The first three posts of this sequence set up two important challenges facing modern science:
- How do scientists go about decompressing structure?
- Can category theory absorb the field of statistics?
The final post of this sequence suggests that these questions are in fact, the same.
- An Introduction To Structural Realism
- The Mathematical Structure Of Physics
- On Bridging The Archipelago
- The Microcosm Of Computer Science
Decision Theory extensions:
Final Report for UW Applied Algorithms class
Rubin’s Causal Framework:
Hi! So, I’m trying out something new. It’s no longer summer, which means I have much less time to follow my own research paths (because class). But this quarter, I want to “live blog” my insights as I go along. The class is:
Exact Inference On Approximate Problem:
- Chordal Graphs [Graphic]. Trees aren’t the only thing supporting perfect elimination orderings (PEOs). An infographic describing the chain of mathematical proofs which ultimately establish chordal graphs as supporting PEOs via the concept of minimal separators.
- Family vs. Universe. Graphical models conjoin graphs with a set of rules, which sample & thereby constrain the entire universe U (solution-space). The constrained solution-space is called a family F.
- Designer Families. A concrete walkthrough of family design, including which heuristics are important to bear in mind.
- Murderous Cliques. How cliques give us insight into making good variable-elimination-ordering choices.
- Murderous Messages. Graphs with no cycles (trees) allow us to re-interpret variable elimination epistemically, as a form of message passing.
- Tree, Generalized. Introduces k-trees, and discusses the relationship between trees, k-trees, and chordal graphs.
Approximate Inference on Exact Problems:
Final Project Posts
In this sequence, we will be exploring this précis of this book. Specifically, we will be exploring the implications of akrasia (the act of behaving against one’s own desires).
- An Introduction To Hyperbolic Discounting. Based on Chapter 1-3. Introduces the concepts of akrasia and utility, proceeds to model akrasia as a symptom of discount curves shaped like hyperbolas.
- Willpower As Preference Bundling. Based on Chapter 5. Discusses how willpower (a therapy against akrasia) comes to make our successive selves consistent with one another. Willpower is presented as the brain subtly manipulating how it instantiates hyperbolic discount functions.
- Personal Rule Feedback Loops. Based on Chapter 6. Builds a mental model of preference bundling, and explores the recursive nature of personal rules.
- Iterated Schizophrenic’s Dilemma. Based on Chapter 6. Grounds Ainslee’s account of willpower (and preference bundling) in a modified form of Iterated Prisoner’s Dilemma.
- Against Willpower. Based on Chapter 9. If willpower is preference bundling, then its mechanisms become available for scrutiny. Ainslee here locates four surprising implications of his theory of willpower, which suggest that it is not the unilaterally-beneficial tool that we might suspect.