def _do_tests(self, dec_reg, hit_reg, iter): active_features = np.where(dec_reg >= 0)[0] hits = hit_reg[active_features] # get uncorrected p values based on hit_reg to_accept_ps = sp.stats.binom.sf(hits - 1, iter, .5).flatten() to_reject_ps = sp.stats.binom.cdf(hits, iter, .5).flatten() # two step multicor process # first we correct for testing several features in each round using FDR to_accept = multicor(to_accept_ps, alpha=self.multi_alpha, method='fdr_bh')[0] to_reject = multicor(to_reject_ps, alpha=self.multi_alpha, method='fdr_bh')[0] # second we correct for testing the same feature over and over again # using bonferroni to_accept2 = to_accept_ps <= self.multi_alpha / float(iter) to_reject2 = to_reject_ps <= self.multi_alpha / float(iter) # combine the two multi corrections, and get indexes to_accept = to_accept * to_accept2 to_reject = to_reject * to_reject2 # find features which are 0 and have been rejected or accepted to_accept = np.where((dec_reg[active_features] == 0) * to_accept)[0] to_reject = np.where((dec_reg[active_features] == 0) * to_reject)[0] # updating dec_reg dec_reg[active_features[to_accept]] = 1 dec_reg[active_features[to_reject]] = -1 return dec_reg
def _do_tests(self, dec_reg, hit_reg, iter):
active_features = np.where(dec_reg >= 0)[0]
hits = hit_reg[active_features]
# get uncorrected p values based on hit_reg
to_accept_ps = sp.stats.binom.sf(hits - 1, iter, .5).flatten()
to_reject_ps = sp.stats.binom.cdf(hits, iter, .5).flatten()
# two step multicor process
# first we correct for testing several features in each round using FDR
to_accept = multicor(to_accept_ps,
alpha=self.multi_alpha,
method='fdr_bh')[0]
to_reject = multicor(to_reject_ps,
alpha=self.multi_alpha,
method='fdr_bh')[0]
# second we correct for testing the same feature over and over again
# using bonferroni
to_accept2 = to_accept_ps <= self.multi_alpha / float(iter)
to_reject2 = to_reject_ps <= self.multi_alpha / float(iter)
# combine the two multi corrections, and get indexes
to_accept = to_accept * to_accept2
to_reject = to_reject * to_reject2
# find features which are 0 and have been rejected or accepted
to_accept = np.where((dec_reg[active_features] == 0) * to_accept)[0]
to_reject = np.where((dec_reg[active_features] == 0) * to_reject)[0]
# updating dec_reg
dec_reg[active_features[to_accept]] = 1
dec_reg[active_features[to_reject]] = -1
return dec_reg
def _do_tests(self, dec_reg, hit_reg, iter):
# get uncorrected p values based on hit_reg
to_accept_ps = sp.stats.binom.sf(hit_reg - 1, iter, 0.5).flatten()
to_reject_ps = sp.stats.binom.cdf(hit_reg, iter, 0.5).flatten()
# correct p values for multiple testing
to_accept = np.where(multicor(to_accept_ps, alpha=self.multi_alpha, method=self.multi_corr_method)[0])[0]
to_reject = np.where(multicor(to_reject_ps, alpha=self.multi_alpha, method=self.multi_corr_method)[0])[0]
# finding those to_accept and to_reject that are 0, and setting them
dec_reg[to_accept[np.where(dec_reg[to_accept] == 0)]] = 1
dec_reg[to_reject[np.where(dec_reg[to_reject] == 0)]] = -1
return dec_reg
def _do_tests(self, dec_reg, hit_reg, iter):
# get uncorrected p values based on hit_reg
to_accept_ps = sp.stats.binom.sf(hit_reg - 1, iter, .5).flatten()
to_reject_ps = sp.stats.binom.cdf(hit_reg, iter, .5).flatten()
# correct p values for multiple testing
to_accept = np.where(multicor(to_accept_ps, alpha=self.multi_alpha,
method=self.multi_corr_method)[0])[0]
to_reject = np.where(multicor(to_reject_ps, alpha=self.multi_alpha,
method=self.multi_corr_method)[0])[0]
# finding those to_accept and to_reject that are 0, and setting them
dec_reg[to_accept[np.where(dec_reg[to_accept] == 0)]] = 1
dec_reg[to_reject[np.where(dec_reg[to_reject] == 0)]] = -1
return dec_reg
def check_pvals(p_vals, params):
"""
Corrects for multiple testing using the user specified method and alpha
value. Returns a boolean mask that can be used to filter the resulting
heatmap.
"""
# basic params
n, p = p_vals.shape
mc_method = params['multi_corr_method']
mc_alpha = params['alpha_val']
# corr matrix is symmetric we only need to correct the lower half
ps_to_check = np.array(np.tril(np.ones((p, p)), k=-1), dtype=np.bool)
ps = multicor(p_vals[ps_to_check], method=mc_method, alpha=float(mc_alpha))
# make Boolean and corrected p-val matrices
p_mask = np.zeros((p, p), dtype=np.bool)
p_mask[ps_to_check] = ps[0]
p_mask = mirror_lower_triangle(p_mask)
p_vals = np.ones((p, p))
p_vals[ps_to_check] = ps[1]
p_vals = mirror_lower_triangle(p_vals)
return p_vals, p_mask
def gpd_spearman(rX, perm_num=10000, prec=None, mc_method='fdr_bh', mc_alpha=0.05):
"""
This is the main function of the module.
The correlation values are calculated in matrix form in parallel, and the
p-values are approximated using Monte Carlo sampling (1e4 by default),
followed by Generalized Paretho Distribution Approximation to make them
more precise.
Then the p values are corrected for multiple testing using the Benjamini
Hochberg FDR with .05 alpha (by default). For this, only the lower triangle
of the correlation matrix is used, to avoid including each value twice.
Parameters
----------
- rX : array of shape [n sample, p features]
Column ranked X matrix of observations and features. Used to calculate
Spearman correlations and their p-values.
- perm_num : int, default = 10000
Number of permutations to use to estimate each correlation's p-value.
- prec : array of shape [p features, p features], default = None
Estimated precision matrix by some Graph Lasso algorithm. If provided,
only those correlations will be considered whose precision is not 0.
- mc_method : string, default = 'fdr_bh'
Method for correction for multiple testing.
- mc_alpha : float, default = 0.05
Threshold for q-values after FDR correction.
Returns
-------
Tuple with three matrices:
- rs : array of shape [p features, p features]
Holds empirical Spearman correlation values.
- p_mask : array of shape [p features, p features]
Mask for those p-values which passed the FDR correction with alpha=0.05
- p_vals : array of shape [p features, p features]
FDR corrected p-values
"""
n, p = rX.shape
# little trick to avoid having many ifs everywhere in code
prec_mask = np.ones((p, p), dtype=np.bool)
if prec is not None:
prec_mask = prec != 0
# calculate empirical Spearman from data
rs = np.corrcoef(rX, rowvar=0)
# get permuted Spearman values, in parallel
r_perms = np.array(Parallel(n_jobs=-1,backend='threading')
(delayed(perm_r)(rX, i) for i in xrange(perm_num)))
# GPD APPROXIMATION OF P-VALUES IN PARALLEL
pGPDs = np.ones((p,p))
# we should only each value once, i.e. the cells below the diagonal
lower_tri_ind = np.tril_indices(p, k=-1)
lower_tri_mask = np.array(np.tril(np.ones((p, p)), k=-1), dtype=np.bool)
pGPDs[lower_tri_ind] = np.array(Parallel(n_jobs=-1,backend='threading')(delayed(perm_gpd)
(prec_mask[lower_tri_ind[0][i], lower_tri_ind[1][i]],
rs[lower_tri_ind[0][i], lower_tri_ind[1][i]],
r_perms[:, lower_tri_ind[0][i], lower_tri_ind[1][i]])
for i in xrange(lower_tri_ind[0].shape[0])))
# correction for multiple testing, make sure that we only include each
# p-value once not twice (symmetric rs), by combining two numpy mask arrays:
# - the lower triangular rs matrix
# - prec_mask, i.e. p-vals whose precision is not 0
ps_to_check = lower_tri_mask * prec_mask
p_vals = np.ones((p, p))
if float(mc_alpha) < 1:
p_mask = np.zeros((p, p), dtype=np.bool)
ps = multicor(pGPDs[ps_to_check], method=mc_method, alpha=float(mc_alpha))
p_mask[ps_to_check] = ps[0]
p_vals[ps_to_check] = ps[1]
else:
# user doesn't want correction for multiple testing
p_mask = np.ones((p, p), dtype=np.bool)
p_vals = np.ones((p, p))
p_vals[ps_to_check] = pGPDs[ps_to_check]
p_mask = mirror_lower_triangle(p_mask)
p_vals = mirror_lower_triangle(p_vals)
return rs, p_vals, p_mask