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"""
Generalized additive models
"""
import numpy as N
from scipy.sandbox.models import family
from scipy.sandbox.models.bspline import SmoothingSpline
from scipy.sandbox.models.glm import model as glm
def default_smoother(x):
_x = x.copy()
_x.sort()
n = x.shape[0]
# taken form smooth.spline in R
if n < 50:
nknots = n
else:
a1 = N.log(50) / N.log(2)
a2 = N.log(100) / N.log(2)
a3 = N.log(140) / N.log(2)
a4 = N.log(200) / N.log(2)
if n < 200:
nknots = 2**(a1 + (a2 - a1) * (n - 50)/150.)
elif n < 800:
nknots = 2**(a2 + (a3 - a2) * (n - 200)/600.)
elif n < 3200:
nknots = 2**(a3 + (a4 - a3) * (n - 800)/2400.)
else:
nknots = 200 + (n - 3200.)**0.2
knots = _x[N.linspace(0, n-1, nknots).astype(N.int32)]
s = SmoothingSpline(knots, x=x.copy())
s.gram(d=2)
s.target_df = 5
return s
class offset:
def __init__(self, fn, offset):
self.fn = fn
self.offset = offset
def __call__(self, *args, **kw):
return self.fn(*args, **kw) + self.offset
class results:
def __init__(self, Y, alpha, design, smoothers, family, offset):
self.Y = Y
self.alpha = alpha
self.smoothers = smoothers
self.offset = offset
self.family = family
self.design = design
self.offset = offset
self.mu = self(design)
def __call__(self, design):
return self.family.link.inverse(self.predict(design))
def predict(self, design):
return N.sum(self.smoothed(design), axis=0) + self.alpha
def smoothed(self, design):
return N.array([self.smoothers[i]() + self.offset[i] for i in range(design.shape[1])])
class additive_model:
def __init__(self, design, smoothers=None, weights=None):
self.design = design
if weights is not None:
self.weights = weights
else:
self.weights = N.ones(self.design.shape[0])
self.smoothers = smoothers or [default_smoother(design[:,i]) for i in range(design.shape[1])]
for i in range(design.shape[1]):
self.smoothers[i].df = 10
self.family = family.Gaussian()
def __iter__(self):
self.iter = 0
self.dev = N.inf
return self
def next(self):
_results = self.results; Y = self.results.Y
mu = _results.predict(self.design)
offset = N.zeros(self.design.shape[1], N.float64)
alpha = (Y * self.weights).sum() / self.weights.sum()
for i in range(self.design.shape[1]):
tmp = self.smoothers[i]()
self.smoothers[i].smooth(Y - alpha - mu + tmp,
weights=self.weights)
tmp2 = self.smoothers[i]()
offset[i] = -(tmp2*self.weights).sum() / self.weights.sum()
mu += tmp2 - tmp
return results(Y, alpha, self.design, self.smoothers, self.family, offset)
def cont(self, tol=1.0e-04):
curdev = (((self.results.Y - self.results.predict(self.design))**2) * self.weights).sum()
if N.fabs((self.dev - curdev) / curdev) < tol:
self.dev = curdev
return False
self.iter += 1
self.dev = curdev
return True
def df_resid(self):
return self.results.Y.shape[0] - N.array([self.smoothers[i].df_fit() for i in range(self.design.shape[1])]).sum()
def estimate_scale(self):
return ((self.results.Y - self.results(self.design))**2).sum() / self.df_resid()
def fit(self, Y):
iter(self)
mu = 0
alpha = (Y * self.weights).sum() / self.weights.sum()
offset = N.zeros(self.design.shape[1], N.float64)
for i in range(self.design.shape[1]):
self.smoothers[i].smooth(Y - alpha - mu,
weights=self.weights)
tmp = self.smoothers[i]()
offset[i] = (tmp * self.weights).sum() / self.weights.sum()
tmp -= tmp.sum()
mu += tmp
self.results = results(Y, alpha, self.design, self.smoothers, self.family, offset)
while self.cont():
self.results = self.next()
return self.results
class model(glm, additive_model):
niter = 10
def __init__(self, design, smoothers=None, family=family.Gaussian()):
glm.__init__(self, design, family=family)
additive_model.__init__(self, design, smoothers=smoothers)
self.family = family
def next(self):
_results = self.results; Y = _results.Y
_results.mu = self.family.link.inverse(_results.predict(self.design))
self.weights = self.family.weights(_results.mu)
Z = _results.predict(self.design) + self.family.link.deriv(_results.mu) * (Y - _results.mu)
m = additive_model(self.design, smoothers=self.smoothers, weights=self.weights)
_results = m.fit(Z)
_results.Y = Y
_results.mu = self.family.link.inverse(_results.predict(self.design))
self.iter += 1
self.results = _results
return _results
def estimate_scale(self, Y=None):
"""
Return Pearson\'s X^2 estimate of scale.
"""
if Y is None:
Y = self.Y
resid = Y - self.results.mu
return (N.power(resid, 2) / self.family.variance(self.results.mu)).sum() / additive_model.df_resid(self)
def fit(self, Y):
self.Y = N.asarray(Y, N.float64)
iter(self)
alpha = self.Y.mean()
Z = self.family.link(alpha) + self.family.link.deriv(alpha) * (Y - alpha)
m = additive_model(self.design, smoothers=self.smoothers)
self.results = m.fit(Z)
self.results.mu = self.family.link.inverse(self.results.predict(self.design))
self.results.Y = Y
while self.cont():
self.results = self.next()
self.scale = self.results.scale = self.estimate_scale()
return self.results
def _run():
import numpy.random as R
n = lambda x: (x - x.mean()) / x.std()
n_ = lambda x: (x - x.mean())
x1 = R.standard_normal(500)
x1.sort()
x2 = R.standard_normal(500)
x2.sort()
y = R.standard_normal((500,))
f1 = lambda x1: (x1 + x1**2 - 3 - 1.5 * x1**3 + N.exp(-x1))
f2 = lambda x2: (x2 + x2**2 - N.exp(x2))
z = n(f1(x1)) + n(f2(x2))
z = n(z) * 0.1
y += z
d = N.array([x1,x2]).T
m = additive_model(d)
m.fit(y)
x = N.linspace(-2,2,50)
import scipy.stats, time
f = family.Binomial()
b = N.asarray([scipy.stats.bernoulli.rvs(p) for p in f.link.inverse(y)])
b.shape = y.shape
m = model(d, family=f)
toc = time.time()
m.fit(b)
tic = time.time()
## import pylab
## pylab.figure(num=1)
## pylab.plot(x1, n(m.smoothers[0](x1)), 'r'); pylab.plot(x1, n(f1(x1)), linewidth=2)
## pylab.figure(num=2)
## pylab.plot(x2, n(m.smoothers[1](x2)), 'r'); pylab.plot(x2, n(f2(x2)), linewidth=2);
print tic-toc
f = family.Poisson()
p = N.asarray([scipy.stats.poisson.rvs(p) for p in f.link.inverse(y)])
p.shape = y.shape
m = model(d, family=f)
toc = time.time()
m.fit(p)
tic = time.time()
print tic-toc
## pylab.figure(num=1)
## pylab.plot(x1, n(m.smoothers[0](x1)), 'b'); pylab.plot(x1, n(f1(x1)), linewidth=2)
## pylab.figure(num=2)
## pylab.plot(x2, n(m.smoothers[1](x2)), 'b'); pylab.plot(x2, n(f2(x2)), linewidth=2)
## pylab.show()
if __name__ == "__main__":
_run()
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