Computational and Graphical Models in Probability

Overview

The course "Computational and Graphical Models in Probability" equips learners with essential skills to analyze complex systems through simulation techniques and network analysis. By exploring advanced concepts such as Exponential Random Graph Models and Probabilistic Graphical Models, students will learn to model and interpret intricate social structures and dependencies within data. What sets this course apart is its emphasis on practical applications using the R programming language, empowering students to simulate random variables effectively and construct sophisticated models for real-world scenarios. Through hands-on projects and exercises, learners will not only deepen their theoretical understanding but also gain valuable experience in solving applied problems across various domains. Upon completion, you will be well-prepared to tackle challenges in data analysis, machine learning, and statistical modeling, making you a valuable asset in any data-driven field. Whether you're looking to enhance your expertise or start a new career, this course offers a unique blend of theory and practical skills that will enable you to excel in today’s data-centric world.

Syllabus

Course Introduction

This course covers advanced techniques in network and probabilistic modeling, including simulation methods, exponential random graph models, and probabilistic graphical models. You will gain practical skills in analyzing complex systems and relational data.

Simulation

This module develops student proficiency in simulating random variables for arbitrary density functions. Students will be introduced to the Inverse Transformation Method and the Rejection Method.

Exponential Random Graph Models

Exponential Random Graph Models introduce the use of exponential random graph models (ERGMs) for network analysis. You will learn how to model and interpret complex social and relational structures.

Probabilistic Graphical Models

This module introduces a framework for encoding probability distributions over complex joint domains over large numbers of random variables that interact with one another. Students will become familiar with probabilistic graph model applications to many machine learning problems.