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 l2_rate(Dp, Dq, ns, iters=50, fast=True):
"""
Collect data for L_2^2 divergence estimation of the distributions Dp, Dq over the set of n-values.
Repeat trials iters times.
"""
ms = []
vs = []
x = np.matrix(np.arange(0, 1, 0.001)).T
truth = np.mean(np.array((Dp.eval(x)- Dq.eval(x)))**2)
truth = numeric_integration(lambda x:
(Dp.eval(np.matrix(x))- Dq.eval(np.matrix(x)))**2,
[0], [1])
for n in ns:
sub_scores = []
for i in range(iters):
pdata = Dp.sample(n)
qdata = Dq.sample(n)
E = estimators.L2Estimator(pdata, qdata, Dp.s)
val = E.eval(fast=fast)
sub_scores.append(np.abs(val-truth))
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_linear_functional2(Dp,
Dq,
ns,
alpha=0.5,
beta=0.5,
iters=10,
fast=True):
"""
Another test case for the linear functional
"""
ms = []
vs = []
T = numeric_integration(
lambda x: np.multiply(np.power(Dp.eval(x), alpha),
np.power(Dq.eval(x), beta)), [0], [1])
print "True Expectation: %f\n" % (T)
for n in ns:
sub_scores = []
for i in range(iters):
pdata = Dp.sample(n)
qdata = Dq.sample(n)
fn1 = lambda x: np.multiply(np.power(Dp.eval(x), alpha - 1),
np.power(Dq.eval(x), beta))
val1 = alpha * np.mean(fn1(pdata))
#fn2 = lambda x: np.multiply(np.power(Dp.eval(x), alpha), np.power(Dq.eval(x), beta-1))
val2 = beta * np.mean(fn1(qdata))
sub_scores.append(np.abs(val1 + val2 - 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 l2_rate(Dp, Dq, ns, iters=50, fast=True):
"""
Collect data for L_2^2 divergence estimation of the distributions Dp, Dq over the set of n-values.
Repeat trials iters times.
"""
ms = []
vs = []
x = np.matrix(np.arange(0, 1, 0.001)).T
truth = np.mean(np.array((Dp.eval(x) - Dq.eval(x)))**2)
truth = numeric_integration(
lambda x: (Dp.eval(np.matrix(x)) - Dq.eval(np.matrix(x)))**2, [0], [1])
for n in ns:
sub_scores = []
for i in range(iters):
pdata = Dp.sample(n)
qdata = Dq.sample(n)
E = estimators.L2Estimator(pdata, qdata, Dp.s)
val = E.eval(fast=fast)
sub_scores.append(np.abs(val - truth))
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 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 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 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_linear_functional(Dp, ns, iters=10, fast=True):
"""
Test the linear functional estimator
"""
ms = [];
vs = [];
T = numeric_integration(lambda x: np.array(Dp.eval(x)) * np.array(x), [0], [1]);
print "True Expectation: %f\n" % (T)
for n in ns:
sub_scores = [];
for i in range(iters):
pdata = Dp.sample(n);
val = np.mean(pdata, axis=0)
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_linear_functional(Dp, ns, iters=10, fast=True):
"""
Test the linear functional estimator
"""
ms = []
vs = []
T = numeric_integration(lambda x: np.array(Dp.eval(x)) * np.array(x), [0],
[1])
print "True Expectation: %f\n" % (T)
for n in ns:
sub_scores = []
for i in range(iters):
pdata = Dp.sample(n)
val = np.mean(pdata, axis=0)
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_linear_functional2(Dp, Dq, ns, alpha=0.5, beta=0.5, iters=10, fast=True):
"""
Another test case for the linear functional
"""
ms = []
vs = []
T = numeric_integration(lambda x: np.multiply(np.power(Dp.eval(x), alpha), np.power(Dq.eval(x), beta)), [0], [1])
print "True Expectation: %f\n" % (T)
for n in ns:
sub_scores = [];
for i in range(iters):
pdata = Dp.sample(n);
qdata = Dq.sample(n)
fn1 = lambda x: np.multiply(np.power(Dp.eval(x), alpha-1), np.power(Dq.eval(x), beta))
val1 = alpha* np.mean(fn1(pdata))
#fn2 = lambda x: np.multiply(np.power(Dp.eval(x), alpha), np.power(Dq.eval(x), beta-1))
val2 = beta* np.mean(fn1(qdata))
sub_scores.append(np.abs(val1+val2-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)