# EE212 Mathematical Foundations for Machine Learning and Data Science

## Announcements

• (Sep. 12) Assignment 01 has been posted (due on September 26).

• (Sep. 05) Welcome to EE212. Course outline has been posted.

## Course Overview

Machine Learning and Data Science are being used these days in a variety of applications including, but not limited to, forecasting in economics and finance, predicting anomalies or signal analysis in engineering, identification of speaker in acoustics, detection of cosmic bubbles in astrophysics and diagnosis in medical imaging.

While machine learning and data science have enabled many success stories, and tools are readily available to analyse data or design machine learning systems, the strong mathematical foundations in these areas are of significant importance to understand, review, analyse and evaluate the technical details of the machine learning systems and data science algorithms that are usually abstracted away from the user. This course focuses on the mathematical foundations that are essential to build an intuitive understanding of the concepts related to Machine Learning and Data Science.

Topics covered are

• Linear Algebra: vectors and matrices, vector spaces, system of linear equations, eigen-value decomposition, singular value decomposition, regression, least-squares, regularization

• Calculus: Multivariate calculus and differentials for optimization, gradient descent

• Probability: probability axioms, Bayes rule, random variable, probability distributions

• Statistics: descriptive stats, inferential stats, statistical tests

• Introduction to Neural Networks: single and multi-layer perceptron(s), feedforward and feedback networks

• Application to machine learning and data science: principal component analysis (PCA), time series forecasting, clustering etc

• Hands-on exercises: Implementation of the exercises will be carried out in Python

## Course Overview Video

• Suggested Books:

• Reference 1 (click to download pdf): S.Boyd and L. Vandenberghe. Introduction to Applied Linear Algebra - Vectors, Matrices, and Least Squares. Cambridge University Press, 2019

• Reference 2 (click to download pdf): M. P. Deisenroth, A. A. Faisal and Cheng Soon Ong. Mathematics for Machine Learning. Cambridge University Press, 2019

• Reference 3: G. Strang. Introduction to Linear Algebra. 2016

• Reference 4: J. A. Gubner, Probability and Random Processes for Electrical and Computer Engineers, Cambridge University Press, 2006.

• Reference 5: S. L. Miller and D. Childers, Probability and Random Processes: With Applications to Signal Processing and Communications.

• Reference 6: A. Papoulis and S.U. Pillai, Probability, Random Variables, and Stochastic Processes.

• Office Hours and Contact Information

• Instructor: Zubair Khalid (zubair.khalid@lums.edu.pk), Office hours: Tuesday, Thursday 5-6 pm

• Lead Teaching Assistant: Zainab Imran (21100153@lums.edu.pk), Office hours: Friday 10:30 am to 12:30 pm

• Teaching Assistant: Sana Jabbar (18060039@lums.edu.pk), Office hours: TBA

• Teaching Assistant: Hamza Khalid (22100118@lums.edu.pk), Office hours: TBA

• Assignments, 20 %

• Programming Assignments, 10 %

• Quizzes, 15 %

• Mid-Exam + Viva, 25 %

• Final Exam + Viva, 30 %

## Assignments

 Assignment Solutions Assignments 01 Solutions Assignments 02 Solutions Assignments 03 Solutions Assignments 04 Solutions Assignments 05 Solutions

## Lecture Plan

• Weeks 01 and 02 (Lecture Notes)

• Course Introduction

• Operations on vectors: linear combination, norm, inner prooduct, angle, distance, correlation coefficient

• Span, basis, linear independence, orthonormal vectors, vector spaces, Gram-Schmidt orthogonalization

• Weeks 03 and 04 (Lecture Notes)

• Matrices Notation, Application Examples and Basic Operations

• Matrix-vector product, Interpretations, Application Examples,Matrix-matrix product

• Systems of Linear Equations, Formulation, Inverses, Left-inverse, Right-inverse, Inverse, Pseudo-inverse, Connection with the linear equations