# Machine Learning

Course Title: Machine Learning
Full Marks: 45 + 30
Course No: C.Sc.561
Pass Marks: 22.5+15
Nature of the Course: Theory + Lab
Credit Hrs: 3

## Course Description:

This course provides a broad introduction to machine learning and statistical pattern recognition. Topics include: supervised learning (generative/discriminative learning, parametric/non-parametric learning, neural networks, support vector machines); unsupervised learning (clustering, dimensionality reduction, kernel methods); learning theory (bias/variance tradeoffs; VC theory; large margins); reinforcement learning and adaptive control. Course Objective Purpose of this course is to present different machine learning techniques and also analyze their pros and cons. In addition to this, this course also concepts on learning theory and their applications Prerequisites Computer Programming, Probability Theory, Linear Algebra

### Unit 1: Introduction 5 hrs

The Motivation & Applications of Machine Learning, The Definition of Machine Learning, The Overview of Supervised Learning, The Overview of Learning Theory, The Overview of Unsupervised Learning, The Overview of Reinforcement Learning

### Unit 2: Supervised learning 12 hrs

Application of Supervised Learning, Linear Regression, Gradient Descent, Batch Gradient Descent, Stochastic Gradient Descent (Incremental Descent), Matrix Derivative Notation for Deriving Normal Equations, Derivation of Normal Equations, The Concept of Underfitting and Overfitting, The Concept of Parametric Algorithms and Non-parametric Algorithms, Locally Weighted Regression, The Probabilistic Interpretation of Linear Regression, The motivation of Logistic Regression, Supervised learning setup, Least Mean squares, Logistic Regression, Perceptron Learning Algorithm, Discriminative Algorithms, Generative Algorithms, Gaussian Discriminant Analysis (GDA), GDA and Logistic Regression, Naive Bayes, Laplace Smoothing,
Intuitions about Support Vector Machine (SVM), Notation for SVM, Functional and Geometric Margins, Optimal Margin Classifier, Lagrange Duality, Karush-Kuhn-Tucker (KKT) Conditions, SVM Dual, The Concept of Kernels, Kernels, Mercer’s Theorem, Non-linear Decision Boundaries and Soft Margin SVM, Coordinate Ascent Algorithm, The Sequential Minimization Optimization (SMO) Algorithm, Applications of SVM

### Unit 3: Learning theory 9 hrs

Bias/variance Tradeoff, Empirical Risk Minimization (ERM), The Union Bound, Hoeffding Inequality, Uniform Convergence – The Case of Finite H, Sample Complexity Bound, Error Bound, Uniform Convergence Theorem & Corollary, Uniform Convergence – The Case of Infinite H, The Concept of ‘Shatter’ and VC Dimension, SVM Example, Model Selection, Cross Validation, Feature Selection, Bayesian Statistics and Regularization, Online Learning, Advice for Applying Machine Learning Algorithms, Debugging/fixing Learning Algorithms, Diagnostics for Bias & Variance, Optimization Algorithm Diagnostics, Diagnostic Example Error Analysis, Getting Started on a Learning Problem

### Unit 4: Unsupervised learning 9 hrs

The Concept of Unsupervised Learning, K-means Clustering Algorithm, K-means Algorithm, Mixtures of Gaussians and the EM Algorithm, Jensen’s Inequality, The EM Algorithm, Mixture of Gaussian, Mixture of Naive Bayes – Text clustering (EM Application), Factor Analysis, Restrictions on a Covariance Matrix, The Factor Analysis Model, EM for Factor Analysis, The Factor Analysis Model, EM for Factor Analysis, Principal Component Analysis (PCA), PCA as a Dimensionality Reduction Algorithm, Applications of PCA, Face Recognition by Using PCA, Latent Semantic Indexing (LSI), Singular Value Decomposition (SVD) Implementation, Independent Component Analysis (ICA), The Application of ICA, Cumulative Distribution Function (CDF), ICA Algorithm, The Applications of ICA

### Unit 5: Reinforcement learning and control 10 hrs

Applications of Reinforcement Learning, Markov Decision Process (MDP), Defining Value & Policy Functions, Value Function, Optimal Value Function, Value Iteration, Policy Iteration, Generalization to Continuous States, Discretization & Curse of Dimensionality,
Models/Simulators, Fitted Value Iteration, Finding Optimal Policy, State-action Rewards, Finite Horizon MDPs, The Concept of Dynamical Systems, Examples of Dynamical Models, Linear Quadratic Regulation (LQR), Linearizing a Non-Linear Model, Computing Rewards, Riccati Equation, Advice for Applying Machine Learning, Debugging Reinforcement Learning (RL) Algorithm, Linear Quadratic Regularization (LQR), Differential Dynamic Programming (DDP), Kalman Filter & Linear Quadratic Gaussian (LQG), Predict/update Steps of Kalman Filter, Linear Quadratic Gaussian (LQG), Partially Observable MDPs (POMDPs), Policy Search, Reinforce Algorithm, Pegasus Algorithm, Pegasus Policy Search, Applications of Reinforcement Learning

## Text Books

• Christopher Bishop, Pattern Recognition and Machine Learning. Springer, 2006 2.Richard Duda, Peter Hart and David Stork, Pattern Classification, 2nd ed. John Wiley & Sons, 2001.

## References

1. Tom Mitchell, Machine Learning. McGraw-Hill, 1997.
2. Richard Sutton and Andrew Barto, Reinforcement Learning: An introduction. MIT Press, 1998