tra-analysis/data analysis/analysis/trueskill/factorgraph.py

200 lines
5.6 KiB
Python

# -*- coding: utf-8 -*-
"""
trueskill.factorgraph
~~~~~~~~~~~~~~~~~~~~~
This module contains nodes for the factor graph of TrueSkill algorithm.
:copyright: (c) 2012-2016 by Heungsub Lee.
:license: BSD, see LICENSE for more details.
"""
from __future__ import absolute_import
import math
from six.moves import zip
from .mathematics import Gaussian, inf
__all__ = ['Variable', 'PriorFactor', 'LikelihoodFactor', 'SumFactor',
'TruncateFactor']
class Node(object):
pass
class Variable(Node, Gaussian):
def __init__(self):
self.messages = {}
super(Variable, self).__init__()
def set(self, val):
delta = self.delta(val)
self.pi, self.tau = val.pi, val.tau
return delta
def delta(self, other):
pi_delta = abs(self.pi - other.pi)
if pi_delta == inf:
return 0.
return max(abs(self.tau - other.tau), math.sqrt(pi_delta))
def update_message(self, factor, pi=0, tau=0, message=None):
message = message or Gaussian(pi=pi, tau=tau)
old_message, self[factor] = self[factor], message
return self.set(self / old_message * message)
def update_value(self, factor, pi=0, tau=0, value=None):
value = value or Gaussian(pi=pi, tau=tau)
old_message = self[factor]
self[factor] = value * old_message / self
return self.set(value)
def __getitem__(self, factor):
return self.messages[factor]
def __setitem__(self, factor, message):
self.messages[factor] = message
def __repr__(self):
args = (type(self).__name__, super(Variable, self).__repr__(),
len(self.messages), '' if len(self.messages) == 1 else 's')
return '<%s %s with %d connection%s>' % args
class Factor(Node):
def __init__(self, variables):
self.vars = variables
for var in variables:
var[self] = Gaussian()
def down(self):
return 0
def up(self):
return 0
@property
def var(self):
assert len(self.vars) == 1
return self.vars[0]
def __repr__(self):
args = (type(self).__name__, len(self.vars),
'' if len(self.vars) == 1 else 's')
return '<%s with %d connection%s>' % args
class PriorFactor(Factor):
def __init__(self, var, val, dynamic=0):
super(PriorFactor, self).__init__([var])
self.val = val
self.dynamic = dynamic
def down(self):
sigma = math.sqrt(self.val.sigma ** 2 + self.dynamic ** 2)
value = Gaussian(self.val.mu, sigma)
return self.var.update_value(self, value=value)
class LikelihoodFactor(Factor):
def __init__(self, mean_var, value_var, variance):
super(LikelihoodFactor, self).__init__([mean_var, value_var])
self.mean = mean_var
self.value = value_var
self.variance = variance
def calc_a(self, var):
return 1. / (1. + self.variance * var.pi)
def down(self):
# update value.
msg = self.mean / self.mean[self]
a = self.calc_a(msg)
return self.value.update_message(self, a * msg.pi, a * msg.tau)
def up(self):
# update mean.
msg = self.value / self.value[self]
a = self.calc_a(msg)
return self.mean.update_message(self, a * msg.pi, a * msg.tau)
class SumFactor(Factor):
def __init__(self, sum_var, term_vars, coeffs):
super(SumFactor, self).__init__([sum_var] + term_vars)
self.sum = sum_var
self.terms = term_vars
self.coeffs = coeffs
def down(self):
vals = self.terms
msgs = [var[self] for var in vals]
return self.update(self.sum, vals, msgs, self.coeffs)
def up(self, index=0):
coeff = self.coeffs[index]
coeffs = []
for x, c in enumerate(self.coeffs):
try:
if x == index:
coeffs.append(1. / coeff)
else:
coeffs.append(-c / coeff)
except ZeroDivisionError:
coeffs.append(0.)
vals = self.terms[:]
vals[index] = self.sum
msgs = [var[self] for var in vals]
return self.update(self.terms[index], vals, msgs, coeffs)
def update(self, var, vals, msgs, coeffs):
pi_inv = 0
mu = 0
for val, msg, coeff in zip(vals, msgs, coeffs):
div = val / msg
mu += coeff * div.mu
if pi_inv == inf:
continue
try:
# numpy.float64 handles floating-point error by different way.
# For example, it can just warn RuntimeWarning on n/0 problem
# instead of throwing ZeroDivisionError. So div.pi, the
# denominator has to be a built-in float.
pi_inv += coeff ** 2 / float(div.pi)
except ZeroDivisionError:
pi_inv = inf
pi = 1. / pi_inv
tau = pi * mu
return var.update_message(self, pi, tau)
class TruncateFactor(Factor):
def __init__(self, var, v_func, w_func, draw_margin):
super(TruncateFactor, self).__init__([var])
self.v_func = v_func
self.w_func = w_func
self.draw_margin = draw_margin
def up(self):
val = self.var
msg = self.var[self]
div = val / msg
sqrt_pi = math.sqrt(div.pi)
args = (div.tau / sqrt_pi, self.draw_margin * sqrt_pi)
v = self.v_func(*args)
w = self.w_func(*args)
denom = (1. - w)
pi, tau = div.pi / denom, (div.tau + sqrt_pi * v) / denom
return val.update_value(self, pi, tau)