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bayes_ic.py
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bayes_ic.py
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import numpy as np
import pandas as pd
import pymc3 as pm
from pymc3.distributions.timeseries import *
from theano.tensor import repeat
class BayesIC(object):
def __init__(self, signal, target):
for i in (signal, target):
if not isinstance(i, pd.DataFrame):
raise TypeError('signal and target must be pandas dataframes')
cols = sorted(set(signal.columns) & set(target.columns))
self.signal = signal[cols]
self.target = target[cols]
def get_stats(self, samples):
s = pd.Series(np.sort(samples))
med = s.median()
avg = s.mean()
prob_sub_zero = s.map(lambda x: 1 if x < 0 else 0).sum() / (s.shape[0] * 1.)
return {'median': med,
'mean': avg,
'prob_sub_zero': prob_sub_zero,
'std': s.std()}
def plot_trace(self, trace):
pm.traceplot(trace)
def fit_all(self, samples=500):
betas = []
for i in self.target.columns:
print
print i
ind = sorted(set(self.signal[i].dropna().index.values) & set(self.target[i].dropna().index.values))
stats, trace = self._fit_single_period_model(self.signal[i].ix[ind], self.target[i].ix[ind], samples)
stats['Id'] = i
betas.append(stats)
self.betas = pd.DataFrame(betas)
def mod_signal(self):
try:
self.betas
except:
raise Exception('must run `fit all` before `mod_signal`')
return self.signal * self.betas.set_index('Id')['prob_sub_zero']
def _fit_single_period_model(self, signal, target, samples):
with pm.Model() as model:
# define priors
alpha = pm.Normal('alpha', mu=0, sd=20)
beta = pm.Normal('beta', mu=0, sd=20)
sigma = pm.Uniform('sigma', lower=0, upper=20)
# define linear regression
y_est = alpha + beta * signal.values
# define likelihood
likelihood = pm.Normal('y', mu=y_est, sd=sigma, observed=target.values)
# inference
start = pm.find_MAP() # Find starting value by optimization
step = pm.NUTS(state=start) # Instantiate MCMC sampling algorithm
trace = pm.sample(samples, step, progressbar=True)
print trace.beta.shape
return self.get_stats(trace.beta), trace
def _fit_time_series_model(self, signal, target, samples):
model_randomwalk = pm.Model()
with model_randomwalk:
sigma_alpha = pm.Exponential('sigma_alpha', 1. / .02, testval=.1)
sigma_beta = pm.Exponential('sigma_beta', 1. / .02, testval=.1)
alpha = GaussianRandomWalk('alpha', sigma_alpha ** -2, shape=len(tar))
beta = GaussianRandomWalk('beta', sigma_beta ** -2, shape=len(tar))
# Define regression
regression = alpha + beta * rev.values
# Assume prices are Normally distributed, the mean comes from the regression.
sd = pm.Uniform('sd', 0, 20)
likelihood = pm.Normal('y',
mu=regression,
sd=sd,
observed=tar.values)
# First optimize random walk
start = pm.find_MAP(vars=[alpha, beta], fmin=optimize.fmin_l_bfgs_b)
step = pm.NUTS(scaling=start)
trace = pm.sample(10, step, start)
# Sample
start2 = trace.point(-1)
step = pm.NUTS(scaling=start2)
trace_rw = pm.sample(samples, step, start=start)