Index

A

• approximate inference
  • about / Learning with approximate inference
  • belief propagation / Belief propagation and pseudo-moment matching
  • pseudo-moment matching / Belief propagation and pseudo-moment matching
• approximate messages
  • about / Propagation with approximate messages
  • computing / Message creation
  • inference / Inference with approximate messages
• assumptions, dynamic Bayesian networks (DBNs)
  • discrete timeline assumption / Discrete timeline assumption
  • Markov assumption / The Markov assumption

B

• Bayesian classifier
  • about / The Naive Bayes model
• Bayesian model averaging
  • about / Methods for the learning structure
• Bayesian models
  • about / Bayesian models
  • representation / Representation
  • factorization, of distribution over network / Factorization of a distribution over a network
  • D-separation / D-separation
  • converting, into Markov models / Converting Bayesian models into Markov models
  • Markov models, converting into / Converting Markov models into Bayesian models
• Bayesian network (2-TBN)
  • about / Model representation
• Bayesian network (BN)
  • about / Factorization of a distribution over a network
• Bayesian networks
  • implementing, pgmpy used / Implementing Bayesian networks using pgmpy
  • representation / Bayesian model representation
  • pattern, reasoning / Reasoning pattern in Bayesian networks
  • and Markov network / Bayesian and Markov networks
  • importance sampling / Importance sampling in Bayesian networks
  • structure learning / Structure learning in Bayesian networks
• Bayesian parameter estimation
  • about / Bayesian parameter estimation
  • priors / Priors
  • for Bayesian networks / Bayesian parameter estimation for Bayesian networks
  • local decomposition / Bayesian parameter estimation for Bayesian networks
• Bayesian score
  • for Bayesian networks / The Bayesian score for Bayesian networks
  • for Markov models / Bayesian score
• belief propagation
  • about / Belief propagation, Belief propagation and pseudo-moment matching
  • clique tree / Clique tree
  • message passing / Message passing
  • using, for MAP / MAP using belief propagation
  • versus variable elimination / A comparison of variable elimination and belief propagation
  • with approximate messages / Propagation with approximate messages
• belief update propagation
  • about / Belief update propagation
  • MAP inference / MAP inference
• Bethe cluster graph
  • about / Bethe cluster graph

C

• causal reasoning
  • about / Reasoning pattern in Bayesian networks
• chordal graphs
  • about / Chordal graphs
• classification error
  • about / Predicting the specific probability values
• clique tree
  • about / Clique tree
  • defining / Clique tree
  • constructing / Constructing a clique tree
  • calibration / Clique tree calibration
• cluster graph belief propagation
  • about / Cluster graph belief propagation
• cluster graphs
  • constructing / Constructing cluster graphs
  • constructing, with pairwise Markov networks / Pairwise Markov networks
  • Bethe cluster graph / Bethe cluster graph
• collapsed importance sampling
  • about / Collapsed importance sampling
• collapsed particles
  • about / Sampling-based approximate methods, Collapsed particles
• conditional independence
  • about / Independence and conditional independence
• conditional probability distribution
  • about / Conditional probability distribution
• constrained satisfaction problem (CSP)
  • about / MAP inference
• constraint-based structure learning
  • about / Methods for the learning structure, Constraint-based structure learning
  • structure score learning / Structure score learning
  • in Markov models / Constraint-based structure learning
  • limitations / Constraint-based structure learning
• context-specific CPDs
  • about / Context-specific CPDs
  • Tree CPD / Tree CPD
  • Rule CPD / Rule CPD
• CPD
  • about / Conditional probability distribution, Representation
  • representing, pgmpy used / Representing CPDs using pgmpy
  • representations / CPD representations
  • deterministic CPDs / Deterministic CPDs
  • context-specific CPDs / Context-specific CPDs

D

• D-separation
  • about / D-separation, Independencies in Markov networks
  • direct connection / Direct connection
  • indirect connection / Indirect connection
• decoding
  • about / MAP inference
• deterministic CPDs
  • about / Deterministic CPDs
• Directed Acyclic Graph (DAG)
  • about / Representation
• discriminative learning
  • about / Discriminative versus generative training
  • versus generative training / Discriminative versus generative training
• distributions
  • and graphs, relating / Relating graphs and distributions
  • graphs, constructing from / Constructing graphs from distributions
• dynamic Bayesian networks (DBNs)
  • about / Dynamic Bayesian networks
  • assumptions / Assumptions
  • model representation / Model representation

E

• 0/1 error
  • about / Predicting the specific probability values
• edges
  • about / Nodes and edges
• energy function
  • about / The energy function
  • energy term / The energy function
  • entropy term / The energy function
• energy term
  • about / The energy function
• entropy term
  • about / The energy function
• exact inference
  • problem solving / Exact inference as an optimization
• expectation-maximization (EM) algorithm
  • about / Computing the state sequence
• expected log-likelihood
  • about / Density estimation

F

• factor
  • about / Introducing the Markov network
• factor division
  • about / Factor division
  • implementing / Factor division
• factor graph
  • about / The factor graph
• factor maximization
  • about / Factor maximization
  • example / Factor maximization
• factor operations, Markov network / Factor operations
• Flat Tyre (F)
  • about / Context-specific CPDs
• forward-backward algorithm
  • about / The forward-backward algorithm
• forward sampling
  • about / Forward sampling
• full particles
  • about / Sampling-based approximate methods

G

• generative learning
  • about / Discriminative versus generative training
  • versus discriminative training / Discriminative versus generative training
• Gibbs distribution
  • and Markov network / Gibbs distributions and Markov networks
• Gibbs sampling
  • about / Gibbs sampling
  • Markov chain / Markov chains
• gradient ascent
  • about / Gradient ascent
• graphs
  • and distributions, relating / Relating graphs and distributions
  • IMAP / IMAP
  • IMAP, to factorization / IMAP to factorization
  • constructing, from distributions / Constructing graphs from distributions
• graph theory
  • about / Graph theory
  • nodes / Nodes and edges
  • edges / Nodes and edges
  • walk / Walk, paths, and trails
  • paths / Walk, paths, and trails
  • trails / Walk, paths, and trails
  • cycles / Walk, paths, and trails

H

• Hamming loss
  • about / Predicting the specific probability values
• hidden Markov model (HMM)
  • about / The Hidden Markov model
  • observation sequence, generating / Generating an observation sequence
  • probability of observation, computing / Computing the probability of an observation
  • forward-backward algorithm / The forward-backward algorithm
  • state sequence, computing / Computing the state sequence
  • applications / Applications
  • HMM-based speech recognition system / Applications
• HMM-based speech recognition system
  • about / Applications
  • acoustic model / The acoustic model
  • language model / The language model

I

• IMAP
  • about / IMAP
  • to factorization / IMAP to factorization
• importance sampling
  • about / Likelihood weighting and importance sampling, Importance sampling
  • in Bayesian networks / Importance sampling in Bayesian networks
  • marginal probabilities, computing / Computing marginal probabilities
  • ratio likelihood weighting / Ratio likelihood weighting
  • normalized likelihood weighting / Normalized likelihood weighting
• independence
  • about / Independence and conditional independence
  • representing, pgmpy used / Representing independencies using pgmpy
• independencies, in Markov network
  • about / Independencies in Markov networks
• induced graphs
  • width / Finding elimination ordering
  • induced width / Finding elimination ordering
  • tree width / Finding elimination ordering
• inference
  • about / Inference
  • example / Inference
  • complexity / Complexity of inference
  • with approximate messages / Inference with approximate messages
  • sum-product expectation propagation / Sum-product expectation propagation
  • belief update propagation / Belief update propagation
• IPython
  • installing / IPython
  • URL / IPython

J

• joint probability distribution
  • about / Independence and conditional independence
  • representing, pgmpy used / Representing joint probability distributions using pgmpy

L

• Lagrangian multipliers
  • using / Exact inference as an optimization
• Lauritzen-Spiegelhalter algorithm
  • about / Factor division
• learning
  • general ideas / General ideas in learning
  • goals / The goals of learning
  • density estimation / Density estimation
  • specific probability values, predicting / Predicting the specific probability values
  • knowledge discovery / Knowledge discovery
  • optimization problem / Learning as an optimization
  • empirical risk / Empirical risk and overfitting
  • overfitting / Empirical risk and overfitting
• learning task
  • about / Learning task
  • model constraints / Model constraints
  • data observability / Data observability
• Lidstone smoothing
  • about / Multinomial Naive Bayes model
• likelihood function
  • about / Likelihood function
  • log-linear model / Log-linear model
  • gradient ascent / Gradient ascent
• likelihood score
  • for Markov models / The likelihood score
• likelihood weighting
  • about / Likelihood weighting and importance sampling
• log-linear model
  • about / Log-linear model

M

• MAP
  • variable elimination, using / MAP using variable elimination
  • belief propagation, using / MAP using belief propagation
• MAP inference
  • about / MAP inference, MAP inference
• marginal probabilities
  • computing / Computing marginal probabilities
• Markov blanket
  • about / Independencies in Markov networks
• Markov chain
  • Gibbs sampling / Markov chains
  • distributions converge, checking / Markov chains
  • using / Using a Markov chain
• Markov chain Monte Carlo methods
  • about / Markov chain Monte Carlo methods
• Markovian
  • about / The Markov assumption
• Markov models
  • Bayesian models, converting into / Converting Bayesian models into Markov models
  • converting, into Bayesian models / Converting Markov models into Bayesian models
  • maximum likelihood parameter estimation / Maximum likelihood parameter estimation
  • structure learning / Structure learning
  • constraint-based structure learning / Constraint-based structure learning
  • score-based structure learning / Score-based structure learning
  • likelihood score / The likelihood score
• Markov models, indecencies
  • local Markov independencies / Constraint-based structure learning
  • pair-wise independencies / Constraint-based structure learning
  • global independencies / Constraint-based structure learning
• Markov network
  • about / Introducing the Markov network
  • parameterizing / Parameterizing a Markov network – factor
  • factor operations / Factor operations
  • and Gibbs distribution / Gibbs distributions and Markov networks
  • independencies / Independencies in Markov networks
  • and Bayesian networks / Bayesian and Markov networks
• Markov networks
  • maximum likelihood parameter estimation / Maximum likelihood parameter estimation
• Markov process
  • about / The Hidden Markov model
• maximization
  • about / Factor maximization
• maximum likelihood parameter estimation
  • in Markov networks / Maximum likelihood parameter estimation
  • likelihood function / Likelihood function
  • learning, with approximate inference / Learning with approximate inference
  • structure learning / Structure learning
  • score-based structure learning / Score-based structure learning
• message passing
  • about / Message passing
  • with division / Message passing with division
  • implementing, with factor division / Factor division
  • variables from different clusters, querying / Querying variables that are not in the same cluster
• model
  • variable states, predicting with pgmpy / Predictions from the model using pgmpy
• moral graph / Converting Bayesian models into Markov models
• moralization, of network / Converting Bayesian models into Markov models
• most probable assignment
  • searching / Finding the most probable assignment
  • example / Finding the most probable assignment
• multinomial Naive Bayes model
  • about / Multinomial Naive Bayes model
• multiple transitioning model
  • about / The multiple transitioning model
• multivariate Bernoulli Naive Bayes model
  • about / Multivariate Bernoulli Naive Bayes model
  • implementation / Multivariate Bernoulli Naive Bayes model
• mutilated network proposal distribution
  • about / Importance sampling in Bayesian networks

N

• Naive Bayes model
  • about / The Naive Bayes model
  • usage / Why does it even work?
  • types / Types of Naive Bayes models
  • multivariate Bernoulli Naive Bayes model / Multivariate Bernoulli Naive Bayes model
  • multinomial Naive Bayes model / Multinomial Naive Bayes model
  • best model, selecting / Choosing the right model
• nodes
  • about / Nodes and edges
• normalized importance sampling estimator
  • about / Importance sampling
• normalized likelihood weighting
  • about / Normalized likelihood weighting

O

• optimization problem
  • about / The optimization problem

P

• pairwise independency
  • about / Independencies in Markov networks
• pairwise Markov networks
  • cluster graphs, constructing / Pairwise Markov networks
• parameter learning
  • about / Parameter learning
  • maximum likelihood estimation / Maximum likelihood estimation
  • maximum likelihood principle / Maximum likelihood principle
  • maximum likelihood estimation, for Bayesian networks / The maximum likelihood estimate for Bayesian networks
• particle
  • about / Sampling-based approximate methods
• particle-based methods
  • about / Sampling-based approximate methods
• Perfect Map
  • about / IMAP
• pgmpy
  • installing / pgmpy
  • URL / pgmpy
  • used, for representing independence / Representing independencies using pgmpy
  • used, for representing joint probability distribution / Representing joint probability distributions using pgmpy
  • used, for implementing CPD / Representing CPDs using pgmpy
  • used, for implementing Bayesian networks / Implementing Bayesian networks using pgmpy
  • used, for predicting variable states from model / Predictions from the model using pgmpy
• probability theory
  • about / Probability theory
  • random variable / Random variable
  • independence / Independence and conditional independence
  • conditional independence / Independence and conditional independence
• propagation based approximation algorithm
  • about / The propagation-based approximation algorithm
  • example / The propagation-based approximation algorithm
  • cluster graph belief propagation / Cluster graph belief propagation
  • cluster graphs, constructing / Constructing cluster graphs
• pseudo-moment matching
  • about / Belief propagation and pseudo-moment matching
• pseudo max-marginals
  • about / MAP inference

R

• random variable
  • about / Random variable
• Rao-Blackwellized particles
  • about / Collapsed particles
• ratio likelihood weighting
  • about / Ratio likelihood weighting
• relative entropy
  • about / The optimization problem
• Rule CPD
  • about / Rule CPD

S

• sampling-based approximate methods
  • about / Sampling-based approximate methods
• score-based structure learning
  • about / Methods for the learning structure
  • in Markov models / Score-based structure learning
  • likelihood score / The likelihood score
  • Bayesian score / Bayesian score
• structure learning
  • about / Structure learning in Bayesian networks
  • in Bayesian networks / Structure learning in Bayesian networks
  • methods / Methods for the learning structure
  • in Markov models / Structure learning
  • constraint-based structure learning / Constraint-based structure learning
• structure learning, methods
  • constraint-based structure learning / Methods for the learning structure
  • score-based structure learning / Methods for the learning structure
  • Bayesian model averaging / Methods for the learning structure
• structure score learning
  • about / Structure score learning
  • likelihood score / The likelihood score
  • Bayesian score / The Bayesian score
• sum-product expectation propagation
  • about / Sum-product expectation propagation

T

• target distribution
  • about / Importance sampling
• tf-idf
  • about / Multivariate Bernoulli Naive Bayes model
• tools
  • IPython, installing / Installing tools
  • pgmpy, installing / Installing tools
• Tree CPD
  • about / Tree CPD
• triangulation
  • about / Converting Markov models into Bayesian models

U

• unnormalized importance sampling estimator
  • about / Importance sampling

V

• variable elimination
  • about / Variable elimination
  • example / Variable elimination
  • analyzing / Analysis of variable elimination
  • elimination order, searching / Finding elimination ordering
  • using, for MAP / MAP using variable elimination
  • versus belief propagation / A comparison of variable elimination and belief propagation
• variable elimination order
  • searching / Finding elimination ordering
  • searching, chordal graph property used / Using the chordal graph property of induced graphs
  • cost criteria / Minimum fill/size/weight/search
• variable elimination order, cost criteria
  • min-neighbors / Minimum fill/size/weight/search
  • min-weight / Minimum fill/size/weight/search
  • min-fill / Minimum fill/size/weight/search
  • weighted-min-fill / Minimum fill/size/weight/search
• variables connection
  • indirect causal effect / Indirect connection
  • indirect evidential effect / Indirect connection
  • common cause / Indirect connection
• vertices
  • about / Nodes and edges

W

• weighted importance sampling estimator
  • about / Importance sampling