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"""
Method MLM.
Code to run the Multivariate Linear Model (MLM) method.
"""
import numpy as np
import pandas as pd
from scipy.sparse import csr_matrix
from pre import extract, match, rename_net, get_net_mat, filt_min_n, return_data
from scipy import stats
from tqdm.auto import tqdm
import numba as nb
@nb.njit(nb.f4[:, :](nb.f4[:, :], nb.f4[:, :], nb.f4[:, :], nb.i8), parallel=True, cache=True)
def fit_mlm(X, y, inv, df):
X = np.ascontiguousarray(X)
n_samples = y.shape[1]
n_fsets = X.shape[1]
coef, sse, _, _ = np.linalg.lstsq(X, y)
if len(sse) == 0:
raise ValueError("""Couldn\'t fit a multivariate linear model. This can happen because there are more sources
(covariates) than unique targets (samples), or because the network\'s matrix rank is smaller than the number of
sources.""")
sse = sse / df
se = np.zeros((n_samples, n_fsets), dtype=nb.f4)
for i in nb.prange(n_samples):
se[i] = np.sqrt(np.diag(sse[i] * inv))
t = coef.T/se
return t.astype(nb.f4)
def mlm(mat, net, batch_size=10000, verbose=False):
# Get dims
n_samples = mat.shape[0]
n_features, n_fsets = net.shape
# Add intercept to network
net = np.column_stack((np.ones((n_features, ), dtype=np.float32), net))
# Compute inv and df for lm
inv = np.linalg.inv(np.dot(net.T, net))
df = n_features - n_fsets - 1
if isinstance(mat, csr_matrix):
# Init empty acts
n_batches = int(np.ceil(n_samples / batch_size))
es = np.zeros((n_samples, n_fsets), dtype=np.float32)
for i in tqdm(range(n_batches), disable=not verbose):
# Subset batch
srt, end = i * batch_size, i * batch_size + batch_size
y = mat[srt:end].toarray().T
# Compute MLM for batch
es[srt:end] = fit_mlm(net, y, inv, df)[:, 1:]
else:
# Compute MLM for all
es = fit_mlm(net, mat.T, inv, df)[:, 1:]
# Get p-values
pvals = 2 * (1 - stats.t.cdf(np.abs(es), df))
return es, pvals
def run_mlm(mat, net, source='source', target='target', weight='weight', batch_size=10000,
min_n=5, verbose=False, use_raw=True):
"""
Multivariate Linear Model (MLM).
MLM fits a multivariate linear model for each sample, where the observed molecular readouts in `mat` are the response
variable and the regulator weights in `net` are the covariates. Target features with no associated weight are set to
zero. The obtained t-values from the fitted model are the activities (`mlm_estimate`) of the regulators in `net`.
Parameters
----------
mat : list, DataFrame or AnnData
List of [features, matrix], dataframe (samples x features) or an AnnData instance.
net : DataFrame
Network in long format.
source : str
Column name in net with source nodes.
target : str
Column name in net with target nodes.
weight : str
Column name in net with weights.
batch_size : int
Size of the samples to use for each batch. Increasing this will consume more memmory but it will run faster.
min_n : int
Minimum of targets per source. If less, sources are removed.
verbose : bool
Whether to show progress.
use_raw : bool
Use raw attribute of mat if present.
Returns
-------
estimate : DataFrame
MLM scores. Stored in `.obsm['mlm_estimate']` if `mat` is AnnData.
pvals : DataFrame
Obtained p-values. Stored in `.obsm['mlm_pvals']` if `mat` is AnnData.
"""
# Extract sparse matrix and array of genes
m, r, c = extract(mat, use_raw=use_raw, verbose=verbose)
# Transform net
net = rename_net(net, source=source, target=target, weight=weight)
net = filt_min_n(c, net, min_n=min_n)
sources, targets, net = get_net_mat(net)
# Match arrays
net = match(c, targets, net)
if verbose:
print('Running mlm on mat with {0} samples and {1} targets for {2} sources.'.format(m.shape[0], len(c), net.shape[1]))
# Run MLM
estimate, pvals = mlm(m, net, batch_size=batch_size, verbose=verbose)
# Transform to df
estimate = pd.DataFrame(estimate, index=r, columns=sources)
estimate.name = 'mlm_estimate'
pvals = pd.DataFrame(pvals, index=r, columns=sources)
pvals.name = 'mlm_pvals'
return return_data(mat=mat, results=(estimate, pvals))
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