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tgv
> We need a lot of data to do this well.

Yup. And once you've got a sufficiently large tagged error corpus, spelling correction will be as simple as a lookup: almost all misspellings (in terms of frequency) will be present in the corpus, and you can drop the (rather simplistic) algorithmic part.

techbio
By way of word2vec, or ?
colejohnson66
But what about “they’re”, “there”, and “their”? And other homonyms people frequently misspell?