zsteve
commented
3 years ago Hi @Marius1311,
Since others have not responded, here are some of my thoughts:
how you would recommend to build a single transition matrix from the transport maps. Would you just row-normalize them and stick them together to form one block matrix with 0s for non-adjacent time-points?
Yes, from my understanding of Cellrank this seems to be the most straightforward option (and the time-series format means transitions in non-adjacent timepoints is impossible). I guess the main issue here would be that the resulting Markov chain is very much non-reversible (and might not be suitable for some downstream computations I suspect). At least for computing absorption probabilities this sounds fine.
Perhaps it may be beneficial to have a subclass for time series experiments (as opposed to single-snapshot experiments), since different analyses might be relevant to time-series.
why do you re-compute PCA for every pair of adjacent time points to compute the cost matrix? Could we use a global PCA for all time points here? I'm asking because that's usually already contained in the AnnData object, so no computational overhead. Also, could we use the KNN graph connectivities for the cost matrix? These would be sparse.
From my understanding it is probably fine to use a global PCA coordinates, at least nothing at the conceptual level is lost. And anyway, except for constructing the cost matrix the actual choice of embedding is not used elsewhere. For the cost matrix, what exactly do you mean by kNN connectivities? If you mean a "sparse" cost matrix (with c(x, y) = +inf for x, y not connected by an edge -- this would correspond to exp(-C/eps) being sparse), unfortunately this doesn't really work (at least for reasonable k). The reason is because there's no guarantee the kNN is connected or allows a feasible solution of the OT problem (and anecdotally this seems to often be the case).
One possibility (which we use quite often) is to use the KeOps library (https://github.com/getkeops/keops) which allows you to do computations with the cost matrix (in terms of mat-vec products) without evaluating explicitly the full matrix.
Perhaps it would be easiest to try adapting WOT to CellRank in the most straightforward manner (i.e. just make a block matrix from the individual transport maps) and see how things go. If that looks promising, I'm happy to help with optimising the implementation :)
Let me know if you have any further questions :)
Stephen
geoffschieb
michalk8
Marius1311
Hi all! As discussed recently with @geoffschieb, I believe WOT and CellRank have complementary strengths that could really benefit from each other. WOT is a fantastic resource to compute transport maps based on time-course scRNA-seq data, and CellRank is a framework to both compute and analyze transition matrices in a Markov-chain based framework, see Fig. 1 below. @geoffschieb and I agreed it would be very cool to interface to WOT from within CellRank through an external kernel - similar to how external packages are interfaced from scanpy through scanpy external. We've done this for StationaryOT already, in collab with @zsteve see here.
Computationally, this means we write a shallow wrapper in CellRank which internally calls WOT to compute a transition matrix based on data in a passed AnnData object. The outputs are then streamlined so that they can use in subsequent CellRank analysis though estimators.
@michalk8 and myself would love to hear your comments/ideas/feedback before we proceed with the actual implementation. In particular, we were wondering
Looking forward to your input!
Fig. 1