Probabilistic Models of Cognition:
Generative models
Table of Contents
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Chapter Content
Generative Model
Example: Plinko Machine
Working Model can be used
for simulation captures some
structure of the world in useful way
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?
Building Generative Models
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Examples with Flip
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)() }
}
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
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
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
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
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
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
Exercise 2 b)
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Exercise 2 c)
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Exercise 3
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)
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