chrestomathy

A crestomathy is, according to Wikipedia:

A chrestomathy (from the Ancient Greek χρηστός, khrēstós, meaning "useful", and μανθάνω, manthánō, meaning "learn") is a collection of selected literary passages [...]; a selection of literary passages from a foreign language assembled for studying the language; or a text in various languages, used especially as an aid in learning a subject. [...] It is different from an anthology because of its didactic purpose.

Each notebook in this unstructured collection explores a different goal, such as performing linear regression on some data, gridding irregular data to make a map (also a regression), or solving a linear algebraic equation. Each exploration involves stating the problem, then looking at different ways to do it, usually in increasingly sophisticated ways.

Notebooks

🥨 Maths and stats flavour

• Averages ✨ New
• Activation functions ✨ New
• Function differentiation ✨ New
• Timeseries extrapolation ✨ New
• Linear regression
• Regression algorithms
• Curse of dimensionality ✨ Updated

⚒️ Geoscience flavour

• Map interpolation
• Unsupervised clustering (of rock properties)
• Phase determination (of seismic data)
• Wavelet estimation (from wells and seismic)

Suggested additions

Topics for the future:

• Ways to represent points in 2-space, very useful for Advent of Code (eg 2018 Day 10 one):
  • Implicit position using counters or enumeration in loops
  • tuple(x, y) or tuple(col, row)
  • complex(x, y)
  • Point class...
  • ...with functools.total_ordering, operator overloading, etc
  • shapely.Point class
• Different ways to make a normal distribution (and/or other distributions as well perhaps).
• Sorting algorithms, but this has been done many times before.
• Pathfinding algorithms, but this is probably beyond me since I've never managed those problems in Advent of Code :D
• Binary classification algorithms: probably can't beat scikit-learn's comparison though.
• Multiclass classification algorithms, using rock property catalog data, and with the multi-class decision surface visualization from Agile.
• Clustering algorithms (or maybe just add to or generalize the existing notebook), but again sklearn's comparison is totally awesome.
• Data assimilation methods, although quite technical, and probably already perfectly well done by, eg, dapper
• Bayesian parameter estimation is perhaps more approachable than data assimilation.
• Distance algorithms are a huge subject — some of these topics deserve whole notebooks to themselves. There are plenty to choose from.
  • All the Minkowski distances (L0, L1 L2, etc) and maybe octile distance
  • Coherence etc for seismic
  • Levenshtein edit distance for words
  • Canberra distance for ranked lists and other things https://en.wikipedia.org/wiki/Canberra_distance
  • Word/doc embedding distance (embeddings and latent spaces in general), eg https://www.andrew.cmu.edu/course/15-121/labs/HW-4%20Document%20Distance/lab.html
  • Pixel and Image distance, eg see below
  • Clock distance (23:55 and 00:05 are very close, use circular distance eg https://gist.github.com/anonymous/7ce6274c630dabd70960c6d7fdd6c580
  • Wasserstein aka Earth mover’s distance for distributions https://en.wikipedia.org/wiki/Earth_mover%27s_distance
  • Probably some others: https://en.wikipedia.org/wiki/Metric_(mathematics)
  • 3D shapes, eg https://arxiv.org/pdf/1911.09204.pdf
  • See table here > https://stats.stackexchange.com/questions/58706/distance-metrics-for-binary-vectors/386952
  • Well logs could use cross-correlation, say. Also see https://quant.stackexchange.com/questions/848/time-series-similarity-measures
  • Curves: Hausdorff distance (no order info), Frechet distance (dog leash distance), dynamic time-warp distance (not a metric as doesn’t meet triangle inequality condition), eg see https://www.youtube.com/watch?v=mxat0UbmDo0
  • Dynamic time warping would be fun to explore; most of the algorithms are closely related.