Probabilistic Graphical Models 2: Inference from Coursera

Probabilistic graphical models (PGMs) are a rich framework for encoding probability distributions over complex domains: joint (multivariate) distributions over large numbers of random variables that interact with each other. These representations sit at the intersection of statistics and computer science, relying on concepts from probability theory, graph algorithms, machine learning, and more. They are the basis for the state-of-the-art methods in a wide variety of applications, such as medical diagnosis, image understanding, speech recognition, natural language processing, and many, many more. They are also a foundational tool in formulating many machine learning problems.

This course is the second in a sequence of three. Following the first course, which focused on representation, this course addresses the question of probabilistic inference: how a PGM can be used to answer questions. Even though a PGM generally describes a very high dimensional distribution, its structure is designed so as to allow questions to be answered efficiently. The course presents both exact and approximate algorithms for different types of inference tasks, and discusses where each could best be applied. The (highly recommended) honors track contains two hands-on programming assignments, in which key routines of the most commonly used exact and approximate algorithms are implemented and applied to a real-world problem.

What's inside

Syllabus

Inference Overview

This module provides a high-level overview of the main types of inference tasks typically encountered in graphical models: conditional probability queries, and finding the most likely assignment (MAP inference).

Variable Elimination

This module presents the simplest algorithm for exact inference in graphical models: variable elimination. We describe the algorithm, and analyze its complexity in terms of properties of the graph structure.

Belief Propagation Algorithms

This module describes an alternative view of exact inference in graphical models: that of message passing between clusters each of which encodes a factor over a subset of variables. This framework provides a basis for a variety of exact and approximate inference algorithms. We focus here on the basic framework and on its instantiation in the exact case of clique tree propagation. An optional lesson describes the loopy belief propagation (LBP) algorithm and its properties.

MAP Algorithms

This module describes algorithms for finding the most likely assignment for a distribution encoded as a PGM (a task known as MAP inference). We describe message passing algorithms, which are very similar to the algorithms for computing conditional probabilities, except that we need to also consider how to decode the results to construct a single assignment. In an optional module, we describe a few other algorithms that are able to use very different techniques by exploiting the combinatorial optimization nature of the MAP task.

Sampling Methods

In this module, we discuss a class of algorithms that uses random sampling to provide approximate answers to conditional probability queries. Most commonly used among these is the class of Markov Chain Monte Carlo (MCMC) algorithms, which includes the simple Gibbs sampling algorithm, as well as a family of methods known as Metropolis-Hastings.

Inference in Temporal Models

In this brief lesson, we discuss some of the complexities of applying some of the exact or approximate inference algorithms that we learned earlier in this course to dynamic Bayesian networks.

Inference Summary

This module summarizes some of the topics that we covered in this course and discusses tradeoffs between different algorithms. It also includes the course final exam.

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Introduces students to probabilistic graphical models (PGMs), a powerful framework for encoding complex probability distributions for large, interconnected sets of variables, and using them to answer questions efficiently

Focuses on probabilistic inference, addressing how PGMs can be used to make predictions and answer questions, even when the distribution they represent is high-dimensional

Covers exact inference algorithms, such as variable elimination and belief propagation, as well as approximate inference algorithms, including sampling methods like Markov Chain Monte Carlo (MCMC) and loopy belief propagation (optional)

Provides hands-on programming assignments (optional) where students implement key routines of exact and approximate inference algorithms and apply them to real-world problems, reinforcing their understanding

Suitable for students with a background in probability, statistics, and machine learning, or those who have completed the first course in the PGM specialization

Reviews summary

Ml foundations course - quite strong

Learners say the challenging Probabilistic Graphical Models 2: Inference course is time-consuming, but worthwhile for improving their understanding of ML foundations theory. Assignments use Matlab/Octave which some learners say is archaic, but is still expressive. One learner felt the course was less worthwhile because they could not complete the honors assignments due to not being fluent in Matlab.

Matlab/Octave is an expressive language.

"it's a language that's expressive enough"

This course is challenging and time-consuming.

"An immersing, challenging and time-consuming course"

This course is worthwhile.

"Helped me improve understanding of ML foundations theory"

This course is time-consuming.

"An immersing, challenging and time-consuming course"

Assignments use Matlab/Octave.

"Programming assignments may look a bit archaic, as I see that Matlab/Octave isn't gaining traction in ML community nowadays"

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Probabilistic Graphical Models 2: Inference with these activities:

Refresh linear algebra and probability concepts

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Strengthen your foundational understanding of linear algebra and probability concepts to support your learning in probabilistic graphical models (PGMs).

Browse courses on Linear Algebra

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Review textbooks or online resources on linear algebra.
Practice solving linear algebra problems, such as matrix operations and vector spaces.
Review concepts of probability theory, including random variables, distributions, and conditional probability.
Solve probability exercises and problems.

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Career center

Learners who complete Probabilistic Graphical Models 2: Inference will develop knowledge and skills that may be useful to these careers:

Data Scientist

A Data Scientist may use probabilistic graphical models to encode probability distributions over complex domains and answer questions about the data efficiently. This course covers exact and approximate algorithms for different types of inference tasks, which can help a Data Scientist build a foundation for developing and applying these models in real-world applications.

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Machine Learning Engineer

Probabilistic graphical models are a fundamental tool in formulating many machine learning problems. A Machine Learning Engineer may use these models to represent complex relationships between variables and make predictions or decisions. This course provides a deep understanding of inference algorithms for probabilistic graphical models, which can help a Machine Learning Engineer design and implement effective machine learning systems.

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Research Scientist

Research Scientists working in fields such as artificial intelligence, machine learning, and statistics may use probabilistic graphical models to develop new algorithms and theories for inference and decision-making. This course provides a comprehensive overview of exact and approximate inference algorithms, as well as their theoretical foundations, which can help a Research Scientist build a strong foundation for conducting research in this area.

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Software Engineer

Software Engineers working on machine learning or data science projects may use probabilistic graphical models to represent complex relationships between variables and make predictions or decisions. This course provides a practical understanding of inference algorithms for probabilistic graphical models, which can help a Software Engineer develop and implement efficient and scalable solutions.

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Quantitative Analyst

Quantitative Analysts use probabilistic models to analyze financial data and make investment decisions. Probabilistic graphical models are a powerful tool for representing complex relationships between financial variables and making predictions about future market behavior. This course provides a foundation in inference algorithms for probabilistic graphical models, which can help a Quantitative Analyst develop and apply these models in the financial domain.

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Risk Analyst

Risk Analysts use probabilistic models to assess and manage risks in various domains, such as finance, insurance, and healthcare. Probabilistic graphical models can help Risk Analysts represent complex relationships between risk factors and make predictions about future events. This course provides a foundation in inference algorithms for probabilistic graphical models, which can help a Risk Analyst develop and apply these models in risk management applications.

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Actuary

Actuaries use probabilistic models to assess and manage financial risks in the insurance industry. Probabilistic graphical models can help Actuaries represent complex relationships between risk factors and make predictions about future events. This course provides a foundation in inference algorithms for probabilistic graphical models, which can help an Actuary develop and apply these models in insurance applications.

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Statistician

Statisticians use probabilistic models to analyze data and draw conclusions. Probabilistic graphical models are a powerful tool for representing complex relationships between variables and making inferences about the underlying population. This course provides a foundation in inference algorithms for probabilistic graphical models, which can help a Statistician develop and apply these models in various statistical applications.

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Data Analyst

Data Analysts use probabilistic models to analyze data and extract insights. Probabilistic graphical models can help Data Analysts represent complex relationships between variables and make predictions about future events. This course provides a foundation in inference algorithms for probabilistic graphical models, which can help a Data Analyst develop and apply these models in data analysis applications.

See salaries and explore the career path for Data Analyst

Business Analyst

Business Analysts use probabilistic models to analyze data and make recommendations for business decisions. Probabilistic graphical models can help Business Analysts represent complex relationships between business factors and make predictions about future outcomes. This course provides a foundation in inference algorithms for probabilistic graphical models, which can help a Business Analyst develop and apply these models in business analysis applications.

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Operations Research Analyst

Operations Research Analysts use probabilistic models to optimize complex systems. Probabilistic graphical models can help Operations Research Analysts represent complex relationships between system components and make predictions about future outcomes. This course provides a foundation in inference algorithms for probabilistic graphical models, which can help an Operations Research Analyst develop and apply these models in optimization applications.

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Financial Analyst

Financial Analysts use probabilistic models to analyze financial data and make investment recommendations. Probabilistic graphical models can help Financial Analysts represent complex relationships between financial variables and make predictions about future market behavior. This course provides a foundation in inference algorithms for probabilistic graphical models, which can help a Financial Analyst develop and apply these models in financial analysis applications.

See salaries and explore the career path for Financial Analyst

Software Developer

Software Developers may use probabilistic graphical models to develop machine learning or data science applications. This course provides a practical understanding of inference algorithms for probabilistic graphical models, which can help a Software Developer implement efficient and scalable solutions.

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Data Engineer

Data Engineers may use probabilistic graphical models to develop and maintain data pipelines for machine learning or data science applications. This course provides a practical understanding of inference algorithms for probabilistic graphical models, which can help a Data Engineer design and implement efficient and reliable data pipelines.

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Product Manager

Product Managers may use probabilistic graphical models to understand user behavior and make product decisions. This course provides a high-level overview of inference algorithms for probabilistic graphical models, which can help a Product Manager make informed decisions about product development and marketing.

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