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In Progress

Investigations 5a and 5b attempt to determine the best default initialization function.

• Investigation 5a. We should change the default init_fn to udv_si_svd when there is missing data and udv_svd otherwise.

• Investigation 5b. More evidence supporting a change to the default initialization function.

Investigations 8 and 9 implement parallel backfitting updates.

• Investigation 8. Parallelizing the backfitting algorithm shows promise.

• Investigation 9. An additional trick is needed to parallelize the backfitting updates performed in this MASH v FLASH GTEx analysis.

Investigation 10. SQUAREM does poorly on FLASH backfits. DAAREM (a more recent algorithm by one of the authors of SQUAREM) does better, but offers smaller performance gains than parallelization.

Investigation 11. The order in which factor/loading pairs are updated (during backfitting) makes some difference, but not much.

Investigation 12. To fit a FLASH model with an arbitrary error covariance matrix, I follow up on a suggestion by Matthew Stephens.

Still Relevant

Notes 1 and 2 and Investigation 4 describe a way to compute the FLASH objective directly (rather than using the indirect method implemented in flashr).

• Note 1. Notes on computing the FLASH objective function. I derive an explicit expression for the KL divergence between prior and posterior.

• Note 2. An alternate algorithm for optimizing the FLASH objective, using the explicit expression derived in the previous note.

• Investigation 4. The alternate algorithm agrees with FLASH with respect to both the objective and fit obtained.

Archived

The bug causing the problem described in Investigations 1-3 was fixed in version 0.1-13 of package ebnm.

• Investigation 1. The FLASH objective function can behave very erratically.

• Investigation 2. This problem only occurs when using ebnm_pn, not ebnm_ash.

• Investigation 3. The objective can continue to get worse as loadings are repeatedly updated. Nonetheless, convergence takes place (from above!).

Investigations 6 and 7 deal with warmstarts, which were implemented in version 0.5-14 of flashr.

• Investigation 6. Poor optim results can produce large decreases in the objective function. We should use warmstarts when ebnm_fn = ebnm_pn.

• Investigation 7. The advantages of warmstarts are not nearly as compelling when ebnm_fn = ebnm_ash.