compute-constrained-bayes/index.md

Dependencies

nimble install https://github.com/nim-lang/bigints https://nimdocs.com/nim-lang/bigints/bigints.html nimble install print https://github.com/treeform/print

Dependencies

The data folder is not included, but its contents are:

. ├── data │   ├── stripped │   └── stripped.gz

Where stripped.gz can be found at https://oeis.org/wiki/JSON_Format,_Compressed_Files

To do

• Exploration of OEIS data
• Subdivide subsequent tasks into steps
  • Simple prediction of the next integer
    • Simple predictions v1
    • Wrangle the return types to something semi-elegant
    • [-] Maybe add some caching, e.g., write continuations to file, and read them next time.
  • JIT Bayesianism:
    • Function to predict with a variable number of hypotheses
    • Function to start predicting with a small number of hypotheses, and get more if the initial ones aren't enough.
    • Add the loop of: start with some small number of sequences, and if these aren't enough, read more.
    • ...
  • Infrabayesianism x1: Predicting interleaved sequences
  • Infrabayesianism x2: Deterministic game of producing a fixed deterministic prediction, and then the adversary picking whatever minimizes your loss
    • Write the actor

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An implementation of Infrabayesianism over OEIS sequences. https://oeis.org/wiki/JSON_Format,_Compressed_Files

Or "Just-in-Time bayesianism", where getting a new hypothesis = getting a new sequence from OEIS which has the numbers you've seen so far.

Implementing Infrabayesianism as a game over OEIS sequences. Two parts:

1. Prediction over interleaved sequences. I choose two OEIS sequences, and interleave them: a1, b1, a2, b2.

• Now, you don't have hypothesis over the whole set, but two hypothesis over the
• I could also have a chemistry like iteration: a1 a2 b1 a3 b2 c1 a4 b3 c2 d1 a5 b4 c3 d2 e1 .................
• And then it would just be computationally absurd to have hypotheses over the whole

2. Game where: You provide a deterministic procedure for estimating the probability of each OEIS sequence giving a list of trailing examples.