Probabilistic Models of Cognition: Generative models Table of - - PowerPoint PPT Presentation

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Probabilistic Models of Cognition: Generative models Table of - - PowerPoint PPT Presentation

Probabilistic Models of Cognition: Generative models Table of Contents Chapter Content Generative Model Example: Plinko Machine Working Model can be used captures some for simulation structure of the world in useful way


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Probabilistic Models of Cognition: Generative models

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Table of Contents

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Chapter Content

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Generative Model

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Example: Plinko Machine

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Working Model can be used for simulation captures some structure of the world in useful way

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Plinko Machine Demo

  • Simulate outcomes (data) many times, shape

emerges

  • Reason about ‘shape of expected outcomes’ (with

probabilistic concepts)

  • How to formally describe simulations/working

models?

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Building Generative Models

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Examples with Flip

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Flip

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Flip Sum

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Flipping Coins Bend

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Flipping Coins Bend

  • var bend = function(coin) {

return function() { (coin() == 'h') ? makeCoin(0.7)() : makeCoin(0.1)() } }

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Flipping Coins Bend

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Flipping Coins Repeat Sum

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Causal Models in Medical Diagnosis

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Advanced Causal Models in Medical Diagnosis

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Probability Concepts and WebPPL

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Probability

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Probability Distribution

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Distributions in WebPPL

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Distributions in WebPPL

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Constructing marginal distributions: Infer

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Constructing marginal distributions: Infer

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The Rules of Probability

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Product Rule

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Product Rule

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Product Rule

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Product Rule

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Product Rule

∣ ○

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Product Rule

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Sum Rule

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Sum Rule

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Sum Rule

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Sum Rule and Product Rule

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Sum Rule and Product Rule

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Sum Rule and Product Rule

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Advanced WebPPL

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Stochastic recursion

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Persistent Randomness: mem

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Persistent Randomness: mem

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Persistent Randomness: mem

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Persistent Randomness: mem

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Example: Intuitive physics

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Example: Intuitive physics

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Example: Intuitive physics

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Example: Intuitive physics

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Example: Intuitive physics

○ ○ ○

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Summary of Chapter Content

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Exercises

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Exercise 1 a)

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Exercise 1 a)

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Exercise 1 a)

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Exercise 1 b)

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Exercise 1 c)

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Exercise 1 c)

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Exercise 1 c)

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Exercise 1 c)

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Exercise 2

Just one execution of flip

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Exercise 2 b)

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Exercise 2 c)

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Exercise 3

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Exercise 3 a)

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Exercise 3 b)

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Exercise 4 a)

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Exercise 4 b)

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Exercise 4 c)

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Exercise 4 c)

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Exercise 5

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Exercise 5 a)

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Exercise 5 a)

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Exercise 6 a)

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Exercise 6 b)

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Exercise 7 a)

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Exercise 7 b)

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Exercise 8 a)

○ ○ ■

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Exercise 8 b)