def l2_rate_experiment(ns, ss, d=1, iters=50, fast=True):
"""
Experiment for plotting rate of convergence of divergence estimator on L_2^2 divergence.
Input:
est_type -- which estimator should we use. "linear" "plugin" and "quadratic" are supported.
ns -- a list of sample sizes to evaluate on. Try np.logspace(1, 4, 20)
ss -- a list which smoothness parameters should we evaluate on?
d -- the dimension
iters -- how many iterations should we use.
fast -- should we use fast numeric integration or slow numeric integration
Returns nothing but writes log files with the results of the experiments to ./data/
"""
for s in ss:
print "s = %s" % (str(s))
if d == 1:
Dp = density.UniTrigDensity(s, 1)
Dq = density.UniTrigDensity(s, 1)
else:
Dp = density.TrigDensity(s, 1, d)
Dq = density.TrigDensity(s, 1, d)
(new_ns, ms, vs) = rates.l2_rate(Dp, Dq, ns, iters=iters, fast=fast)
f = open("./data/l2_error_d=%d_s=%s.out" % (d, str(s)), "w")
f.write("ns " + " ".join([str(n) for n in ns]) + "\n")
f.write("ms " + " ".join([str(m) for m in ms]) + "\n")
f.write("vs " + " ".join([str(v) for v in vs]))
f.close()
return
def divergences_rate(est_type, ns, ss, d=1, iters=50, fast=True):
"""
Experiment for plotting rate of convergence of divergence estimator on Renyi and Tsallis divergence.
Input:
est_type -- which estimator should we use. "linear" "plugin" and "quadratic" are supported.
ns -- a list of sample sizes to evaluate on. Try np.logspace(1, 4, 20)
ss -- a list which smoothness parameters should we evaluate on?
d -- the dimension
iters -- how many iterations should we use.
fast -- should we use fast numeric integration or slow numeric integration
Returns nothing but writes log files with the results of the experiments to ./data/
"""
E = None
if est_type == "plugin":
E = estimators.PluginEstimator
elif est_type == "linear":
E = estimators.LinearEstimator
elif est_type == "quadratic":
E = estimators.QuadraticEstimator
else:
print "Estimator %s not supported" % (est_type)
return
for s in ss:
print "s = %s" % (str(s))
if d == 1:
Dp = density.UniTrigDensity(s, 1)
Dq = density.UniTrigDensity(s, 1)
else:
Dp = density.TrigDensity(s, 1, d)
Dq = density.TrigDensity(s, 1, d)
(new_ns, ms, vs) = rates.renyi_rate(E,
Dp,
Dq,
ns,
alpha=0.5,
iters=iters,
fast=fast)
f = open("./data/%s_renyi_error_d=%d_s=%s.out" % (est_type, d, str(s)),
"w")
f.write("ns " + " ".join([str(n) for n in ns]) + "\n")
f.write("ms " + " ".join([str(m) for m in ms]) + "\n")
f.write("vs " + " ".join([str(v) for v in vs]))
f.close()
(new_ns, ms, vs) = rates.tsallis_rate(E,
Dp,
Dq,
ns,
alpha=0.5,
iters=iters,
fast=fast)
f = open(
"./data/%s_tsallis_error_d=%d_s=%s.out" % (est_type, d, str(s)),
"w")
f.write("ns " + " ".join([str(n) for n in ns]) + "\n")
f.write("ms " + " ".join([str(m) for m in ms]) + "\n")
f.write("vs " + " ".join([str(v) for v in vs]))
f.close()
return
def kde_rate(ns, ss, d=1, iters=50, fast=True):
"""
Experiment for the KDE rate of convergence.
ns -- which ns should we run the experiment on. Try np.logspace(1, 4, 20)
ss -- which smoothnesses should we run the experiment on
d -- the dimension
iters -- how many iterations should we use
Returns nothing but writes log files with the results of the experiments to ./data/
"""
ps = [1, 2, 3]
for s in ss:
print "s = %s" % (str(s))
if d == 1:
D = density.UniTrigDensity(s, 1)
else:
D = density.TrigDensity(s, 1, d)
(new_ns, ms, vs) = rates.kde_rate(D, ns, ps, iters=iters)
for i in range(len(ps)):
f = open(
"./data/kde_error_d=%d_p=%d_s=%s.out" % (d, ps[i], str(s)),
"w")
f.write("ns " + " ".join([str(n) for n in ns]) + "\n")
f.write("ms " + " ".join([str(m) for m in ms[i]]) + "\n")
f.write("vs " + " ".join([str(v) for v in vs[i]]))
f.close()
return
def estimator_rate(est_type, ns, ss, alpha, beta, d=1, iters=50, fast=True):
"""
Experiment for the rate of convergence of the estimator for T(p,q) = \int p^\alpha q^\beta.
est_type -- which estimator, "linear" "plugin" or "quadratic"
ns -- which ns should we run the experiment on. Try np.logspace(1, 4, 20)
ss -- which smoothnesses should we run the experiment on
alpha -- the exponent for p
beta -- the exponent for q
d -- the dimension
iters -- how many iterations should we use
Returns nothing but writes log files with the results of the experiments to ./data/
"""
E = None
if est_type == "plugin":
E = estimators.PluginEstimator
elif est_type == "linear":
E = estimators.LinearEstimator
elif est_type == "quadratic":
E = estimators.QuadraticEstimator
else:
print "Estimator %s not supported" % (est_type)
return
for s in ss:
print "s = %s" % (str(s))
if d == 1:
Dp = density.UniTrigDensity(s, 1)
Dq = density.UniTrigDensity(s, 1)
else:
Dp = density.TrigDensity(s, 1, d)
Dq = density.TrigDensity(s, 1, d)
(new_ns, ms, vs) = rates.estimator_rate(E,
Dp,
Dq,
ns,
alpha=alpha,
beta=beta,
iters=iters,
fast=fast)
f = open("./data/%s_error_d=%d_s=%s.out" % (est_type, d, str(s)), "w")
f.write("ns " + " ".join([str(n) for n in ns]) + "\n")
f.write("ms " + " ".join([str(m) for m in ms]) + "\n")
f.write("vs " + " ".join([str(v) for v in vs]))
f.close()
return
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
if __name__ == '__main__':
print "Generating two uni-trig-densities"
Dp = density.UniTrigDensity(2, 2)
Dq = density.UniTrigDensity(2, 2)
alpha = 1
beta = 1
T = Truth(Dp, Dq, alpha, beta)
print "Numeric integration of true functional"
tr = T.eval(100)
print "T(p,q) approx %0.2f" % (tr)
pl_scores = []
lin_scores = []
for n in range(100, 1000, 100):
print "n = %d" % (n)
pl_sub_scores = []
lin_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)
if __name__ == '__main__':
D = density.UniTrigDensity(2, 2)
(ns, ms, vs) = test_linear_functional(D, np.logspace(1, 4, 20), iters=50)
plot_estimator_rate(ns, ms, vs, 0.5)
(m, b) = plot_log_log(ns, ms)
print m, b
# To rescale a rate of n^{-\gamma}, plot ns versus
# [np.exp(np.log(ms[i]) + gamma*np.log(ns[i])) for i in range(len(ns))]
# And you should see the constant \gamma come out.
# To empirically verify the parameter \gamma, plot ns versus
# [- np.log(ms[i])/np.log(ns[i]) for i in range(len(ns))]
# And you should see the line approach \gamma.
"""
assert False, "Deprecated"
coords = np.matrix(np.arange(0, 1, 0.01)).T
vals = self.eval(coords)
truth = true_p.eval(coords).reshape(coords.shape[0],)
return 1.0/coords.shape[0]* np.linalg.norm(np.array(vals-truth)[0,:], ord=p_norm)**p_norm
if __name__=='__main__':
do_one_d = True
do_two_d = False #True
n = 10000
s = 2
if do_one_d:
print "One dimensional example"
D = density.UniTrigDensity(s, 10)
print "Sampling %d samples from univariate density" % (n)
data = D.sample(n)
K = KDE(data, s)
pts = np.matrix(np.arange(0, 1.0, 0.001)).T
print "Evaluating KDE on %d points" % (pts.shape[0])
vals = K.eval(pts)
fig = plt.figure(1, figsize=(10, 5))
ax1 = fig.add_subplot(131)
D.plot_fn(ax=ax1)
plt.axis((0,1,0, 1.25));