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Finite Factored Sets

May 25, 2021 by Scott Garrabrant

This is an introduction to a new way of thinking about time, based on finite factored sets.

A factored set is a set understood as a Cartesian product, in the same sense that a partition is a way to understand a set as a disjoint union.

This sequence begins by applying finite factored sets to temporal inference, showing some advantages of this framework over Judea Pearl's theory of causal inference. Finite factored sets have many potential applications outside of temporal inference, however, and future writing will explore embedded agency and other topics through the lens of finite factored sets.

The "Details and Proofs" section of this sequence is also available as an arXiv paper: "Temporal Inference with Finite Factored Sets."

 

Overview

149Finite Factored Sets
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Scott Garrabrant
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Details and Proofs

36Finite Factored Sets: Introduction and Factorizations
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Scott Garrabrant
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34Finite Factored Sets: Orthogonality and Time
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Scott Garrabrant
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29Finite Factored Sets: Conditional Orthogonality
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Scott Garrabrant
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21Finite Factored Sets: Polynomials and Probability
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23Finite Factored Sets: Inferring Time
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34Finite Factored Sets: Applications
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Applications and Discussion

162Saving Time
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Scott Garrabrant
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41[AN #163]: Using finite factored sets for causal and temporal inference
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Rohin Shah
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59AXRP Episode 9 - Finite Factored Sets with Scott Garrabrant
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DanielFilan
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183Finite Factored Sets in Pictures
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Magdalena Wache
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55Exploring Finite Factored Sets with some toy examples
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Thomas Kehrenberg
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53A simple example of conditional orthogonality in finite factored sets
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DanielFilan
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47A second example of conditional orthogonality in finite factored sets
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DanielFilan
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40Counterfactability
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Scott Garrabrant
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47Countably Factored Spaces
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Diffractor
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