def test_linear_regression():
"""
Check if fitting a linear model works.
This requires several things to work properly:
- Passing expressions to distributions
- Generating with certain fixed observed values
- Fitting in general
"""
from mle import Normal, vec, var
import numpy as np
x = vec('x', observed=True)
y = vec('y', observed=True)
a = par('a')
b = par('b')
sigma = par('sigma')
dist = Normal(y, a * x + b, sigma)
np.random.seed(42)
xs = linspace(0, 1, 20)
data = dist.sample(20, {'x': xs, 'a': 1, 'b': 0, 'sigma': 0.5})
data['x'] = xs
results = dist.fit(data, {'a': 2, 'b': 1, 'sigma': 1})
def sfa_inner(lnrptA, lnmptA, SBInvestRatioA, fundScaleA, ALRatioA, institutionRatioA):
# Define model
lnrpt = var('lnrpt', observed=True, vector=True)
lnmpt = var('lnmpt', observed=True, vector=True)
SBInvestRatio = var('SBInvestRatio', observed=True, vector=True)
fundScale = var('fundScale', observed=True, vector=True)
ALRatio = var('ALRatio', observed=True, vector=True)
institutionRatio = var('institutionRatio', observed=True, vector=True)
a1 = var('a1')
a2 = var('a2')
a3 = var('a3')
a4 = var('a4')
b0 = var('b0')
b1 = var('b1')
sigma = var('sigma')
model = Normal(lnrpt, b1 * lnmpt + (a1 * SBInvestRatio) + (a2 * fundScale) + (a3 * ALRatio) + (a4 * institutionRatio) + b0, sigma)
# Fit model to data
result = model.fit({'lnrpt': lnrptA, 'lnmpt': lnmptA,
'SBInvestRatio': SBInvestRatioA, 'fundScale': fundScaleA,
'ALRatio': ALRatioA, 'institutionRatio': institutionRatioA},
{'a1': 1, 'a2': 1, 'a3': 1, 'a4': 1, 'b0': 1, 'b1': 1, 'sigma': 1})
return result.x['b1'];
def test_pdf_product():
"""
Check if PDF models can be joined
"""
from mle import var, Normal, Join
x = var('x', vector=True, observed=True)
y = var('y', observed=True)
mu = var('mu')
sigma = var('sigma')
model = Join(Join(Normal(x, mu, sigma)), Normal(y, mu, sigma))
assert (model.observed == [x, y])
def test_simple_fit():
"""
Check if generating/fitting Gaussian data works
"""
from mle import Normal, vec, var
import numpy as np
x = vec('x', observed=True)
mu = var('mu')
sigma = var('sigma')
dist = Normal(x, mu, sigma)
np.random.seed(42)
data = dist.sample(1e6, {'mu': 0, 'sigma': 1})
results = dist.fit(data, {'mu': 1, 'sigma': 2}, method='L-BFGS-B')
def test_const():
"""
Check if parameters can be set to be constant.
"""
from mle import var, vec, Normal
import numpy as np
x = vec('x', observed=True)
mu = var('mu', const=True)
sigma = var('sigma')
model = Normal(x, mu, sigma)
np.random.seed(42)
data = model.sample(200, {'mu': 0, 'sigma': 1})
results = model.fit(data, {'mu': 1, 'sigma': 1})
assert (results.x['mu'] == 1)
def test_const():
"""
Check if parameters can be set to be constant.
"""
from mle import var, Normal
import numpy as np
x = var('x', vector=True, observed=True)
mu = var('mu', const=True)
sigma = var('sigma')
model = Normal(x, mu, sigma)
np.random.seed(42)
data = np.random.normal(0, 1, 200)
results = model.fit({'x': data}, {'mu': 1, 'sigma': 1})
assert(results.x['mu'] == 1)
def test_const():
"""
Check if parameters can be set to be constant.
"""
from mle import var, Normal
import numpy as np
x = var('x', vector=True, observed=True)
mu = var('mu', const=True)
sigma = var('sigma')
model = Normal(x, mu, sigma)
np.random.seed(42)
data = np.random.normal(0, 1, 200)
results = model.fit({'x': data}, {'mu': 1, 'sigma': 1})
assert (results.x['mu'] == 1)
def sfa_inner(lnrptA, lnmptA, SBInvestRatioA, fundScaleA, ALRatioA,
institutionRatioA):
# Define model
lnrpt = var('lnrpt', observed=True, vector=True)
lnmpt = var('lnmpt', observed=True, vector=True)
SBInvestRatio = var('SBInvestRatio', observed=True, vector=True)
fundScale = var('fundScale', observed=True, vector=True)
ALRatio = var('ALRatio', observed=True, vector=True)
institutionRatio = var('institutionRatio', observed=True, vector=True)
a1 = var('a1')
a2 = var('a2')
a3 = var('a3')
a4 = var('a4')
b0 = var('b0')
b1 = var('b1')
sigma = var('sigma')
model = Normal(
lnrpt, b1 * lnmpt + (a1 * SBInvestRatio) + (a2 * fundScale) +
(a3 * ALRatio) + (a4 * institutionRatio) + b0, sigma)
# Fit model to data
result = model.fit(
{
'lnrpt': lnrptA,
'lnmpt': lnmptA,
'SBInvestRatio': SBInvestRatioA,
'fundScale': fundScaleA,
'ALRatio': ALRatioA,
'institutionRatio': institutionRatioA
}, {
'a1': 1,
'a2': 1,
'a3': 1,
'a4': 1,
'b0': 1,
'b1': 1,
'sigma': 1
})
return result.x['b1']
def test_simple_fit():
"""
Check if fitting Gaussian data works
"""
from mle import Normal, var
import numpy as np
x = var('x', vector=True, observed=True)
mu = var('mu')
sigma = var('sigma')
dist = Normal(x, mu, sigma)
np.random.seed(42)
data = np.random.normal(0, 1, 100000)
try:
dist.fit({'x': data}, {'mu': 1, 'sigma': 2}, method='BFGS')
except:
assert False, 'Fitting generated data failed'
def test_linear_regression():
"""
Check if fitting a linear model works.
"""
from mle import Normal, var
import numpy as np
x = var('x', vector=True, observed=True)
y = var('y', vector=True, observed=True)
a = var('a')
b = var('b')
sigma = var('sigma')
model = Normal(y, a * x + b, sigma)
np.random.seed(42)
xs = np.linspace(0, 1, 20)
ys = 0.5 * xs - 0.3 + np.random.normal(0, 0.2, 20)
results = model.fit({'x': xs, 'y': ys}, {'a': 2, 'b': 1, 'sigma': 1})
print(results)
def test_simple_fit():
"""
Check if generating/fitting Gaussian data works
"""
from mle import Normal, var
import numpy as np
x = var('x', vector=True, observed=True)
mu = var('mu')
sigma = var('sigma')
dist = Normal(x, mu, sigma)
np.random.seed(42)
try:
data = dist.sample(1e6, {'mu': 0, 'sigma': 1})
except:
assert False, 'Generating data failed'
try:
results = dist.fit(data, {'mu': 1, 'sigma': 2}, method='BFGS')
except:
assert False, 'Fitting generated data failed'
def test_linear_regression():
"""
Check if fitting a linear model works.
"""
from mle import Normal, var
import numpy as np
x = var('x', vector=True, observed=True)
y = var('y', vector=True, observed=True)
a = var('a')
b = var('b')
sigma = var('sigma')
model = Normal(y, a * x + b, sigma)
np.random.seed(42)
xs = np.linspace(0, 1, 20)
ys = 0.5 * xs - 0.3 + np.random.normal(0, 0.2, 20)
results = model.fit({'x': xs, 'y':ys}, {'a': 2, 'b': 1, 'sigma': 1})
print(results)
def test_simple_fit():
"""
Check if generating/fitting Gaussian data works
"""
from mle import Normal, var
import numpy as np
x = var('x', vector=True, observed=True)
mu = var('mu')
sigma = var('sigma')
dist = Normal(x, mu, sigma)
np.random.seed(42)
try:
data = dist.sample(1e6, {'mu': 0, 'sigma': 1})
except:
assert False, 'Generating data failed'
try:
results = dist.fit(data, {'mu': 1, 'sigma': 2}, method='BFGS')
except:
assert False, 'Fitting generated data failed'
def test_error_on_illegal_bound():
"""
Check if exception is raised when user specifies illegal bound.
Some distributions automatically apply certain bounds.
Example: sigma > 0 for the Normal distribution.
If a user-specified bound conflicts with that, an exception should be thrown.
"""
from mle import var, Normal
x = var('x', vector=True, observed=True)
mu = var('mu')
sigma = var('sigma', lower=-1)
Normal(x, mu, sigma)
import numpy as np
from mle import var, Normal
# Define model
x = var("x", observed=True, vector=True)
y = var("y", observed=True, vector=True)
a = var("a")
b = var("b")
sigma = var("sigma")
model = Normal(y, a * x + b, sigma)
# Generate data
xs = np.linspace(0, 2, 20)
ys = 0.5 * xs + 0.3 + np.random.normal(0, 0.1, 20)
# Fit model to data
result = model.fit({"x": xs, "y": ys}, {"a": 1, "b": 1, "sigma": 1})
print(result)
from numpy import linspace, array, append
import matplotlib.pyplot as plt
from scipy.stats import norm
from time import clock
from pandas import DataFrame
from mle import Normal, var, par, Mix2
x = var("x")
mu1 = par("mu1")
sigma1 = par("sigma1")
mu2 = par("mu2")
sigma2 = par("sigma2")
frac = par("frac")
model = Mix2(frac, Normal(x, mu1, sigma1), Normal(x, mu2, sigma2))
N = int(1e5)
data = array(append(normal(3, 1, N), normal(-3, 1, 2 * N)),
dtype=[("x", float)])
initial = {"frac": 0.5, "mu1": 2, "sigma1": 4, "mu2": 2, "sigma2": 4}
start = clock()
result = model.fit(data, initial, method="Powell")
print("Fit took {:5.1f} s".format(clock() - start))
print(result)
from mle.tests import kolsmi, chisquare
import numpy as np
from mle import var, Normal
# Define model
x = var('x', observed=True, vector=True)
y = var('y', observed=True, vector=True)
a = var('a')
b = var('b')
sigma = var('sigma')
model = Normal(y, a * x + b, sigma)
# Generate data
xs = np.linspace(0, 2, 20)
ys = 0.5 * xs + 0.3 + np.random.normal(0, 0.1, 20)
# Fit model to data
result = model.fit({'x': xs, 'y': ys}, {'a': 1, 'b': 1, 'sigma': 1})
print(result)
