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An important step in moving probabilistic programming from research laboratories out into the real world.
Practical Probabilistic Programming introduces the working programmer to probabilistic programming. In it, you'll learn how to use the PP paradigm to model application domains and then express those probabilistic models in code. Although PP can seem abstract, in this book you'll immediately work on practical examples, like using the Figaro language to build a spam filter and applying Bayesian and Markov networks, to diagnose computer system data problems and recover digital images.
Part 1: Introducing probabilistic programming and Figaro
1. Probabilistic programming in a nutshell
1.1. What is probabilistic programming?
1.1.1. How do we make judgment calls?
1.1.2. Probabilistic reasoning systems help make decisions
1.1.3. Probabilistic reasoning systems can reason in three ways
1.1.4. Probabilistic programming systems: probabilistic reasoning systems expressed in a programming language
1.2. Why probabilistic programming?
1.2.1. Better probabilistic reasoning
1.2.2. Better simulation languages
1.3. Introducing Figaro: a probabilistic programming language
1.3.1. Figaro vs. Java: building a simple probabilistic programming system
1.4. Summary
1.5. Exercises
2. A quick Figaro tutorial
2.1. Introducing Figaro
2.2. Creating models and running inference: Hello World revisited
2.2.1. Building your first model
2.2.2. Running inference and answering a query
2.2.3. Building up models and making observations
2.2.4. Understanding how the model is built
2.2.5. Understanding repeated elements: when are they the same and when are they different?
2.3. Working with basic building blocks: atomic elements
2.3.1. Discrete atomic elements
2.3.2. Continuous atomic elements
2.4. Combining atomic elements by using compound elements
2.4.1. If
2.4.2. Dist
2.4.3. Compound versions of atomic elements
2.5. Building more-complex models with Apply and Chain
2.5.1. Apply
2.5.2. Chain
2.6. Specifying evidence by using conditions and constraints
2.6.1. Observations
2.6.2. Conditions
2.6.3. Constraints
2.7. Summary
2.8. Exercises
3. Creating a probabilistic programming application
3.1. Understanding the big picture
3.2. Running the code
3.3. Exploring the architecture of a spam-filter application
3.3.1. Reasoning component architecture
3.3.2. Learning component architecture
3.4. Designing an email model
3.4.1. Choosing the elements
3.4.2. Defining the dependencies
3.4.3. Defining the functional forms
3.4.4. Using numerical parameters
3.4.5. Working with auxiliary knowledge
3.5. Building the reasoning component
3.6. Creating the learning component
3.7. Summary
3.8. Exercises
Part 2: Writing probabilistic programs
4. Probabilistic models and probabilistic programs
4.1. Probabilistic models defined
4.1.1. Expressing general knowledge as a probability distribution over possible worlds
4.1.2. Exploring probability distributions further
4.2. Using a probabilistic model to answer queries
4.2.1. Conditioning on the evidence to produce the posterior probability distribution
4.2.2. Answering queries
4.2.3. Using probabilistic inference
4.3. The ingredients of probabilistic models
4.3.1. Variables
4.3.2. Dependencies
4.3.3. Functional forms
4.3.4. Numerical parameters
4.4. Generative processes
4.5. Models with continuous variables
4.5.1. Using the beta-binomial model
4.5.2. Representing continuous variables
4.6. Summary
4.7. Exercises
5. Modeling dependencies with Bayesian and Markov networks
5.1. Modeling dependencies
5.1.1. Directed dependencies
5.1.2. Undirected dependencies
5.1.3. Direct and indirect dependencies
5.2. Using Bayesian networks
5.2.1. Bayesian networks defined
5.2.2. How a Bayesian Network defines a probability distribution
5.2.3. Reasoning with Bayesian networks
5.2.4. Designing a computer system diagnosis model
5.2.5. Reasoning with the computer system diagnosis model
5.3. Exploring a Bayesian network example
5.3.1. Designing a computer system diagnosis model
5.3.2. Reasoning with the computer system diagnosis model
5.4. Using probabilistic programming to extend Bayesian networks: predicting product success
5.4.1. Designing a product success prediction model
5.4.2. Reasoning with the product success prediction model
5.5. Using Markov networks
5.5.1. Markov networks defined
5.5.2. Representing and reasoning with Markov networks
5.6. Summary
5.7. Exercises
6. Using Scala and Figaro collections to build up models
6.1. Using Scala collections
6.1.1. Modeling dependence of many variables on a single variable
6.1.2. Creating hierarchical models
6.1.3. Modeling simultaneous dependence on two variables
6.2. Using Figaro collections
6.2.1. Understanding why Figaro collections are useful
6.2.2. Revisiting the hierarchical model with Figaro collections
6.2.3. Using Scala and Figaro collections together
6.3. Modeling situations with an unknown number of objects
6.3.1. Open universe situations with an unknown number of objects
6.3.2. Variable-size arrays
6.3.3. Operations on variable-size arrays
6.3.4. Example: predicting sales of an unknown number of new products
6.4. Working with infinite processes
6.4.1. The Process trait
6.4.2. Example: a temporal health process
6.4.3. Using the process
6.5. Summary
6.6. Exercises
7. Object-oriented probabilistic modeling
7.1. Using object-oriented probabilistic models
7.1.1. Understanding elements of object-oriented modeling
7.1.2. Revisiting the printer model
7.1.3. Reasoning about multiple printers
7.2. Extending OO probability models with relations
7.2.1. Describing general class-level models
7.2.2. Describing a situation
7.2.3. Representing the social media model in Figaro
7.3. Modeling relational and type uncertainty
7.3.1. Element collections and references
7.3.2. Social media model with relational uncertainty
7.3.3. Printer model with type uncertainty
7.4. Summary
7.5. Exercises
8. Modeling dynamic systems
8.1. Dynamic probabilistic models
8.2. Types of dynamic models
8.2.1. Markov chains
8.2.2. Hidden Markov models
8.2.3. Dynamic Bayesian networks
8.2.4. Models with variable structure over time
8.3. Modeling systems that go on indefinitely
8.3.1. Understanding Figaro universes
8.3.2. Using universes to model ongoing systems
8.3.3. Running a monitoring application
8.4. Summary
8.5. Exercises
Part 3: Inference
9. The three rules of probabilistic inference
9.1. The chain rule: building joint distributions from conditional probability distributions
9.2. The total probability rule: getting simple query results from a joint distribution
9.3. Bayes rule: inferring causes from effects
9.3.1. Understanding, cause, effect and inference
9.3.2. Bayes rule in practice
9.4. Bayesian modeling
9.4.1. Estimating the bias of a coin
9.4.2. Predicting the next coin toss
9.5. Summary
9.6. Exercises
10. Factored inference algorithms
10.1. Factors
10.1.1. What is a factor?
10.1.2. Factoring a probability distribution by using the chain rule
10.1.3. Defining queries with factors by using the total probability rule
10.2. The variable elimination algorithm
10.2.1. Graphical interpretation of VE
10.2.2. VE as algebraic operations
10.3. Using VE
10.3.1. Figaro-specific considerations for VE
10.3.2. Designing your model to support efficient VE
10.3.3. Applications of VE
10.4. Belief propagation
10.4.1. The essential idea of BP
10.4.2. Properties of loopy BP
10.5. Using BP
10.5.1. Figaro-specific considerations for BP
10.5.2. Designing your model to support effective BP
10.5.3. Applications of BP
10.6. Summary
10.7. Exercises
11. Sampling algorithms
11.1. The sampling principle
11.1.1. Forward sampling
11.1.2. Rejection sampling
11.2. Importance sampling
11.2.1. How importance sampling works
11.2.2. Using importance sampling in Figaro
11.2.3. Making importance sampling work for you
11.2.4. Applications of importance sampling
11.3. Markov chain Monte Carlo sampling
11.3.1. How MCMC works
11.3.2. Figaro's MCMC algorithm: Metropolis-Hastings
11.4. Getting MH to work well
11.4.1. Customized proposals
11.4.2. Avoiding hard conditions
11.4.3. Applications of MH
11.5. Summary
11.6. Exercises
12. Solving other inference tasks
12.1. Computing joint distributions
12.2. Computing the most probable explanation
12.2.1. Computing and querying the MPE in Figaro
12.2.2. Using algorithms for solving MPE queries
12.2.3. Exploring applications of MPE algorithms
12.3. Computing the probability of evidence
12.3.1. Observing evidence for probability-of-evidence computation
12.3.2. Running probability-of-evidence algorithms
12.4. Summary
12.5. Exercises
13. Dynamic reasoning and parameter learning
13.1. Monitoring the state of a dynamic system
13.1.1. Mechanics of monitoring
13.1.2. The particle-filtering algorithm
13.1.3. Applications of filtering
13.2. Learning model parameters
13.2.1. Bayesian learning
13.2.2. Maximum likelihood and MAP learning
13.3. Going further with Figaro
13.4. Summary
13.5. Exercises
Appendixes
Appendix A: Obtaining and installing Scala and Figaro
Appendix B: A Brief survey of probabilistic programming systems
About the Technology
The data you accumulate about your customers, products, and website users can help you not only to interpret your past, it can also help you predict your future! Probabilistic programming uses code to draw probabilistic inferences from data. By applying specialized algorithms, your programs assign degrees of probability to conclusions. This means you can forecast future events like sales trends, computer system failures, experimental outcomes, and many other critical concerns.
About the book
Practical Probabilistic Programming introduces the working programmer to probabilistic programming. In this book, you?ll immediately work on practical examples like building a spam filter, diagnosing computer system data problems, and recovering digital images. You?ll discover probabilistic inference, where algorithms help make extended predictions about issues like social media usage. Along the way, you?ll learn to use functional-style programming for text analysis, object-oriented models to predict social phenomena like the spread of tweets, and open universe models to gauge real-life social media usage. The book also has chapters on how probabilistic models can help in decision making and modeling of dynamic systems.
What's inside
- Introduction to probabilistic modeling
- Writing probabilistic programs in Figaro
- Building Bayesian networks
- Predicting product lifecycles
- Decision-making algorithms
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