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 third in a sequence of three. Following the first course, which focused on representation, and the second, which focused on inference, this course addresses the question of learning: how a PGM can be learned from a data set of examples. The course discusses the key problems of parameter estimation in both directed and undirected models, as well as the structure learning task for directed models. The (highly recommended) honors track contains two hands-on programming assignments, in which key routines of two commonly used learning algorithms are implemented and applied to a real-world problem.
Ce cours fait partie de la Spécialisation Probabilistic Graphical Models
Probabilistic Graphical Models 3: Learning
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À propos de ce cours
4.6
171 notes
Compétences que vous acquerrez
AlgorithmsExpectation–Maximization (EM) AlgorithmGraphical ModelMarkov Random Field
Programme du cours : ce que vous apprendrez dans ce cours
Semaine
1Learning: Overview
This module presents some of the learning tasks for probabilistic graphical models that we will tackle in this course.
1 vidéo (Total 16 min)
1 vidéo
Learning: Overview15 min
Review of Machine Learning Concepts from Prof. Andrew Ng's Machine Learning Class (Optional)
This module contains some basic concepts from the general framework of machine learning, taken from Professor Andrew Ng's Stanford class offered on Coursera. Many of these concepts are highly relevant to the problems we'll tackle in this course.
6 vidéos (Total 59 min)
6 vidéos
Regularization: Cost Function 10 min
Evaluating a Hypothesis 7 min
Model Selection and Train Validation Test Sets 12 min
Diagnosing Bias vs Variance 7 min
Regularization and Bias Variance11 min
Parameter Estimation in Bayesian Networks
This module discusses the simples and most basic of the learning problems in probabilistic graphical models: that of parameter estimation in a Bayesian network. We discuss maximum likelihood estimation, and the issues with it. We then discuss Bayesian estimation and how it can ameliorate these problems.
5 vidéos (Total 77 min), 2 quiz
5 vidéos
Maximum Likelihood Estimation for Bayesian Networks15 min
Bayesian Estimation15 min
Bayesian Prediction13 min
Bayesian Estimation for Bayesian Networks17 min
2 exercices pour s'entraîner
Learning in Parametric Models18 min
Bayesian Priors for BNs8 min
Semaine
2Learning Undirected Models
In this module, we discuss the parameter estimation problem for Markov networks - undirected graphical models. This task is considerably more complex, both conceptually and computationally, than parameter estimation for Bayesian networks, due to the issues presented by the global partition function.
3 vidéos (Total 52 min), 2 quiz
3 vidéos
Maximum Likelihood for Conditional Random Fields13 min
MAP Estimation for MRFs and CRFs9 min
1 exercice pour s'entraîner
Parameter Estimation in MNs6 min
Semaine
3Learning BN Structure
This module discusses the problem of learning the structure of Bayesian networks. We first discuss how this problem can be formulated as an optimization problem over a space of graph structures, and what are good ways to score different structures so as to trade off fit to data and model complexity. We then talk about how the optimization problem can be solved: exactly in a few cases, approximately in most others.
7 vidéos (Total 106 min), 3 quiz
7 vidéos
Likelihood Scores16 min
BIC and Asymptotic Consistency11 min
Bayesian Scores20 min
Learning Tree Structured Networks12 min
Learning General Graphs: Heuristic Search23 min
Learning General Graphs: Search and Decomposability15 min
2 exercices pour s'entraîner
Structure Scores10 min
Tree Learning and Hill Climbing8 min
Semaine
4Learning BNs with Incomplete Data
In this module, we discuss the problem of learning models in cases where some of the variables in some of the data cases are not fully observed. We discuss why this situation is considerably more complex than the fully observable case. We then present the Expectation Maximization (EM) algorithm, which is used in a wide variety of problems.
5 vidéos (Total 83 min), 3 quiz
5 vidéos
Expectation Maximization - Intro16 min
Analysis of EM Algorithm11 min
EM in Practice11 min
Latent Variables22 min
2 exercices pour s'entraîner
Learning with Incomplete Data8 min
Expectation Maximization14 min
4.6
28 avis83%
14%
Meilleurs avis
par LL•Jan 30th 2018
very good course for PGM learning and concept for machine learning programming. Just some description for quiz of final exam is somehow unclear, which lead to a little bit confusing.
par ZZ•Feb 14th 2017
Great course! Very informative course videos and challenging yet rewarding programming assignments. Hope that the mentors can be more helpful in timely responding for questions.
Enseignant
Daphne Koller
ProfessorSchool of Engineering
À propos de Stanford University
The Leland Stanford Junior University, commonly referred to as Stanford University or Stanford, is an American private research university located in Stanford, California on an 8,180-acre (3,310 ha) campus near Palo Alto, California, United States.
À propos de la Spécialisation Probabilistic Graphical Models
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.
Foire Aux Questions
Quand aurai-je accès aux vidéos de cours et aux devoirs ?
Une fois que vous êtes inscrit(e) pour un Certificat, vous pouvez accéder à toutes les vidéos de cours, et à tous les quiz et exercices de programmation (le cas échéant). Vous pouvez soumettre des devoirs à examiner par vos pairs et en examiner vous-même uniquement après le début de votre session. Si vous préférez explorer le cours sans l'acheter, vous ne serez peut-être pas en mesure d'accéder à certains devoirs.
À quoi ai-je droit si je m'abonne à cette Spécialisation ?
Lorsque vous vous inscrivez au cours, vous bénéficiez d'un accès à tous les cours de la Spécialisation, et vous obtenez un Certificat lorsque vous avez réussi. Votre Certificat électronique est alors ajouté à votre page Accomplissements. À partir de cette page, vous pouvez imprimer votre Certificat ou l'ajouter à votre profil LinkedIn. Si vous souhaitez seulement lire et visualiser le contenu du cours, vous pouvez accéder gratuitement au cours en tant qu'auditeur libre.
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Learning Outcomes: By the end of this course, you will be able to
Compute the sufficient statistics of a data set that are necessary for learning a PGM from data
Implement both maximum likelihood and Bayesian parameter estimation for Bayesian networks
Implement maximum likelihood and MAP parameter estimation for Markov networks
Formulate a structure learning problem as a combinatorial optimization task over a space of network structure, and evaluate which scoring function is appropriate for a given situation
Utilize PGM inference algorithms in ways that support more effective parameter estimation for PGMs
Implement the Expectation Maximization (EM) algorithm for Bayesian networks
Honors track learners will get hands-on experience in implementing both EM and structure learning for tree-structured networks, and apply them to real-world tasks
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