GmGM 0.0.8

An implementation of the Gaussian multi-Graphical Model

GmGM-python

A python package for the GmGM algorithm. Read the pre-print here.

This is a very early version so the API is subject to change.

Installation

We recommend installing this package in a conda environment, by first running:

conda create -n {YOUR ENVIRONMENT NAME} "python>=3.9"
conda activate {YOUR ENVIROMENT NAME}

Afterwards you can install it via pip.

# Pip
python -m pip install GmGM

Conda install coming soon.

About

This package learns a graphical representation of every "axis" of your data. For example, if you had a paired scRNA+scATAC multi-omics dataset, then your axes would be "genes" (columns of scRNA matrix), "axes" (columns of scATAC matrix), and "cells" (rows of both matrices).

This package works on any dataset that can be expressed as multiple tensors of arbitrary length (so multi-omics, videos, etc...). The only restriction is that no tensor can have the same axis twice (no "genes x genes" matrix); the same axis can appear multiple times, as long as it only appears once per matrix.

Usage

The first step is to express your dataset as a Dataset object. Suppose you had a cells x genes scRNA matrix and cells x peaks scATAC matrix, then you could create a Dataset object like:

from GmGM.dataset import Dataset
dataset: Dataset = Dataset(
    dataset={
        "scRNA": scRNA,
        "scATAC": scATAC
    },
    structure={
        "scRNA": ("cell", "gene"),
        "scATAC": ("cell", "peak")
    }
)

The basic form of the algorithm is as follows:

1. Create gram matrices (either by centering and grammifying or using the nonparanormal skeptic)
2. Analytically calculate_eigenvectors
3. Iteratively calculate_eigenvalues
4. Recompose your precision matrices, and threshold them to be sparse (can be done in one go as recompose_sparse_precisions to prevent unnecessary memory use

from GmGM.core.preprocessing import center, grammify
from GmGM.core.core import calculate_eigenvectors, calculate_eigenvalues
from GmGM.core.presparse_methods import recompose_sparse_precisions

center(dataset)
grammify(dataset)
calculate_eigenvectors(dataset, seed=RANDOM_STATE)
calculate_eigenvalues(dataset)
recompose_sparse_precisions(
    dataset,
    to_keep=N_NEIGHBORS,
    threshold_method='rowwise-col-weighted',
    batch_size=1000
)

This has quadratic memory due to the computation of the Gram matrices. When you only have a single matrix as input, you can skip this step using direct_svd, leading to linear memory use by directly producing the right eigenvectors from the raw data!

from GmGM.dataset import Dataset
from GmGM.core.preprocessing import center
from GmGM.core.core import direct_svd, calculate_eigenvalues
from GmGM.core.presparse_methods import recompose_sparse_precisions

center(dataset)
direct_svd(dataset, k=N_COMPONENTS, seed=RANDOM_STATE)
calculate_eigenvalues(dataset)
recompose_sparse_precisions(
    dataset,
    to_keep=N_NEIGHBORS,
    threshold_method='rowwise-col-weighted',
    batch_size=1000
)

All these functions are updating dataset in-place; the computed precision matrices are available through the precision_matrices attribute of dataset. This is a dictionary which you index by axis name, i.e. dataset.precision_matrices['cell'].

Roadmap

• Add direct support for AnnData and MuData objects (so that converson to Dataset is not needed)
• Stabilize API
• Add comprehensive docs
• Have generate_data directly generate Dataset objects
• Add conda distribution
• Add example notebook