Package: lsmmdma
Large-Scale MMD-MAInstallation|Command line instructions|Examples|Input|Output|Citation|ContactThe objective ofMMD-MAis to
match points coming from two different spaces in a lower dimensional space. To
this end, two sets of points are projected, from two different spaces endowed
with a positive definite kernel, to a shared Euclidean space of lower dimensionlow_dim. The mappings from high to low dimensional space are
obtained using functions belonging to the respective RKHS. To obtain the
mappings, we minimise aloss functionthat is composed of three terms:an MMD term between the low dimensional representations of the two views,
which encourages them to have the same distribution. The RBF kernel is used
to compute MMD.two non-collapsing penalty terms (corresponding to thepen_dualorpen_primalfunctions), one for each view. These terms ensure that
the low dimensional representations are mutually orthogonal, preventing
collapsing.two distortion penalties (corresponding to thedis_dualordis_primalfunctions), one for each view. These terms encourage the
low dimensional representation to obtain the same pairwise structure as
the original views.MMD-MA can be formulated using either the primal (when we use the linear
kernel in the input spaces) or the dual problem. Each has
advantages or disadvantages depending on the input data. For each view,
when the number of featurespis larger than the number of samplesnp >> n, then the dual formulation is beneficial in terms
of runtime and memory, while ifn >> p, the primal
formulation is favorable.Additionally, in order to scale the computation of MMD to a large number of
samples, we propose either to use theKeOpslibrary which
lets you compute large kernel operations on GPUs without memory overflow.InstallationTo install the latest release of lsmmdma, use the following command:$pipinstalllsmmdmaTo install thedevelopmentversion, use the following command instead:$pipinstallgit+https://github.com/google-research/large-scale-mmdmaAlternatively, it can be installed from sources with the following command:$pythonsetup.pyinstallIn Google Colab, use the following command:$!pipinstalllsmmdmaThe KeOps library might require to be installed separately in advance, according
to the giveninstructions. Typically, in Google Colab one would run this command before installinglsmmmdma:$!pipinstallpykeopsCommand line instructionsThe algorithm can be run with a command line using:python3-mlsmmmda.main[flags]A set of flags is available to determine the IO, the model, the hyperparameters
and the seed.Input/OutputIt is possible to give as input either a path and filenames pointing to the
user input or to choose to generate data with thedata_pipeline.generate_datafunction. In the
case one wants to generate simulation data, the input flags are:--data: str, it can be either 'branch', 'triangle' or '' (default). The
simulated data is described in the pydoc ofdata_pipeline.generate_data. ''
means that simulated data is not used.--n: int (default 300), number of samples for both views.--p: int (default 1000), number of features for both views.For data given by the user, the input flags are:--input_dir: str (default None), input directory.--input_fv: str (default None), filename of the array (n1 x p1 or n1 x n1)
that serves as first set of points.--input_sv: str (default None), filename of the array (n2 x p2 or n2 x n2)
that serves as second set of points.--rd_vec: str (default None), filename of the vector that contains the indices
of the samples from the first view that match (ground truth) the samples from
the second view. This is only used at evaluation time. If--rd_vecis not
used, we assume that the samples of both views follow the same ordering.--labels_fv: str (default None), filename of the vector that contains the
labels of the samples from the first view. Must match the order of the samples
ininput_fv.--labels_sv: str (default None), filename of the vector that contains the
labels of the samples from the second view, following the same ordering.In both cases, two other flags are also available:--kernel: bool (default False), whether the input data given by the user is
a kernel (n x n instead of n x p). This parameter can only be set to True when--mis 'dual'.--output_dir: str (default None), output directory.ModelThe flags allow you to choose between four algorithms, using either
the 'primal' or 'dual' formulation, and using KeOps or not.--m: str, either 'primal' or 'dual' (default).--keops: integer, either 1 (use keops), 0 (not not use keops) or -1 (automatic, uses keops
from 4000 samples onwards) (default).--use_unbiased_mmd: bool (default True), determines whether or not to use
the unbiased version of MMD (seeGretton et al. 2012Lemma 6).SeedsThe seed for the training phase, and for generating the data when--datais not '', is fixed with the flag--seed(int, default value is 0).
If one wishes to use multipe starts when training (X seeds and selection
of the best one based on the value of the loss), it is possible to also define
the number of seeds to try with:--ns(int, default value is 1).Model hyperparametersSeveral hyperparameters ought to be fixed in advance:--d: int (default 5), dimension of the latent space.--init: str (default 'uniform,0.,0.1'), initialisation for the learned
parameters. It can be sampled from a 'uniform', 'normal', 'xavier_uniform' or
'xavier_normal' distributions. The parameters of the initialisation functions
are passed to the same flag separated by a coma. Seeinitializers.pyandtrain.py.--l1: float (default 1e-4), hyperparameter in front of both penalty terms. Note that
the penalty terms are automatically scaled by 1/sqrt(p).--l2: float (default 1e-4), hyperparameter in front of both distortion terms. Note that
the distortion terms are automatically scaled by 1/(n*sqrt(p)).--lr: float (default 1e-5), learning rate.--s: float (default 1.0), scale parameter of the RBF kernel in MMD.Training and evaluationSeveral flags structure the training loop:--e: int (default 5001), number of epochs for the training process.--ne: int (default 100), regular interval at which the evaluation (call tometrics.Evaluation)
is done, every 'ne' epochs. 0 means that the results are never evaluated.--nr: int (default 100), regular interval at which the components
of the loss are recorded, every 'ne' epochs. 0 means that they are never
recorded. The loss is recorded every epoch nonetheless.--pca: int (default 100), regular interval at which PCA is performed on the
embeddings, every 'pca' epochs. 0 means that PCA is not used on the output.--short_eval: bool (default True), whether or not to compute all the metrics
(False) or only a set of them (True) (seemetrics.py).--nn: int (default 5), number of neighbours taken into account in
the computation of the Label Transfer Accuracy metrics.Stopping criterionTwo flags enable to control thestopping criterion:--ws: int (default 0), window size on which the loss is averaged for the stopping criterion. If set to 0, the algorithm stops at the last epoch without loss-based stopping criterion.--threshold: float (default 1e-3), threshold for the stopping criterion.TimingTiming the method is possible when the flag--timeis set to True
(default False).ExamplesWe show now a few examples of usage of the command line to run the algorithm. We
also introduce two notebooks that display the usage of the algorithm and its
runtime.To run the algorithm on simulated data fromdata_pipeline.py,
a minimal set of commands is:python3-mlsmmdma.main--output_diroutdir\--databranch--n300--p400\--e1001--d5--keopsFalse--mdualTo run the algorithm on simulated data fromdata_pipeline.py, one can
also choose when to record the intermediate results, to set the hyperparameters
and to allow for 5 multiple starts:python3-mlsmmdma.main--output_diroutdir\--databranch--n300--p400\--seed4--ns5\--keopsFalse--mdual\--e1001--nr100--ne100--pca100\--d5--lr1e-5--l11e-4--l21e-4--s1.0--init'uniform,0,0.1'To run the algorithm on user input data, in the form n_sample x p_feature.--datashould be '' (default) and--kernelshould be False (default). The
argument--keopscan be True or False,--mcan be 'dual' or 'primal'.python3-mlsmmdma.main--input_dirdatadir--output_diroutdir\--input_fvmy_data_1--input_svmy_data_2--kernelFalse\--seed4--ns5\--keopsTrue--mdual\--e1001--nr100--ne100--pca100\--d5--lr1e-5--l11e-4--l21e-4--s1.0--init'uniform,0,0.1'To run the algorithm on user kernel data, in the form n_sample x n_sample.--datashould be '' (default) and--kernelshould be True. The
argument--keopscan be True or False,--mcan only be 'dual'.python3-mlsmmdma.main--input_dirdatadir--output_diroutdir\--input_fvmy_data_1--input_svmy_data_2--kernelTrue\--seed4--ns5\--keopsTrue--mdual\--e1001--nr100--ne100--pca100\--d5--lr1e-5--l11e-4--l21e-4--s1.0--init'uniform,0,0.1'Atutorialand abenchmarknotebooks are also available inexamples/.InputIn case the user is providing the input data, supported formats are AnnData
objects (.h5ad), numpy arrays (.npy), tab-separated arrays (.tsv),
coma-separated arrays (.csv) and white-space separated arrays.OutputWhen one usesmain.py,
several files are saved in the output directoryFLAGS.output_dir:[key:val].tsv: results of the model at the last epoch.[key:val]_tracking.json: loss and its components during training,
evaluation metrics during training, seed, number of epochs.[key:val]_model.json: model and optimiser state dictionaries,
loss, number of epochs, seed.[key:val]_pca_X.npy: 2D representation obtained with PCA on the
embeddings during training (for the first and second views).[key:val]_embeddings_X.npy: embeddings during training (for the first and
second views).generated_data_X: first view, second view andrd_vecgenerated bydata_pipeline.generate_data.[key:val]represents a list of key:value as determined by the flags and
written inmain.py.CitationIf you have found our work useful, please consider citing us:@article{meng2022lsmmd,
  title={LSMMD-MA: Scaling multimodal data integration for single-cell genomics data analysis},
  author={Meng-Papaxanthos, Laetitia and Zhang, Ran and Li, Gang and Cuturi, Marco and Noble, William Stafford and Vert, Jean-Philippe},
  journal={bioRxiv},
  year={2022},
  publisher={Cold Spring Harbor Laboratory}
}ContactIn case you have questions, reach out tolpapaxanthos@google.com.DisclaimerThis is not an officially supported Google product.