By Abraham Ginzburg
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Common sense Propositions and fact Values Logical Connectives and fact Tables Tautologies and Contradictions Logical Equivalence and Logical Implication The Algebra of Propositions Arguments Formal facts of the Validity of Arguments Predicate common sense Arguments in Predicate common sense Mathematical evidence the character of evidence Axioms and Axiom platforms equipment of evidence Mathematical Induction units units and MembershipSubsetsOperations on SetsCounting TechniquesThe Algebra of units households of units The Cartesian Product forms and Typed Set TheoryRelations relatives and Their Representations houses of kin.
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Elements correspond to variables in your model, like the height of the center forward or the outcome of the corner kick. Figaro Probabilistic model Figaro elements Scala The evidence is information about the values of elements. You write Scala code to create these elements. Inference algorithm You perform inference by running one of Figaro’s inference algorithms on your model, using the evidence. Evidence Figaro algorithms Queries Scala Inference is invoked by a Scala function call. Answers The answers provide the probabilities of different values of elements.
Probabilistic reasoning has been used for applications as diverse as predicting stock prices, recommending movies, diagnosing computers, and detecting cyber intrusions. Many of these applications use techniques you’ll learn in this book. info 16 CHAPTER 1 Probabilistic programming in a nutshell From the previous section, two points stand out: ■ ■ Probabilistic reasoning can be used to predict the future, infer the past, and learn from the past to better predict the future. Probabilistic programming is probabilistic reasoning using a Turing-complete programming language for representation.
You then supply evidence about this particular corner kick, namely, that the center forward is tall, the goalie is inexperienced, and the wind is strong. You tell the system that you want to know whether a goal will be scored. The inference algorithm returns the answer that a goal will be scored with 20% probability. info 7 What is probabilistic programming? In probabilistic reasoning, you create a model that captures all the relevant general knowledge of your domain in quantitative, probabilistic terms.
Algebraic Theory of Automata by Abraham Ginzburg