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sampling.py
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sampling.py
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# -*- coding: utf-8 -*-
"""
Created on Wed Jan 25 15:48:39 2017
@author: rober
"""
from IPython.display import display
from sympy.interactive import printing
import sympy as sm
from sympy import oo
import numpy as nm
import BayesianUtils as bay
PROB_DOMAIN = sm.Interval(0, 1)
def max_univariate_value(expr, symbol, domain=sm.S.Reals):
printing.init_printing(use_latex='png')
diff = sm.diff(expr, symbol).simplify()
if not symbol in diff.free_symbols: #for constant exprs
return sm.Interval(0,0);
solution = sm.solveset(sm.Eq(diff, 0), symbol, domain).intersection(domain)
display(solution)
#new_solutions = []
#for new_sol in solution:
# for old_sol in solutions:
# in_sol = sm.solveset(sm.Eq(symbol, new_sol), symbol, domain)
# new_solutions.append(in_sol.intersection(old_sol))
#solutions = new_solutions
maximum = sm.imageset(symbol, expr, solution).sup
result = sm.solveset(sm.Eq(expr, maximum), symbol, domain)
return result
def burn_and_thin_markov(markov, val=0, burn=1, thin=10, samples=1):
"""
Return samples samples gotten from the markov method given, after burning burn samples and thinning.
"""
val = thin_markov(markov, val, burn) #burn-in
samples = [val]
for i in range(0, samples - 1): #there's already one sample from after the burn-in
val = thin_markov(markov, val, thin)
samples.append(val)
return samples
def thin_markov(markov, val=None, iters=1): #returns the last value
for i in range(0, iters):
val = markov(val)
return val
def random_from_set(s): #make faster
inf = s.inf.evalf()
sup = s.sup.evalf()
val = rand_between(inf, sup)
while not val in s:
val = rand_between(inf, sup)
return val.evalf()
def rand_between(minimum, maximum):
return (maximum - minimum)*nm.random.rand() + minimum
def bound_slice_sample(symbol, distr, domain=sm.S.Reals):
return lambda x: slice_sample(symbol, distr, prev_x=x, domain=domain)
SLICE_X = sm.symbols('SLICE_X')
SLICE_Y = sm.symbols('SLICE_Y')
def slice_sample(symbol, distr, prev_x=None, domain=sm.S.Reals, __cache={}):
"""
Return a randomly chosen value of x in domain from distr.
"""
distr = distr.subs(symbol, SLICE_X)
sm.pretty_print(distr)
if prev_x == None:
prev_x = random_from_set(max_univariate_value(distr, SLICE_X, domain))
free_symbols = distr.free_symbols
if len(free_symbols) > 1:
others = []
others.extend(free_symbols)
others.remove(SLICE_X)
distr = bay.without(distr, others) #get marginal distribution
if not (distr, domain) in __cache:
__cache[distr, domain] = sm.solveset(distr >= SLICE_Y, SLICE_X, domain=domain)
at_least_set = __cache[distr, domain]
max_y = distr.subs(SLICE_X, prev_x).evalf()
y = nm.random.rand() * max_y
x_slice = at_least_set.subs(SLICE_Y, y).reduce().intersection(domain)
sm.pretty_print(x_slice)
#x_slice = sm.solveset(distr >= y, symbol, domain=domain).intersection(domain)
return random_from_set(x_slice)
def bound_gibbs_sample(distr, sample=bound_slice_sample):
"""
Return a partially bound gibbs sample function that only takes the values.
"""
return lambda v: gibbs_sample(v, distr, sample)
def gibbs_sample(values, distr, sample=bound_slice_sample, internal_sample_iters=5):
n_values = values.copy()
for symbol in values:
cond_distr = distr
for other in values:
if other != symbol:
cond_distr = cond_distr.subs(other, n_values[other])
n_values[symbol] = thin_markov(sample(symbol, distr), iters=internal_sample_iters)
return n_values