def normalized_sample(self, W):
""" Normalized sampling without division.
Args:
W: a set of weights from which to sample.
Returns: an integer in [0,len(W)] corresponding to the index sampled.
"""
t = gmpy2.fsum(W) # compute total weight
C = [gmpy2.fsum(W[0:i + 1])
for i in range(0, len(W))] # compute cumulative weights
# Determine the maximum power of two for sampling
i_max = 0
while gmpy2.exp2(i_max) > t:
i_max -= 1
while gmpy2.exp2(i_max) <= t:
i_max += 1
# sample a random number
s = gmpy2.exp2(i_max + 1)
while s > t:
s = self.get_random_value(i_max, self.context.precision)
# return the element that matches the sampled index
for i in range(0, len(W)):
if C[i] >= s:
return i
def hessian(x, y, t_1, t_2):
psigmoid = [sigmoid(i, t_1, t_2) for i in x]
u = [p * (1 - p) * q * q for (p, q) in zip(psigmoid, x)]
d1 = gmpy2.fsum(u)
v = [p * (1 - p) * q for (p, q) in zip(psigmoid, x)]
d2 = gmpy2.fsum(v)
w = [p * (1 - p) for p in psigmoid]
d3 = gmpy2.fsum(w)
H = np.array([[d1, d2], [d2, d3]])
return H
def logLikelihood(x, y, t_1, t_2):
psigmoid = [sigmoid(i, t_1, t_2) for i in x]
u = [
q * gmpy2.log(p) + (1 - q) * gmpy2.log(1 - p)
for (p, q) in zip(psigmoid, y)
]
return gmpy2.fsum(u)
def optimized_normalized_sample(self, W):
""" Optimized Normalized sampling without division.
Args:
W: a set of weights from which to sample.
Returns: an integer in [0,len(W)] corresponding to the index sampled.
WARNING: introduces a timing channel for differing weight distributions.
"""
t = gmpy2.fsum(W) # compute total weight
C = [gmpy2.fsum(W[0:i + 1])
for i in range(0, len(W))] # compute cumulative weights
s = 0
log2t = 0
while gmpy2.exp2(log2t) > t:
log2t -= 1
while gmpy2.exp2(log2t) <= t:
log2t += 1
j = log2t - 1
remaining = [i for i in range(0, len(W))]
if t < gmpy2.exp2(log2t):
remaining.append(len(W)) # add a dummy value
C.append(gmpy2.exp2(log2t))
while len(remaining) > 1:
r = self.rng()
s = s + r * gmpy2.exp2(j)
to_remove = []
for i in remaining: # check if each remaining index is still reachable
if C[i] <= s:
to_remove.append(i)
if i > 0:
if C[i - 1] >= s + gmpy2.exp2(j):
to_remove.append(i)
for i in to_remove:
remaining.remove(i)
if len(remaining) == 1 and remaining[0] == len(W):
s = 0
j = log2t # don't subtract 1, it's going to be decremented
remaining = [i for i in range(0, len(W))]
if t < gmpy2.exp2(log2t):
remaining.append(len(W)) # add a dummy value
C.append(gmpy2.exp2(log2t))
j -= 1
return remaining[0]
def dot(self, other):
"""Return the dot product of this MPFRVector with another MPFRVector."""
if not isinstance(other, MPFRVector):
raise ValueError(
"cannot take dot product of MPFRVector with non-MPFRVector")
if len(self.entries) != len(other.entries):
raise ValueError(
"cannot take dot product MPFRVectors with different lengths")
return gmpy2.fsum(x * y for x, y in zip(self.entries, other.entries))
def gradient(x, y, t_1, t_2):
psigmoid = [sigmoid(i, t_1, t_2) for i in x]
u = [q - p for (p, q) in zip(psigmoid, y)]
v = [t * k for (t, k) in zip(u, x)]
return np.array([[gmpy2.fsum(v), gmpy2.fsum(u)]])
def log_likelihood(x,y, t_1, t_2): sigmoidP = [sigmoid(i, t_1, t_2) for i in x] u = [q*gmpy2.log(p) + (1 - q)*gmpy2.log(1 - p) for p,q in zip(sigmoidP,y)] return gmpy2.fsum(u)
def norm_squared(self):
"""Return the squared Euclidean norm of this MPFRVector."""
return gmpy2.fsum(map(gmpy2.square, self.entries))