17 ms·

Sparse matrix representations in SciPy (2017)

72 points by heydenberk 8y ago

joe_the_user 8y ago
There seems to be no end of sparse formats, potential sparse formats and algorithms for dealing with them. But it also seems like for a given sparse matrix in a given situation, there's no guaranteed that there's algorithm for handling it. The whole thing requires deep experience or black magic.
- perimo 8y ago
  To get the best performance you typically want to know something about the sparsity structure of your problem. Do most nonzeros fall near the diagonal? Or do they clump into dense submatrices? If you don't have that information, you can look at how your matrix will be accessed. Do you need fast access to random rows, or columns? Do you need to write new values? Are those values already in the sparsity structure? All of these questions can lead you to choosing the right sparse format, but it does take some experience to know where to look.
  - timr 8y ago
    That's true, but mostly you just want to be able to store massive sparse matrices without filling your RAM with zeros (or spending tons of time reading/writing zeros from disk). Any implementation will do, as long as it works.
    - srean 8y ago
      Storage is a minor worry. The main thing is whether the storage makes the frequent operations efficient. The tuple (index_position, value) is reasonably storage efficient but abysmal for linear algebraic operations. So one cannot decouple storage efficiency concerns from compute concerns too much. I think this is one of those shibboleths that separate folks who are experts in ML/data-science at scale vs those who are coming more from a enterprise/DBA background. I often have to convince folks why its not a great idea to write sparse matrix multiplication in SQL.
      - timr 8y ago
        "Storage is a minor worry." For many domains, it's a big worry. I routinely encounter large, sparse datasets where I/O and storage dominate other concerns. Big sparse tensors are worse than the "slowness" associated with a suboptimal sparse vector math implementation. "I think this is one of those shibboleths that separate folks who are experts in ML/data-science at scale vs those who are coming more from a enterprise/DBA background." I've been doing ML work for a long time. This is actually a shibboleth that separates folks who mostly do image classification from other kinds of ML people.
        srean 8y ago
        "Minor" in the sense relatively easy to solve if not constrained by the compute needs. Interesting comment regarding image classification. I would have assumed they are the ones who don't have to worry about sparsity much. Physics, and image and video are some of the places you encounter large and dense matrices. Lapack's wet dream :)
goerz 8y ago
A good sparse matrix implementation is key to any serious numerics. SciPy's implementation is very nice and quite complete, and a foundation for the entire scientific Python ecosystem. Unfortunately, though, many of the low-level sparse operations are not implemented very efficiently, which has lead to some projects having to do their own implementation, see e.g. this discussion for the QuTiP project: https://github.com/qutip/qutip/issues/850#issuecomment-384005667 https://github.com/qutip/qutip/issues/850#issuecomment-38400... It would be really nice if all of the sparse linear algebra in SciPy could be heavily optimized (to a similar extent as e.g. Intel optimizes their sparse operations in MKL), so that the entire ecosystem could benefit from that. This is probably something that would require some corporate support, but given how many data science and finance companies use Python for their workflow these days, it might be a wise investment.
- timr 8y ago
  This is true across the board. NumPy, Tensorflow, Pytorch...no library has anywhere near 100% coverage of core functionality in sparse tensors. It's just sort of generally assumed that if you're using sparse tensors, you're on your own. Tensorflow is better than most, in that it at least implements most ops for sparse tensors, even if it doesn't have efficient implementations for things. I was recently frustrated to find that PyTorch doesn't implement a lot of basic functionality for sparse tensors at all -- it just throws an exception.
  - yvdriess 8y ago
    TensorFlow is indeed the one-eyed king here. We found that running with large SparseTensors, CPU training jobs is actually faster than on GPU nodes. An individual job is faster on GPU, but SparseMatMul just blows up GPU memory use to the point that only one train job fits in its memory. SparseMatMul is inefficient on CPU as well, but you can keep getting some decent speedup by cranking up the parallel trade jobs per node. I did have great success using Netflix Vectorflow. I roughly gained 2x performance for my use case. It does leave some other performance on the table, no vectorized minibatches etc. If you are training on huge sparse datasets with a shallow ffw network, Vectorflow is a good alternative.
- 8y ago

72 points by heydenberk 8y ago

There seems to be no end of sparse formats, potential sparse formats and algorithms for dealing with them. But it also seems like for a given sparse matrix in a given situation, there's no guaranteed that there's algorithm for handling it. The whole thing requires deep experience or black magic.

perimo 8y ago
To get the best performance you typically want to know something about the sparsity structure of your problem. Do most nonzeros fall near the diagonal? Or do they clump into dense submatrices? If you don't have that information, you can look at how your matrix will be accessed. Do you need fast access to random rows, or columns? Do you need to write new values? Are those values already in the sparsity structure? All of these questions can lead you to choosing the right sparse format, but it does take some experience to know where to look.
- timr 8y ago
  That's true, but mostly you just want to be able to store massive sparse matrices without filling your RAM with zeros (or spending tons of time reading/writing zeros from disk). Any implementation will do, as long as it works.
  - srean 8y ago
    Storage is a minor worry. The main thing is whether the storage makes the frequent operations efficient. The tuple (index_position, value) is reasonably storage efficient but abysmal for linear algebraic operations. So one cannot decouple storage efficiency concerns from compute concerns too much. I think this is one of those shibboleths that separate folks who are experts in ML/data-science at scale vs those who are coming more from a enterprise/DBA background. I often have to convince folks why its not a great idea to write sparse matrix multiplication in SQL.
    - timr 8y ago
      "Storage is a minor worry." For many domains, it's a big worry. I routinely encounter large, sparse datasets where I/O and storage dominate other concerns. Big sparse tensors are worse than the "slowness" associated with a suboptimal sparse vector math implementation. "I think this is one of those shibboleths that separate folks who are experts in ML/data-science at scale vs those who are coming more from a enterprise/DBA background." I've been doing ML work for a long time. This is actually a shibboleth that separates folks who mostly do image classification from other kinds of ML people.
      - srean 8y ago
        "Minor" in the sense relatively easy to solve if not constrained by the compute needs. Interesting comment regarding image classification. I would have assumed they are the ones who don't have to worry about sparsity much. Physics, and image and video are some of the places you encounter large and dense matrices. Lapack's wet dream :)

goerz 8y ago

A good sparse matrix implementation is key to any serious numerics. SciPy's implementation is very nice and quite complete, and a foundation for the entire scientific Python ecosystem. Unfortunately, though, many of the low-level sparse operations are not implemented very efficiently, which has lead to some projects having to do their own implementation, see e.g. this discussion for the QuTiP project: https://github.com/qutip/qutip/issues/850#issuecomment-384005667 https://github.com/qutip/qutip/issues/850#issuecomment-38400... It would be really nice if all of the sparse linear algebra in SciPy could be heavily optimized (to a similar extent as e.g. Intel optimizes their sparse operations in MKL), so that the entire ecosystem could benefit from that. This is probably something that would require some corporate support, but given how many data science and finance companies use Python for their workflow these days, it might be a wise investment.

timr 8y ago
This is true across the board. NumPy, Tensorflow, Pytorch...no library has anywhere near 100% coverage of core functionality in sparse tensors. It's just sort of generally assumed that if you're using sparse tensors, you're on your own. Tensorflow is better than most, in that it at least implements most ops for sparse tensors, even if it doesn't have efficient implementations for things. I was recently frustrated to find that PyTorch doesn't implement a lot of basic functionality for sparse tensors at all -- it just throws an exception.
- yvdriess 8y ago
  TensorFlow is indeed the one-eyed king here. We found that running with large SparseTensors, CPU training jobs is actually faster than on GPU nodes. An individual job is faster on GPU, but SparseMatMul just blows up GPU memory use to the point that only one train job fits in its memory. SparseMatMul is inefficient on CPU as well, but you can keep getting some decent speedup by cranking up the parallel trade jobs per node. I did have great success using Netflix Vectorflow. I roughly gained 2x performance for my use case. It does leave some other performance on the table, no vectorized minibatches etc. If you are training on huge sparse datasets with a shallow ffw network, Vectorflow is a good alternative.
8y ago