Learning Languages with the Help of Algorithms
3 days ago
- #NP-hard problems
- #language learning
- #vocabulary optimization
- Learning a new language efficiently involves boosting vocabulary through reading books with high vocabulary impact.
- Vocabulary impact is measured by a weighted sum of words in a book, weighted by their frequency in the language.
- Finding the single best book for vocabulary coverage is solvable in linear time using hashing and filtering stop words.
- Finding the best two books for joint vocabulary coverage requires quadratic time in the general case.
- Selecting the best k books for vocabulary coverage is an NP-hard problem, making exact solutions impractical for large k.
- Submodular problems allow for approximate solutions with guaranteed accuracy, using greedy algorithms.
- The Python submodlib package provides fast solutions for submodular maximization problems.
- Advanced strategies like blocking and look-ahead can improve solution quality but increase computational complexity.
- Heuristics, such as discarding books with redundant vocabulary, can sometimes improve performance.
- References to key papers and resources on submodular optimization and maximal coverage problems are provided.