# Testing the fall-through algorithm

    library(morphemepiece)
    library(dplyr)

This vignette is developer-focused, and outlines an example process for evaluating different (versions of) fall-through algorithms for the morphemepiece tokenizer. The basic approach is...

- Obtain a list of words with known breakdown, which are also representative of words that would actually hit the algorithm. The words should not be too common (else they will always be in the lookup), nor too rare/artificial (otherwise they are not a good representation of actual usage). A reasonable prescription here is to take the difference between the large/small lookup tables.
- Process this list of words using each candidate algorithm.
- Score each result by comparing the algorithmic breakdown to the known breakdown. We compute score by finding the "F1" when comparing the two sets of tokens to each other (identical breakdowns score a 1.0, while any missing tokens in either direction will reduce the score).

    # These are local paths for illustration purposes
    vocab_path <- "/shared/morphemepiece_vocabs/mp_vocab_large.txt"
    lookup_path <- "/shared/morphemepiece_vocabs/mp_lookup_large.txt"
    # We will be interested in words that are in the large lookup, but not the small
    # one (as a proxy for the most common words that will hit the fallthrough
    # algorithm).
    lookup_path_small <- "/shared/morphemepiece_vocabs/mp_lookup_small.txt"

    mp_vocab <- load_or_retrieve_vocab(vocab_path)
    mp_lookup <- load_or_retrieve_lookup(lookup_path)
    mp_lookup_small <- load_or_retrieve_lookup(lookup_path_small)

Obtain the words, and process...

    breakdown1 <- list()
    breakdown2 <- list()
    words_to_do <- setdiff(names(mp_lookup), names(mp_lookup_small))
    # It takes about an hour to do all words in this set.
    for (word in words_to_do) {
      bd1 <- morphemepiece:::.mp_tokenize_word_bidir(word,
                                                     mp_vocab,
                                                     allow_compounds = FALSE)
      bd2 <- morphemepiece:::.mp_tokenize_word_bidir(word,
                                                     mp_vocab,
                                                     allow_compounds = TRUE)
      breakdown1 <- append(breakdown1, paste0(bd1, collapse = " "))
      breakdown2 <- append(breakdown2, paste0(bd2, collapse = " "))
    }

    actual_bd <- mp_lookup[words_to_do]
    wdtbl <- dplyr::tibble(words_to_do, actual_bd, bd1 = unlist(breakdown1), bd2 = unlist(breakdown2))

    calc_score <- function(bd0, bd) {
      bd0 <- stringr::str_split(bd0, " ", simplify = FALSE)
      bd <- stringr::str_split(bd, " ", simplify = FALSE)
      bd0 <- purrr::map(bd0, function(b) {b[b != "##"]} )
      bd <- purrr::map(bd, function(b) {b[b != "##"]} )

      purrr::map2_dbl(bd0, bd, function(a, b) {
        re <- mean(a %in% b)
        pr <- mean(b %in% a)
        if (re == 0 & pr == 0) {
          return(0)
        }
        f1 <- 2*re*pr / (re + pr)
        return(f1)
        })
    }

    scored <- wdtbl %>%
      # The filter helps focus on the difference between the two algorithms.
      # To measure absolute performance, we'd take out this filter.
      filter(bd1 != bd2) %>%
      mutate(score1 = calc_score(actual_bd, bd1)) %>%
      mutate(score2 = calc_score(actual_bd, bd2))

    # what was the mean score of each algorithm? (1=old, 2=new)
    mean(scored$score1) # 0.3717737
    mean(scored$score2) # 0.4134288

    # what fraction of words did each algorithm score 100% on?
    mean(scored$score1 == 1) # 0.03477313
    mean(scored$score2 == 1) # 0.1674262

    # what fraction of words did each algorithm score 0% on?
    mean(scored$score1 == 0) # 0.1803051
    mean(scored$score2 == 0) # 0.2317713

    # in what fraction of cases was the old or new algorithm strictly better?
    scored %>%
      mutate(old_better = score1 > score2) %>%
      mutate(new_better = score1 < score2) %>%
      summarize(mean(old_better), mean(new_better))

    # # A tibble: 1 x 2
    #   `mean(old_better)` `mean(new_better)`
    #                <dbl>              <dbl>
    # 1              0.343              0.536

By almost all measures, the new algorithm gives breakdowns closer to "correct" than the old one. However, the new algorithm scores 0 more often than the old, so the comparison isn't completely one-sided.