Probabilistic Graphical Models 1: Representation

Go to Course: https://www.coursera.org/learn/probabilistic-graphical-models

Introduction

### Course Review: Probabilistic Graphical Models 1: Representation **Overview** If you are delving into the world of data science, artificial intelligence, or machine learning, you may have come across the term "Probabilistic Graphical Models" (PGMs). Coursera's course "Probabilistic Graphical Models 1: Representation" provides an insightful exploration of this essential framework that integrates aspects of statistics, computer science, and probability theory. The course lays a solid foundation, making it a valuable resource for anyone looking to understand the intricacies of modeling complex systems that involve uncertainty and interdependent variables. **Course Structure and Syllabus** The course is organized into several well-structured modules, each building upon the last, which ensures a gradual and comprehensive understanding of PGMs. 1. **Introduction and Overview** - This module serves as a gentle introduction to the core concepts of PGMs. By delineating fundamental ideas, the course prepares learners for more complex discussions on how these models operate and apply in real-world scenarios. 2. **Bayesian Network (Directed Models)** - Diving deeper, this module introduces Bayesian networks and their semantics. Understanding the relationship between graphical structure and independence properties is critical, and this section provides practical insights on how to effectively model real-world situations using these directed models. 3. **Template Models for Bayesian Networks** - This module tackles recurring structures in probability distributions, such as temporal scenarios and similar entity modeling through Hidden Markov Models and Plate Models. This is particularly useful for learners interested in dynamic systems and time series data. 4. **Structured CPDs for Bayesian Networks** - Here, the focus shifts to Conditional Probability Distributions (CPDs) and how to represent them efficiently. The growing complexity of table-based representations is addressed with alternative structural representations that allow for a more compact modeling approach. 5. **Markov Networks (Undirected Models)** - This module explores Markov networks, which provide an alternative perspective to Bayesian networks using undirected graphs. By comparing both models, learners gain insight into selecting the appropriate framework based on specific scenarios and independence properties. 6. **Decision Making** - One of the most intriguing aspects of PGMs involves decision-making under uncertainty. This module covers decision theory and introduces Influence Diagrams, enhancing learners' understanding of how graphical models can be used to inform complex decisions and optimize information gathering. 7. **Knowledge Engineering & Summary** - Concluding the course, this module revisits key concepts and highlights practical considerations in modeling with graphical models. It is capped off with a final exam, reinforcing the knowledge acquired throughout the course. **Recommendation** This course is an excellent choice for anyone seeking to deepen their understanding of probabilistic reasoning and graphical models. It suits a wide audience—from students and researchers in data science to professionals looking to enhance their modeling capabilities. The combination of theoretical foundations with practical applications prepares learners to tackle complex problems in various domains, such as healthcare, finance, and artificial intelligence. The user-friendly interface, coupled with engaging instructional videos and exercises, makes the learning experience enjoyable. Moreover, the course is offered by esteemed institutions, ensuring that the content is both relevant and based upon current industry practices. In summary, if you are interested in mastering the representation of probabilistic graphical models and applying these techniques in real-world scenarios, "Probabilistic Graphical Models 1: Representation" on Coursera is a highly recommended course that can significantly bolster your quantitative modeling skills. Embrace the challenge and enrich your knowledge in this captivating field!

Syllabus

Introduction and Overview

This module provides an overall introduction to probabilistic graphical models, and defines a few of the key concepts that will be used later in the course.

In this module, we define the Bayesian network representation and its semantics. We also analyze the relationship between the graph structure and the independence properties of a distribution represented over that graph. Finally, we give some practical tips on how to model a real-world situation as a Bayesian network.

In many cases, we need to model distributions that have a recurring structure. In this module, we describe representations for two such situations. One is temporal scenarios, where we want to model a probabilistic structure that holds constant over time; here, we use Hidden Markov Models, or, more generally, Dynamic Bayesian Networks. The other is aimed at scenarios that involve multiple similar entities, each of whose properties is governed by a similar model; here, we use Plate Models.

A table-based representation of a CPD in a Bayesian network has a size that grows exponentially in the number of parents. There are a variety of other form of CPD that exploit some type of structure in the dependency model to allow for a much more compact representation. Here we describe a number of the ones most commonly used in practice.

In this module, we describe Markov networks (also called Markov random fields): probabilistic graphical models based on an undirected graph representation. We discuss the representation of these models and their semantics. We also analyze the independence properties of distributions encoded by these graphs, and their relationship to the graph structure. We compare these independencies to those encoded by a Bayesian network, giving us some insight on which type of model is more suitable for which scenarios.

In this module, we discuss the task of decision making under uncertainty. We describe the framework of decision theory, including some aspects of utility functions. We then talk about how decision making scenarios can be encoded as a graphical model called an Influence Diagram, and how such models provide insight both into decision making and the value of information gathering.

This module provides an overview of graphical model representations and some of the real-world considerations when modeling a scenario as a graphical model. It also includes the course final exam.