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
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));
ax2 = fig.add_subplot(132)
D.plot_data_histogram(data, ax=ax2)
ax3 = fig.add_subplot(133)
ax3.plot(pts, vals)
plt.axis((0,1,0, 1.25));
if do_two_d:
print "Two dimensional example"
D = density.TrigDensity(s, 5, 2)
print "Sampling %d samples from 2-d density" % (n)
data = D.sample(n)
K = KDE(data, s)
t = 100
x = np.arange(0, 1, 1.0/t)
y = np.arange(0, 1, 1.0/t)
X,Y = np.meshgrid(x,y)
v = np.matrix(zip(X.reshape(t**2,), Y.reshape(t**2,)))
print "Evaluating KDE on %d points" % (len(x)*len(y))
z = K.eval(v)
z = np.array(z)
Z = z.reshape(len(x), len(y))