many data science problems require solving a least-squares problem min_x || a x - b ||^2. efficiently solving this problem becomes a challenge when a has millions of rows, or even higher. i am developing solutions based on randomized numerical linear algebra:

1. if a is small enough to fit in working memory, an efficient solution is conjugate gradient with randomized preconditioning.

2. if a is too large to fit in working memory but x fits in memory, an intriguing possibility is randomized kaczmarz.

3. if x is too large to fit in working memory, the final possibility is randomly sparsified richardson iteration.