def run(n_times=5, n_grid=5, n=200, n_iter=200, vartype="continuous", ax=None):
rhos = [0.1, 0.25, 0.4, 0.5, 0.75, 0.9]
true_mis = np.zeros(len(rhos))
mis = np.zeros((n_times, len(rhos)))
for i, rho in enumerate(rhos):
print("Rho: %1.1f" % (rho,))
if vartype == "categorical":
p, true_mi = _gen_categorical_joint_dist(rho, n_grid)
metadata = {
"x_1": {"dtype": "categorical", "values": [i for i in range(n_grid)]},
"x_2": {"dtype": "categorical", "values": [i for i in range(n_grid)]},
}
elif vartype == "continuous":
true_mi = -0.5 * log(1.0 - rho ** 2.0)
metadata = {}
else:
raise ValueError("invalid vartype")
for t in range(n_times):
if vartype == "categorical":
x = _sample_from_bivariate_discrete(p, n)
elif vartype == "continuous":
sigma = np.array([[1, rho], [rho, 1]])
mu = np.zeros(2)
x = np.random.multivariate_normal(mu, sigma, size=n)
else:
raise ValueError("invalid vartype")
df = pd.DataFrame(x, columns=["x_1", "x_2"])
engine = Engine(df, n_models=1, metadata=metadata, use_mp=False)
engine.init_models()
engine.run(n_iter)
true_mis[i] = true_mi
mis[t, i] = engine.mutual_information("x_1", "x_2", n_samples=500, normed=False)
if ax is not None:
ax.errorbar(rhos, y=np.mean(mis, axis=0), yerr=np.std(mis, axis=0), label="BaxCat")
ax.plot(rhos, true_mis, label="True")
ax.set_xlabel("rho")
ax.set_ylabel("Mutual Information")
ax.set_title(vartype)
ax.legend(loc=0)
else:
return mis, true_mis
def run(n_times=5, n_grid=5, n=200, n_iter=200, vartype='continuous', ax=None):
rhos = [.1, .25, .4, .5, .75, .9]
true_mis = np.zeros(len(rhos))
mis = np.zeros((
n_times,
len(rhos),
))
for i, rho in enumerate(rhos):
print('Rho: %1.1f' % (rho, ))
if vartype == 'categorical':
p, true_mi = _gen_categorical_joint_dist(rho, n_grid)
metadata = {
'x_1': {
'dtype': 'categorical',
'values': [i for i in range(n_grid)]
},
'x_2': {
'dtype': 'categorical',
'values': [i for i in range(n_grid)]
}
}
elif vartype == 'continuous':
true_mi = -.5 * log(1. - rho**2.)
metadata = {}
else:
raise ValueError('invalid vartype')
for t in range(n_times):
if vartype == 'categorical':
x = _sample_from_bivariate_discrete(p, n)
elif vartype == 'continuous':
sigma = np.array([[1, rho], [rho, 1]])
mu = np.zeros(2)
x = np.random.multivariate_normal(mu, sigma, size=n)
else:
raise ValueError('invalid vartype')
df = pd.DataFrame(x, columns=['x_1', 'x_2'])
engine = Engine(df, n_models=1, metadata=metadata, use_mp=False)
engine.init_models()
engine.run(n_iter)
true_mis[i] = true_mi
mis[t, i] = engine.mutual_information('x_1',
'x_2',
n_samples=500,
normed=False)
if ax is not None:
ax.errorbar(rhos,
y=np.mean(mis, axis=0),
yerr=np.std(mis, axis=0),
label='BaxCat')
ax.plot(rhos, true_mis, label='True')
ax.set_xlabel('rho')
ax.set_ylabel('Mutual Information')
ax.set_title(vartype)
ax.legend(loc=0)
else:
return mis, true_mis
# We can view which columns are dependent on which other columns by plotting
# a n_cols by n_cols matrix where each cell is the dependence probability
# between two columns. Note that the dependence probability is simply the
# probability that a dependence exists, not the strength of the dependence.
engine.heatmap('dependence_probability', plot_kwargs={'figsize': (10, 10,)})
plt.show()
engine.heatmap('row_similarity', plot_kwargs={'figsize': (10, 10,)})
plt.show()
# The paint job is an important part of what makes a pine wood derby car fast,
# but does it matter for animals? We'll use the linfoot information to
# determine how predictive variables are of whether an animal is fast. Linfoot
# if basically the information-theoretic counterpart to correlation.
linfoot_lean = engine.mutual_information('fast', 'lean', linfoot=False)
linfoot_stripes = engine.mutual_information('fast', 'stripes', linfoot=False)
print('Linfoot(fast, lean) = %f' % (linfoot_lean,))
print('Linfoot(fast, stripes) = %f' % (linfoot_stripes,))
# We can also figure out which animals are more similar. Is a wolf more
# similar to a dalmatian or a rat.
sim_wolves = engine.row_similarity('chihuahua', 'wolf')
sim_rats = engine.row_similarity('chihuahua', 'rat')
print('Similarity between Chihuahuas and wolves is %f' % (sim_wolves,))
print('Similarity between Chihuahuas and rats is %f' % (sim_rats,))
# Which animals are outliers with respect to their being fast. We can find out
10,
10,
)})
plt.show()
engine.heatmap('row_similarity', plot_kwargs={'figsize': (
10,
10,
)})
plt.show()
# The paint job is an important part of what makes a pine wood derby car fast,
# but does it matter for animals? We'll use the linfoot information to
# determine how predictive variables are of whether an animal is fast. Linfoot
# if basically the information-theoretic counterpart to correlation.
linfoot_lean = engine.mutual_information('fast', 'lean', linfoot=False)
linfoot_stripes = engine.mutual_information('fast', 'stripes', linfoot=False)
print('Linfoot(fast, lean) = %f' % (linfoot_lean, ))
print('Linfoot(fast, stripes) = %f' % (linfoot_stripes, ))
# We can also figure out which animals are more similar. Is a wolf more
# similar to a dalmatian or a rat.
sim_wolves = engine.row_similarity('chihuahua', 'wolf')
sim_rats = engine.row_similarity('chihuahua', 'rat')
print('Similarity between Chihuahuas and wolves is %f' % (sim_wolves, ))
print('Similarity between Chihuahuas and rats is %f' % (sim_rats, ))
# Which animals are outliers with respect to their being fast. We can find out
# by calculating the surprisal (self infotmation).
