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# Copyright 2008 by Norbert Dojer. All rights reserved.
# Adapted by Bartek Wilczynski.
# This code is part of the Biopython distribution and governed by its
# license. Please see the LICENSE file that should have been included
# as part of this package.
"""Approximate calculation of appropriate thresholds for motif finding
"""
import math, random
class ScoreDistribution(object):
""" Class representing approximate score distribution for a given motif.
Utilizes a dynamic programming approch to calculate the distribution of
scores with a predefined precision. Provides a number of methods for calculating
thresholds for motif occurences.
"""
def __init__(self,motif,precision=10**3):
self.min_score=min(0.0, motif.min_score())
self.interval=max(0.0, motif.max_score())-self.min_score
self.n_points=precision*motif.length
self.step=self.interval/(self.n_points-1)
self.mo_density=[0.0]*self.n_points
self.mo_density[-self._index_diff(self.min_score)]=1.0
self.bg_density=[0.0]*self.n_points
self.bg_density[-self._index_diff(self.min_score)]=1.0
self.ic=motif.ic()
for lo, mo in zip(motif.log_odds(), motif.pwm()):
self.modify(lo, mo, motif.background)
def _index_diff(self,x,y=0.0):
return int((x-y+0.5*self.step)//self.step)
def _add(self, i, j):
return max(0, min(self.n_points-1, i+j))
def modify(self, scores, mo_probs, bg_probs):
mo_new=[0.0]*self.n_points
bg_new=[0.0]*self.n_points
for k, v in scores.items():
d=self._index_diff(v)
for i in range(self.n_points):
mo_new[self._add(i, d)]+=self.mo_density[i]*mo_probs[k]
bg_new[self._add(i, d)]+=self.bg_density[i]*bg_probs[k]
self.mo_density=mo_new
self.bg_density=bg_new
def threshold_fpr(self, fpr):
"""
Approximate the log-odds threshold which makes the type I error (false positive rate).
"""
i=self.n_points
prob=0.0
while prob<fpr:
i-=1
prob+=self.bg_density[i]
return self.min_score+i*self.step
def threshold_fnr(self, fnr):
"""
Approximate the log-odds threshold which makes the type II error (false negative rate).
"""
i=-1
prob=0.0
while prob<fnr:
i+=1
prob+=self.mo_density[i]
return self.min_score+i*self.step
def threshold_balanced(self,rate_proportion=1.0,return_rate=False):
"""
Approximate the log-odds threshold which makes FNR equal to FPR times rate_proportion
"""
i=self.n_points
fpr=0.0
fnr=1.0
while fpr*rate_proportion<fnr:
i-=1
fpr+=self.bg_density[i]
fnr-=self.mo_density[i]
if return_rate:
return self.min_score+i*self.step, fpr
else:
return self.min_score+i*self.step
def threshold_patser(self):
"""Threshold selection mimicking the behaviour of patser (Hertz, Stormo 1999) software.
It selects such a threshold that the log(fpr)=-ic(M)
note: the actual patser software uses natural logarithms instead of log_2, so the numbers
are not directly comparable.
"""
return self.threshold_fpr(fpr=2**-self.ic)
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