Probability Learner

This notebook uses a pure Python implementation of a simplified version of the model described in this paper.



In [1]:

    
from __future__ import division
import numpy as np
from scipy import stats
import matplotlib as mpl
import matplotlib.pyplot as plt
import seaborn as sns



In [2]:

    
import optlearner

Initialize the learner



In [3]:

    
learner = optlearner.ProbabilityLearner()



In [4]:

    
p_grid = learner.p_grid
I_grid = learner.I_grid

Show the Bayes net



In [5]:

    
with mpl.rc_context({"font.size": 16}):
    learner.show_model();

Basic timing data



In [6]:

    
%timeit optlearner.ProbabilityLearner()









    



1 loops, best of 3: 27.2 s per loop



In [7]:

    
%timeit learner.fit([0])









    



1000 loops, best of 3: 2.42 ms per loop

Transition matrices



In [8]:

    
def plot_slices(grid, joint, cmap, step=2, var=""):
    pal = sns.blend_palette(sns.mpl_palette(cmap, 6), as_cmap=True)
    f, axes = plt.subplots(4, 4, figsize=(7, 7), sharex=True, sharey=True)
    xx, yy = np.meshgrid(grid, grid)
    for k, ax in zip(np.arange(learner._I_size) * step, axes.flat):
        ax.contour(xx, yy, joint[:, :, k], cmap=pal, vmin=joint.min(), vmax=joint.max())
    if var:
        for ax in axes[-1, :]:
            ax.set_xlabel(r"$%s_{i+1}$" % var, size=14)
        for ax in axes[:, 0]:
            ax.set_ylabel(r"$%s_{i}$" % var, size=14)
    plt.tight_layout()



In [9]:

    
plot_slices(learner.p_grid, learner._p_trans, "PuBuGn_d", var="p")

Example model fits



In [10]:

    
learner = optlearner.ProbabilityLearner()



In [11]:

    
static_p = np.ones(500) * .65
static_y = stats.binom.rvs(1, static_p)



In [12]:

    
learner.reset()
learner.fit(static_y)



In [13]:

    
learner.plot_history(ground_truth=static_p)



In [14]:

    
learner.plot_joint()

Nonstationary probabilities, static volatility



In [15]:

    
moving_p = np.repeat([.75, .25, .75, .25, .75, .25], 100)
moving_y= stats.binom.rvs(1, moving_p)



In [16]:

    
learner.reset()
learner.fit(moving_y)



In [17]:

    
learner.plot_history(ground_truth=moving_p)



In [18]:

    
learner.plot_joint()

Nonstationary probabilities and volatility



In [19]:

    
metavol_p = np.repeat([.75, .75, .75, .25, .75, .25], 100)
metavol_y= stats.binom.rvs(1, metavol_p)



In [20]:

    
learner.reset()
learner.fit(metavol_y)



In [21]:

    
learner.plot_history(ground_truth=metavol_p)



In [22]:

    
learner.plot_joint()

Sinusoidal probabilities



In [23]:

    
x = np.linspace(0, 60, 600)
sin_p = (np.sin(x / 3) + 1.5) / 3
sin_y = stats.binom.rvs(1, sin_p)



In [24]:

    
learner.reset()
learner.fit(sin_y)



In [25]:

    
learner.plot_history(ground_truth=sin_p)



In [26]:

    
learner.plot_joint()