def eval(self, fast=True, pts=1000):
"""
Evaluate the true divergence by performing numeric integration on the n^d grid of points.
"""
if not fast:
print "using slow integration"
if self.dim == 1:
val = numeric_integration(lambda x: np.multiply(
np.power(self.p.eval(np.matrix(x)), self.alpha),
np.power(self.q.eval(np.matrix(x)), self.beta)),
[lb], [ub])
if self.dim == 2:
val = numeric_integration(lambda x,y: np.multiply(
# np.power(self.p.eval(np.concatenate(np.matrix(x), np.matrix(y))), self.alpha),
# np.power(self.q.eval(np.concatenate(np.matrix(x), np.matrix(y))), self.beta)),
np.power(self.p.eval(np.concatenate(np.matrix(x), np.matrix(y))), self.alpha),
np.power(self.q.eval(np.concatenate(np.matrix(x), np.matrix(y))), self.beta)),
[lb, lb], [ub, ub])
if fast:
print "using fast integration"
if self.dim == 1:
val = fast_integration(lambda x: np.multiply(
np.power(self.p.eval(np.matrix(x)), self.alpha),
np.power(self.q.eval(np.matrix(x)), self.beta)),
[lb], [ub], pts=pts)
if self.dim == 2:
val = fast_integration(lambda x: np.multiply(
np.power(self.p.eval(np.matrix(x)), self.alpha),
np.power(self.q.eval(np.matrix(x)), self.beta)),
[lb,lb], [ub,ub])
return val
def test_bilinear_term_estimator(Dp, Dq, ns, iters=10, fast=True):
"""
Test the bilinear functional estimator
"""
ms = []
vs = []
T = fast_integration(lambda x: np.array(Dp.eval(x)) * np.array(Dq.eval(x)),
[0], [1])
print "Truth: %f" % (T)
for n in ns:
sub_scores = []
for i in range(iters):
pdata = Dp.sample(n)
qdata = Dq.sample(n)
Q = estimators.QuadraticEstimator(pdata, pdata, 0.5, 0.5, Dp.s)
val = Q.bilinear_term_slow(lambda x: 1, pdata, qdata)
val2 = Q.bilinear_term_fast(
lambda x: np.matrix(np.ones((x.shape[0], 1))), pdata, qdata)
print "truth = %0.3f, slow = %0.3f, fast = %0.3f" % (T, val2, val)
sub_scores.append(np.abs(val - T))
sub_scores.sort()
sub_scores = sub_scores[int(0.2 * iters):int(0.8 * iters)]
ms.append(np.mean(sub_scores))
vs.append(np.std(sub_scores))
print "n = %d, av_er = %0.2f, std_er = %0.4f" % (
n, np.mean(sub_scores), np.std(sub_scores))
return (ns, ms, vs)
def quad_term_fast(self, fn, data):
"""
Fast routine for estimating the quadratic term
fn -- a lambda expression for the function \psi.
data1 -- data from the distribution we are trying to estimate
Returns the value of the estimator
Note: this shouldn't be called externally
"""
n = data.shape[0]
total = 0.0
for k in lattice.lattice(self.dim, self.m):
sub1 = np.array(self.comp_exp(k, data))
sub2 = sub1*np.array(fn(data))
total += np.sum((np.sum(sub2) - sub2) * sub1)
term2 = 0.0
for k in lattice.lattice(self.dim, self.m):
for kp in lattice.lattice(self.dim, self.m):
bi = fast_integration(lambda x: np.array(self.comp_exp(k,x))*np.array(self.comp_exp(kp,x))*np.array(fn(x)),
[0.0 for t in range(self.dim)], [1.0 for t in range(self.dim)], pts=100)
sub1 = np.array(self.comp_exp(k, data))
sub2 = np.array(self.comp_exp(kp, data))
term2 += np.sum(bi* sub1* (np.sum(sub2) - sub2))
# print (np.real(2.0*total/(n*(n-1))), np.real(term2/(n*(n-1))))
return np.real(2.0*total/(n*(n-1))) - np.real(term2/(n*(n-1)))
def quad_term_slow(self, fn, data):
"""
Deprected
Slow routine for estimating the quadratic terms
fn -- a lambda expression for the function \psi.
data1 -- data from the distribution we are trying to estimate
Returns the value of the estimator
"""
assert False, "Deprecated"
n = data.shape[0]
total = 0.0
for k in lattice.lattice(self.dim, self.m):
for i in range(n):
for j in range(n):
if j != i:
total += self.comp_exp(k, data[i,:])*self.comp_exp(k, data[j,:])*fn(data[j,:])
term2 = 0.0
for k in lattice.lattice(self.dim, self.m):
for kp in lattice.lattice(self.dim, self.m):
bi = fast_integration(lambda x: np.array(self.comp_exp(k,x))*np.array(self.comp_exp(kp,x))*np.array(fn(x)),
[0 for t in range(self.dim)], [1 for t in range(self.dim)])
for i in range(n):
for j in range(n):
if j != i:
term2 += bi*self.comp_exp(k, data[i,:])*self.comp_exp(kp, data[j,:])
return np.real(2.0*total/(n*(n-1)) - 1.0*term2/(n*(n-1)))
def eval(self, fast=True, pts=1000):
"""
Evaluate the true divergence by performing numeric integration on the n^d grid of points.
"""
if not fast:
print "using slow integration"
if self.dim == 1:
val = numeric_integration(
lambda x: np.multiply(
np.power(self.p.eval(np.matrix(x)), self.alpha),
np.power(self.q.eval(np.matrix(x)), self.beta)), [lb],
[ub])
if self.dim == 2:
val = numeric_integration(
lambda x, y: np.multiply(
# np.power(self.p.eval(np.concatenate(np.matrix(x), np.matrix(y))), self.alpha),
# np.power(self.q.eval(np.concatenate(np.matrix(x), np.matrix(y))), self.beta)),
np.power(
self.p.eval(
np.concatenate(np.matrix(x), np.matrix(y))),
self.alpha),
np.power(
self.q.eval(
np.concatenate(np.matrix(x), np.matrix(y))),
self.beta)),
[lb, lb],
[ub, ub])
if fast:
print "using fast integration"
if self.dim == 1:
val = fast_integration(lambda x: np.multiply(
np.power(self.p.eval(np.matrix(x)), self.alpha),
np.power(self.q.eval(np.matrix(x)), self.beta)), [lb],
[ub],
pts=pts)
if self.dim == 2:
val = fast_integration(
lambda x: np.multiply(
np.power(self.p.eval(np.matrix(x)), self.alpha),
np.power(self.q.eval(np.matrix(x)), self.beta)),
[lb, lb], [ub, ub])
return val
def eval(self, fast=True):
"""
Evaluate the estimator by performing numeric integration on the n^d grid of points.
Currently we ignore the fast parameter -- we are always doing fast numeric integration.
"""
val = fast_integration(lambda x: np.multiply(
np.power(self.Kp.eval(np.matrix(x)), self.alpha),
np.power(self.Kq.eval(np.matrix(x)), self.beta)),
[lb for i in range(self.dim)], [ub for i in range(self.dim)])
return val
def kde_error(self, true_p, p_norm, fast=True):
"""
Compute the error of this estimator in ell_p^p norm.
"""
if fast:
integrator = lambda x,y,z: helper.fast_integration(x,y,z)
else:
integrator = lambda x,y,z: helper.numeric_integration(x,y,z)
fn_handle = lambda x: np.power(np.array(np.abs(self.eval(np.matrix(x)) - true_p.eval(np.matrix(x)).reshape(x.shape[0],)))[0,:], p_norm)
return integrator(fn_handle, [0.1 for i in range(self.d)], [0.9 for i in range(self.d)])
def eval(self, fast=True):
"""
Evaluate the estimator by performing numeric integration on the n^d grid of points.
Currently we ignore the fast parameter -- we are always doing fast numeric integration.
"""
val = fast_integration(
lambda x: np.multiply(
np.power(self.Kp.eval(np.matrix(x)), self.alpha),
np.power(self.Kq.eval(np.matrix(x)), self.beta)),
[lb for i in range(self.dim)], [ub for i in range(self.dim)])
return val
def kde_error(self, true_p, p_norm, fast=True):
"""
Compute the error of this estimator in ell_p^p norm.
"""
if fast:
integrator = lambda x, y, z: helper.fast_integration(x, y, z)
else:
integrator = lambda x, y, z: helper.numeric_integration(x, y, z)
fn_handle = lambda x: np.power(
np.array(
np.abs(
self.eval(np.matrix(x)) - true_p.eval(np.matrix(x)).
reshape(x.shape[0], )))[0, :], p_norm)
return integrator(fn_handle, [0.1 for i in range(self.d)],
[0.9 for i in range(self.d)])
def test_quadratic_term_estimator(Dp, ns, iters=10, fast=True):
"""
Test the quadratic term estimator.
"""
ms = []
vs = []
T = fast_integration(lambda x: np.array(Dp.eval(x))**2, [0], [1])
print "Truth: %f" % (T)
for n in ns:
sub_scores = []
for i in range(iters):
pdata = Dp.sample(n)
Q = estimators.QuadraticEstimator(pdata, pdata, 0.5, 0.5, Dp.s)
val = Q.quad_term_slow(lambda x: 1, pdata)
val2 = Q.quad_term_fast(lambda x: 1, pdata)
print "truth = %0.3f, fast = %0.3f, slow = %0.3f" % (T, val2, val)
sub_scores.append(np.abs(val-T))
sub_scores.sort();
sub_scores = sub_scores[int(0.2*iters): int(0.8*iters)];
ms.append(np.mean(sub_scores))
vs.append(np.std(sub_scores))
print "n = %d, av_er = %0.2f, std_er = %0.4f" % (n, np.mean(sub_scores), np.std(sub_scores))
return (ns, ms, vs)
def test_bilinear_term_estimator(Dp, Dq, ns, iters=10, fast=True):
"""
Test the bilinear functional estimator
"""
ms = []
vs = []
T = fast_integration(lambda x: np.array(Dp.eval(x))*np.array(Dq.eval(x)), [0], [1])
print "Truth: %f" % (T)
for n in ns:
sub_scores = []
for i in range(iters):
pdata = Dp.sample(n)
qdata = Dq.sample(n)
Q = estimators.QuadraticEstimator(pdata, pdata, 0.5, 0.5, Dp.s)
val = Q.bilinear_term_slow(lambda x: 1, pdata, qdata)
val2 = Q.bilinear_term_fast(lambda x: np.matrix(np.ones((x.shape[0], 1))), pdata, qdata)
print "truth = %0.3f, slow = %0.3f, fast = %0.3f" % (T, val2, val)
sub_scores.append(np.abs(val-T))
sub_scores.sort();
sub_scores = sub_scores[int(0.2*iters): int(0.8*iters)];
ms.append(np.mean(sub_scores))
vs.append(np.std(sub_scores))
print "n = %d, av_er = %0.2f, std_er = %0.4f" % (n, np.mean(sub_scores), np.std(sub_scores))
return (ns, ms, vs)
def test_quadratic_term_estimator(Dp, ns, iters=10, fast=True):
"""
Test the quadratic term estimator.
"""
ms = []
vs = []
T = fast_integration(lambda x: np.array(Dp.eval(x))**2, [0], [1])
print "Truth: %f" % (T)
for n in ns:
sub_scores = []
for i in range(iters):
pdata = Dp.sample(n)
Q = estimators.QuadraticEstimator(pdata, pdata, 0.5, 0.5, Dp.s)
val = Q.quad_term_slow(lambda x: 1, pdata)
val2 = Q.quad_term_fast(lambda x: 1, pdata)
print "truth = %0.3f, fast = %0.3f, slow = %0.3f" % (T, val2, val)
sub_scores.append(np.abs(val - T))
sub_scores.sort()
sub_scores = sub_scores[int(0.2 * iters):int(0.8 * iters)]
ms.append(np.mean(sub_scores))
vs.append(np.std(sub_scores))
print "n = %d, av_er = %0.2f, std_er = %0.4f" % (
n, np.mean(sub_scores), np.std(sub_scores))
return (ns, ms, vs)
def kde_error(self, true_p, p_norm, pts=1000):
"""
compute the error of this estimator in ell_p^p norm.
"""
fn_handle = lambda x: np.power(np.array(np.abs(self.eval(np.matrix(x)) - true_p.eval(np.matrix(x)).reshape(x.shape[0],)))[0,:], p_norm)
return helper.fast_integration(fn_handle, [0.0 for i in range(self.d)], [1.0 for i in range(self.d)], pts=pts)