Thursday, June 7, 2018

Statistical and Mathematical Methods for Data Science


Statistical and Mathematical Methods for Data Science
Credit Hours: 3
Prerequisites: None

Date : 7 June 2018


Course Contents:

Probability:
Probability basics (axioms of probability,



conditional probability,



random variables,



expectation, independence,




etc.), (Ignored)


multivariate distributions,


Maximum a posteriori and maximum likelihood estimation;






https://en.wikipedia.org/wiki/Maximum_a_posteriori_estimation


Statistics:

introduction to concentration bounds,



laws of large numbers,



central limit theorem,




https://www.youtube.com/watch?v=JNm3M9cqWyc


minimum mean - squared error estimation,




confidence intervals;




Linear algebra:
Vector spaces,





Projections (will also cover the least regression),



linear transformations,




singular value decomposition (this substitute for PCA),





eigen decomposition,



power method;





Optimization:
Matrix calculus with Lagrange Multipliers,







derivatives/constrained-optimization/a/lagrange-multipliers-examples




gradient descent,


coordinate descent,



introduction to convex optimization.




Teaching Methodology: Lectures, Problem based learning

Course Assessment:
Sessional Exam, Home Assignments, Quizzes, Project, Presentations, Final Exam

Reference Materials
Books:
1. Probability and Statistics for Computer Scientists, 2nd Edition, Michael Baron
2. Linear Algebra and Its Applications, 5th Edition, David C. Lay and Steven R. Lay
3. Introduction to Linear Algebra, 5th Edition, Gilbert Strang
4. Probability for Computer Scientists, online Edition, David Forsyth.

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