ideas of residual analysis, diagnostic checking, forecasting.

[2]. Stochastic Processes, S.M Ross, Wiley India Pvt. Ltd, 2008.

[2]. Introduction to Probability and Stochastic Processes with Applications, B..C. Liliana, A Viswanathan, S. Dharmaraja, Wiley Pvt. Ltd, 2012.

ESE - 50%

Categorical data analysis deals with the study of information captured through expressions or verbal forms. This course equips the students with the theory and methods to analyse and categorical responses.

Categorical response data - Probability distributions for categorical data - Statistical inference for discrete data

Probability structure for contingency tables - Comparing proportions with 2x2 tables - The odds ratio - Tests for independence - Exact inference - Extension to three-way and larger tables

Components of a generalized linear model - GLM for binary and count data - Statistical inference and model checking - Fitting GLMs

Interpreting the logistic regression model - Inference for logistic regression - Logistic regression with categorical predictors - Multiple logistic regression - Summarising effects - Building and applying logistic regression models - Multicategory logit models

Loglinear models for two-way and three-way tables - Inference for Loglinear models - the log-linear-logistic connection - Independence graphs and collapsibility - Models for matched pairs: Comparing dependent proportions, Logistic regression for matched pairs - Comparing margins of square contingency tables - symmetry issues

 2. Agresti, A. (2010). Analysis of ordinal categorical. John Wiley & Sons.

 3. Stokes, M. E., Davis, C. S., & Koch, G. G. (2012). Categorical data analysis using SAS. SAS Institute.

 4. Agresti, A. (2018). An introduction to categorical data analysis. John Wiley & Sons.

 5. Bilder, C. R., & Loughin, T. M. (2014). Analysis of categorical data with R. Chapman and Hall/CRC.

ESE:50%

Course Description and Course Objectives This course lays the foundation of Multivariate data analysis. The exposure provided to multivariate data structure, multinomial and multivariate normal distribution, estimation and testing of parameters, various data reduction methods would help the students in having a better understanding of research data, its presentation and analysis.

CO1: Understand multivariate data structure, multinomial and multivariate normal distribution

CO2: Apply Multivariate analysis of variance (MANOVA) of one and two-way classified data.

Basic concepts on multivariate variable. Multivariate normal distribution, Marginal and conditional distribution, Concept of random vector: Its expectation and VarianceCovariance matrix. Marginal and joint distributions. Conditional distributions and Independence of random vectors. Multinomial distribution. Sample mean vector and its distribution. 

Sample mean vector and its distribution. Likelihood ratio tests: Tests of hypotheses about the mean vectors and covariance matrices for multivariate normal populations. Independence of sub vectors and sphericity test.

Multivariate analysis of variance (MANOVA) of one and two- way classified data. Multivariate analysis of covariance. Wishart distribution, Hotelling’s T2 and Mahalanobis’ D2 statistics, Null distribution of Hotelling’s T2. Rao’s U statistics and its distribution.

Bayes, minimax, and Fisher’s criteria for discrimination between two multivariate normal populations. Sample discriminant function. Tests associated with discriminant functions. Probabilities of misclassification and their estimation. Discrimination for several multivariate normal populations 

Principal components, sample principal components asymptotic properties. Canonical variables and canonical correlations: definition, estimation, computations. Test for significance of canonical correlations. Factor analysis: Orthogonal factor model, factor loadings, estimation of factor loadings, factor scores. Applications

[2]. Everitt B, Hothorn T, 2011. An Introduction to Applied Multivariate Analysis with R, Springer.

[3]. Barry J. Babin, Hair, Rolph E Anderson, and William C. Blac, 2013, Multivariate Data Analysis, Pearson New International Edition.

[2] Chatfield, C. and Collins, A.J. 1982. Introduction to Multivariate analysis. Prentice Hall

[3] Srivastava, M.S. and Khatri, C.G. 1979. An Introduction to Multivariate Statistics. North Holland

ESE - 50%

This course is designed to introduce the concepts of theory of estimation and testing of hypothesis. This paper also deals with the concept of parametric tests for large and small samples. It also provides knowledge about non-parametric tests and its applications.

CO2: Apply the idea of sampling distributions of the difference statistics in the testing of hypotheses.

CO3: Infer the concept of nonparametric tests for single sample and two samples.

Classification of Stochastic Processes, Markov Processes – Markov Chain - Countable State Markov Chain. Transition Probabilities, Transition Probability Matrix. Chapman - Kolmogorov's Equations, Calculation of n - step Transition Probability and it's limit.

Classification of States, Recurrent and Transient States - Transient Markov Chain, Random Walk , and Gambler's Ruin Problem. Continuous-Time Markov Process: Poisson Processes, Birth and Death Processes, Kolmogorov’s Differential Equations, Applications.

Branching Processes – Galton – Watson Branching Process - Properties of Generating Functions – Extinction Probabilities – Distribution of Total Number of Progeny. Concept of Weiner Process.

Renewal Processes – Renewal Process in Discrete and Continuous Time – Renewal Interval – Renewal Function and Renewal Density – Renewal Equation – Renewal theorems: Elementary Renewal Theorem. Probability Generating Function of Renewal Processes.

Stationary Processes: Discrete Parameter Stochastic Process – Application to Time Series. Auto-covariance and Auto-correlation functions and their properties. Moving Average, Autoregressive, Autoregressive Moving Average, Autoregressive Integrated Moving Average Processes. Basic ideas of residual analysis, diagnostic checking, forecasting.

[2]. Stochastic Processes, S.M Ross, Wiley India Pvt. Ltd, 2008.

Theobjectiveofthiscourseistoprovideintroductiontotheprinciplesanddesignofmachine learning algorithms. The course is aimed at providing foundations for conceptual aspects of machine learning algorithms along with their applications to solve real world problems.

MachineLearning-ExamplesofMachineApplications-LearningAssociations-Classification- Regression-UnsupervisedLearning-Reinforcement Learning.Supervised Learning: Learning class from examples- Probably Approach Correct(PAC) Learning-Noise-Learning Multiple classes. Regression-Model Selection and Generalization.

IntroductiontoParametricmethods-MaximumLikelihood Estimation:Bernoulli Density- Multinomial Density-Gaussian Density, Nonparametric Density Estimation: Histogram Estimator-Kernel Estimator-K-Nearest NeighbourEstimator.

 Lab Exercise:

1.      Data Exploration using parametric methods

2.      Data Exploration using non-parametric methods

3.      Regression analysis

Dimensionality Reduction: Introduction- Subset Selection-Principal Component Analysis, Feature Embedding-Factor Analysis-Singular Value Decomposition-Multidimensional Scaling-Linear Discriminant Analysis- Bayesian Decision Theory.

Lab Exercise:

1.      Data reduction using Principal ComponentAnalysis

2.      Data reduction using multi-dimensional scaling

Multilayer Perceptron:

Introduction, training a perceptron- learning Boolean functions- multilayer perceptron- backpropogation algorithm- training procedures.

Combining Multiple Learners

Rationale-Generating diverse learners- Model combination schemes- voting, Bagging- Boosting- fine tuning an Ensemble.

Lab Exercise

1.  Classification using MLP

2.  Ensemble Learning

Clustering

Introduction-Mixture Densities, K-Means Clustering- Expectation-Maximization algorithm- Mixtures of Latent Varaible Models-Supervised Learning after Clustering-Spectral Clustering- Hierachial Clustering-Clustering- Choosing the number of Clusters.

Lab Exercise

1.  K means clustering

2.  Hierarchical clustering

ESE: 50%

The objectives of this course is to provide introduction to the principles and design of machine learning algorithms. The course is aimed at providing foundations for conceptual aspects of machine learning algorithms along with their applications to solve real world problems.

• Understand the basic principles of machine learning techniques.
• Understand how machine learning problems are formulated and solved.
• Apply machine learning algorithms to solve real world problems.

Machine Learning - Examples of Machine Applications - Learning Associations - Classification - Regression -Unsupervised Learning - Reinforcement Learning

Supervised Learning: Learning class from examples - Probably Approach Correct (PAC) Learning - Noise - Learning Multiple classes. Regression-Model Selection and Generalization.

Introduction to Parametric methods - Maximum Likelihood Estimation: Bernoulli Density - Multinomial Density-Gaussian Density, Nonparametric Density Estimation: Histogram Estimator-Kernel Estimator-K-Nearest Neighbour Estimator.

1. Data Exploration using Parametric Methods
2. Data Exploration using Non-Parametric Methods
3. Regression Analysis

Dimensionality Reduction: Introduction- Subset Selection - Principal Component Analysis, Feature Embedding-Factor Analysis-Singular Value Decomposition-Multidimensional Scaling - Linear Discriminant Analysis - Bayesian Decision Theory.

1. Data reduction using Principal Component Analysis
2. Data reduction using Multi-Dimensional Scaling

Introduction - optical separating hyperplane- v-SVM, kernel tricks - vertical kernel - vertical kernel - defining kernel - multiclass kernel machines - one-class kernel machines.

Linear Discrimination: Introduction - Generalizing the Linear Model-Geometry of the Linear Discriminant - Pairwise Separation - Gradient Descent - Logistic Discrimination

1. Linear Discrimination
2. Logistic Discrimination
3. Classification using Kernel Machines

Introduction, training a perceptron - learning Boolean functions - multilayer perceptron - backpropogation algorithm - training procedures

1. Classification using MLP
2. Enesemble Learning

Rationale - Generating diverse learners - Model combination schemes - voting, Bagging- Boosting - fine tuning an Ensemble.

Clustering - Introduction - Mixture Densities, K-Means Clustering - Expectation-Maximization algorithm - Mixtures of Latent Varaible Models - Supervised Learning after Clustering - Spectral Clustering - Hierachial Clustering - Clustering - Choosing the number of Clusters

1. K Means Clustering
2. Hierarchical Clustering

The subject is intended to give the knowledge of Big Data evolving in every real-time applications and how they are manipulated using the emerging technologies. This course breaks down the walls of complexity in processing Big Data by providing a practical approach to developing Java applications on top of the Hadoop platform. It describes the Hadoop architecture and how to work with the Hadoop Distributed File System (HDFS) and HBase in Ubuntu platform.

Distributed file system – Big Data and its importance, Four Vs, Drivers for Big data, Big data analytics, Big data applications, Algorithms using map reduce, Matrix-Vector Multiplication by Map Reduce.

Apache Hadoop– Moving Data in and out of Hadoop – Understanding inputs and outputs ofMapReduce - Data Serialization, Problems with traditional large-scale systems-Requirements for a new approach-Hadoop – Scaling-Distributed Framework-Hadoop v/s RDBMS-Brief history of Hadoop.

Lab Exercise

1. Installing and Configuring Hadoop

Hadoop Processes (NN, SNN, JT, DN, TT)-Temporary directory – UI-Common errors when running Hadoop cluster, solutions.

Setting up Hadoop on a local Ubuntu host: Prerequisites, downloading Hadoop, setting up SSH, configuring the pseudo-distributed mode, HDFS directory, NameNode, Examples of MapReduce, Using Elastic MapReduce, Comparison of local versus EMR Hadoop.

Understanding MapReduce:Key/value pairs,TheHadoop Java API for MapReduce, Writing MapReduce programs, Hadoop-specific data types, Input/output.

Developing MapReduce Programs: Using languages other than Java with Hadoop, Analysing a large dataset.

Lab Exercise

1.      1. Word count application in Hadoop.

2.      2. Sorting the data using MapReduce.

3.      3. Finding max and min value in Hadoop.

Simple, advanced, and in-between Joins, Graph algorithms, using language-independent data structures.

Hadoop configuration properties - Setting up a cluster, Cluster access control, managing the NameNode, Managing HDFS, MapReduce management, Scaling.

Lab Exercise: 

1. Implementation of decision tree algorithms using MapReduce.

 2. Implementation of K-means Clustering using MapReduce.

3. Generation of  Frequent Itemset using MapReduce. 

Hadoop Streaming  -   Streaming  Command  Options - Specifying  a  Java  Class  as  the  Mapper/Reducer - Packaging Files With Job Submissions - Specifying Other Plug-ins for Jobs.

Lab Exercise: 

1.      1. Count the number of missing and invalid values through joining two large given datasets.

2.      2. Using hadoop’s map-reduce, Evaluating Number of Products Sold in Each Country in the online shopping portal. Dataset is given.

3.      3. Analyze the sentiment for product reviews, this work proposes a MapReduce technique provided by Apache Hadoop.

Architecture, Installation, Configuration, Hive vs RDBMS, Tables, DDL & DML, Partitioning & Bucketing, Hive Web Interface, Pig, Use case of Pig, Pig Components, Data Model, Pig Latin.

Lab Exercise

1. Trend Analysis based on Access Pattern over Web Logs using Hadoop.

2. Service Rating Prediction by Exploring Social Mobile Users Geographical Locations.

RDBMS VsNoSQL, HBasics, Installation, Building an online query application – Schema design, Loading Data, Online Queries, Successful service.

Hands On: Single Node Hadoop Cluster Set up in any cloud service provider- How to create instance.How to connect that Instance Using putty.InstallingHadoop framework on this instance. Run sample programs which come with Hadoop framework.

Lab Exercise:

1.      1. Big Data Analytics Framework Based Simulated Performance and Operational Efficiencies Through Billons of Patient Records in Hospital System.

[2] Tom White, Hadoop: The Definitive Guide, O’Reilly Media Inc., 2015.

[3] Garry Turkington, Hadoop Beginner's Guide, Packt Publishing, 2013.

[2] Jonathan R. Owens, Jon Lentz and Brian Femiano, Hadoop Real-World Solutions Cookbook, Packt Publishing, 2013.

[3] Tom White, HADOOP: The definitive Guide, O Reilly, 2012.

ESE - 50%

This course will provide a basic foundation towards digital image processing and video analysis. This course will also provide brief introduction about various Object Detection, Recognition, Segmentation and Compression methods which will help the students to demonstrate real-time image and video analytics applications.

Digital image representation, Sampling and Quantization, Types of Images, Basic Relations between Pixels - Neighbors, Connectivity, Distance Measures between pixels, Linear and Non Linear Operations, Introduction to Digital Video, Sampled Video, Video Transmission.

Gray-Level Processing: Image Histogram, Linear and Non-linear point operations on Images, Arithmetic Operations between Images, Geometric Image Operations, Image Thresholding, Region labeling, Binary Image Morphology.

Lab Programs:

1.  Program to perform Resize, Rotation of binary, Gray-scale and color images using various methods.

2. Program to implement contrast stretching.

Spatial domain-Linear and Non-linear Filtering, Introduction to Fourier Transform and the frequency Domain– Filtering in Frequency domain, Homomorphic Filtering, Brief introduction towards Wavelets, Wavelet based image denoising, A model of The Image Degradation / Restoration, Noise Models and basic methods for image restoration. Blotch detection and Removal.

Lab Programs:

3.  Program to implement various image enhancement techniques using Built-in and user defined functions.

4. Program to implement Non-linear Spatial Filtering using Built-in and userdefined functions.

Image Compression: Huffman Coding, Run length Coding, LZW Coding, Basics of Wavelets based image compression.

Video Compression: Basic Concepts and Techniques of Video compression, MPEG-1 and MPEG-2 Video Standards.

Lab Programs: 

5.     Program to implement homomorphic Filtering

6.     Extraction of frames from videos and analyzing frames

Introduction to feature detectors, descriptors, matching and tracking, Basic edge detectors – canny, sobel, prewitt etc., Image Segmentation - Region Based Segmentation – Region Growing and Region Splitting and Merging, Thresholding – Basic global thresholding, optimum global thresholding using Otsu’s Method.

Lab Programs:

7.     Implement multi-resolution image decomposition and reconstruction using wavelet. 

8.     Implement image compression using wavelets.

Descriptors: Boundary descriptors - Fourier descriptors - Regional descriptors - Topological descriptors - moment invariants

Object detection and recognition in image and video: Minimum distance classifier, K-NN classifier and Bayes, Applications in image and video analysis, object tracking in videos.

 Lab Programs:

9.   Extracting feature descriptors from the image dataset.

10. Implement image classification using extracted relevant features.

 [2] Alan Bovik, Handbook of Image and Video Processing, Second Edition, Academic Press, 2005.

[2] RichardSzeliski,ComputerVision–AlgorithmsandApplications,Springer,2011.

[3] Oge Marques, Practical Image and Video Processing Using MatLab, Wiley, 2011.

[4] John W. Woods, Multidimensional Signal, Image, Video Processing and Coding, Academic Press, 2006.

ESE: 50%

The explosive growth of the “Internet of Things” is changing our world and the rapid growth of IoT components is allowing people to innovate new designs and products at home. Wireless Sensor Networks form the basis of the Internet of Things. To latch on to the applications in the field of IoT of the recent times, this course provides a deeper understanding of the underlying concepts of IoT and Wireless Sensor Networks.

1.   1. Introduction to ICs and Sensors. A basic program can be shown which makes use of logic gates IC s for understanding the basics of sensor nodes. Different sensors which find application in IoT projects can be shown,their working explained.

2.    2.Introduction to Arduino/Raspberry Pi. Sample sketches or code can be selected from theArduinosoftwareandexecuted,making use of different sensors.