Commit 9a00ce57 authored by Philipp Arras's avatar Philipp Arras
Browse files

Rewrite InverseGammaModel with linear Interpolation

parent 0a0258b4
......@@ -30,7 +30,7 @@ from ..sugar import makeOp
class InverseGammaModel(Operator):
def __init__(self, domain, alpha, q):
def __init__(self, domain, alpha, q, delta):
"""Model which transforms a Gaussian into an inverse gamma distribution.
The pdf of the inverse gamma distribution is defined as follows:
......@@ -42,6 +42,9 @@ class InverseGammaModel(Operator):
The mean of the pdf is at q / (alpha - 1) if alpha > 1.
The mode is q / (alpha + 1).
This transformation is implemented as a linear interpolation which
maps a Gaussian onto a inverse gamma distribution.
Parameters
----------
domain : Domain, tuple of Domain or DomainTuple
......@@ -51,30 +54,38 @@ class InverseGammaModel(Operator):
The alpha-parameter of the inverse-gamma distribution.
q : float
The q-parameter of the inverse-gamma distribution.
delta : float
distance between sampling points for linear interpolation.
"""
self._domain = self._target = DomainTuple.make(domain)
self._alpha = alpha
self._q = q
self._alpha, self._q, self._delta = alpha, q, delta
def apply(self, x):
self._check_input(x)
lin = isinstance(x, Linearization)
val = x.val.local_data if lin else x.local_data
# MR FIXME?!
points = np.clip(val, None, 8.2)
points = invgamma.ppf(norm.cdf(points), self._alpha, scale=self._q)
points = Field.from_local_data(self._domain, points)
val = np.clip(val, None, 8.2)
# Precompute
x0 = val.min()
dx = self._delta
xs = np.arange(x0, val.max()+2*dx, dx)
table = np.log(invgamma.ppf(norm.cdf(xs), self._alpha, scale=self._q))
# Operator
fi = np.array(np.floor((val - x0)/dx), dtype=np.int)
w = (val - xs[fi])/dx
res = np.exp((1 - w)*table[fi] + w*table[fi + 1])
points = Field.from_local_data(self._domain, res)
if not lin:
return points
inner = norm.pdf(val)
outer_inv = invgamma.pdf(invgamma.ppf(norm.cdf(val),
self._alpha,
scale=self._q),
self._alpha, scale=self._q)
# FIXME
outer_inv = np.clip(outer_inv, 1e-20, None)
outer = 1/outer_inv
jac = makeOp(Field.from_local_data(self._domain, inner*outer))
# Derivative of linear interpolation
inner_der = (table[fi + 1] - table[fi])/dx
der = inner_der*res
jac = makeOp(Field.from_local_data(self._domain, der))
jac = jac(x.jac)
return x.new(points, jac)
......
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