def _compute_ev_det_loglike(physics, event, det):
# load the station tuple and compute basic event-station attributes like
# distance, travel time, azimuth, and azimuth difference
stanum = det.stanum
station = STATIONS[stanum]
dist = compute_distance((station.lon, station.lat),
(event.lon, event.lat))
ttime = compute_travel_time(dist)
sta_to_ev_az = compute_azimuth((station.lon, station.lat),
(event.lon, event.lat))
# the azimuth difference of observed to theoretical
degdiff = compute_degdiff(sta_to_ev_az, det.azimuth)
loglike = 0
# detection probability
detprob = logistic(physics.mu_d0[stanum]
+ physics.mu_d1[stanum] * event.mag
+ physics.mu_d2[stanum] * dist)
loglike += log(detprob)
# detection time
loglike += laplace.logpdf(det.time,
event.time + ttime + physics.mu_t[stanum],
physics.theta_t[stanum])
# detection azimuth
loglike += laplace.logpdf(degdiff, physics.mu_z[stanum],
physics.theta_z[stanum])
# detection slowness
loglike += laplace.logpdf(det.slowness,
compute_slowness(dist) + physics.mu_s[stanum],
physics.theta_s[stanum])
# detection amplitude
loglike += norm.logpdf(log(det.amp),
physics.mu_a0[stanum]
+ physics.mu_a1[stanum] * event.mag
+ physics.mu_a2[stanum] * dist,
physics.sigma_a[stanum])
return loglike
def _compute_ev_det_loglike(physics, event, det):
# load the station tuple and compute basic event-station attributes like
# distance, travel time, azimuth, and azimuth difference
stanum = det.stanum
station = STATIONS[stanum]
dist = compute_distance((station.lon, station.lat), (event.lon, event.lat))
ttime = compute_travel_time(dist)
sta_to_ev_az = compute_azimuth((station.lon, station.lat),
(event.lon, event.lat))
# the azimuth difference of observed to theoretical
degdiff = compute_degdiff(sta_to_ev_az, det.azimuth)
loglike = 0
# detection probability
detprob = logistic(physics.mu_d0[stanum] +
physics.mu_d1[stanum] * event.mag +
physics.mu_d2[stanum] * dist)
loglike += log(detprob)
# detection time
loglike += laplace.logpdf(det.time,
event.time + ttime + physics.mu_t[stanum],
physics.theta_t[stanum])
# detection azimuth
loglike += laplace.logpdf(degdiff, physics.mu_z[stanum],
physics.theta_z[stanum])
# detection slowness
loglike += laplace.logpdf(det.slowness,
compute_slowness(dist) + physics.mu_s[stanum],
physics.theta_s[stanum])
# detection amplitude
loglike += norm.logpdf(
log(det.amp), physics.mu_a0[stanum] +
physics.mu_a1[stanum] * event.mag + physics.mu_a2[stanum] * dist,
physics.sigma_a[stanum])
return loglike
def _log_likelihood(self, y, X, beta):
"""
Overwrites the _log_likelihood method inherited from the RegressorMCMC
class to calculate the log-likelihood of the linear regression
coefficients given normally-distributed data. It is used in the
model fitting process.
Parameters
----------
y : numpy array
A 1-D vector of 0s and 1s representing the two classes.
X : numpy array
A 2-D matrix where rows represent observations and columns
represent variables.
beta : numpy array
A 1-D vector of coefficients in a logistic regression model.
Returns
-------
_log_likelihood : float
The log-likelihood of the beta vector given the data.
"""
# Predict y given the current coefficients and X.
predicted_y = np.matmul(X, beta)
# Calculate the log-likelihood of beta given the data.
_log_likelihood = np.sum(laplace.logpdf(y,
loc=predicted_y,
scale=self._y_scale))
return _log_likelihood
def test_scipy(self):
x = [8, 9]
if SP:
assert_almost_equal(
laplace.logpdf(x, loc=self.parameters['mu'], scale=1./self.parameters['tau']).sum(),
laplace_like(x, **self.parameters)
)
def test_scipy(self):
x = [8, 9]
if SP:
assert_almost_equal(
laplace.logpdf(x,
loc=self.parameters['mu'],
scale=1. / self.parameters['tau']).sum(),
laplace_like(x, **self.parameters))
def test_logprob(self):
mu = Variable(torch.randn(100))
b = torch.exp(Variable(torch.randn(100)))
value = Variable(torch.randn(100))
dist = Laplace(mu, b)
# test log probability
res1 = dist.log_prob(value).data
res2 = laplace.logpdf(value.data.numpy(), mu.data.numpy(),
b.data.numpy())
self.assertEqual(res1, res2)
def test_log_pdf(self, dtype, location, location_is_samples, scale,
scale_is_samples, rv, rv_is_samples, num_samples):
is_samples_any = any(
[location_is_samples, scale_is_samples, rv_is_samples])
rv_shape = rv.shape[1:] if rv_is_samples else rv.shape
n_dim = 1 + len(
rv.shape) if is_samples_any and not rv_is_samples else len(
rv.shape)
location_np = numpy_array_reshape(location, location_is_samples, n_dim)
scale_np = numpy_array_reshape(scale, scale_is_samples, n_dim)
rv_np = numpy_array_reshape(rv, rv_is_samples, n_dim)
log_pdf_np = laplace.logpdf(rv_np, location_np, scale_np)
var = Laplace.define_variable(shape=rv_shape, dtype=dtype).factor
location_mx = mx.nd.array(location, dtype=dtype)
if not location_is_samples:
location_mx = add_sample_dimension(mx.nd, location_mx)
var_mx = mx.nd.array(scale, dtype=dtype)
if not scale_is_samples:
var_mx = add_sample_dimension(mx.nd, var_mx)
rv_mx = mx.nd.array(rv, dtype=dtype)
if not rv_is_samples:
rv_mx = add_sample_dimension(mx.nd, rv_mx)
variables = {
var.location.uuid: location_mx,
var.scale.uuid: var_mx,
var.random_variable.uuid: rv_mx
}
log_pdf_rt = var.log_pdf(F=mx.nd, variables=variables)
assert np.issubdtype(log_pdf_rt.dtype, dtype)
assert array_has_samples(mx.nd, log_pdf_rt) == is_samples_any
if is_samples_any:
assert get_num_samples(mx.nd, log_pdf_rt) == num_samples
if np.issubdtype(dtype, np.float64):
rtol, atol = 1e-7, 1e-10
else:
rtol, atol = 1e-4, 1e-5
assert np.allclose(log_pdf_np,
log_pdf_rt.asnumpy(),
rtol=rtol,
atol=atol)
def __call__(self, u: np.ndarray, y: float) -> np.ndarray:
return laplace.logpdf(x=u, loc=y, scale=self.scale)
def _logp(self, value, loc, scale, k):
return np.sum(laplace.logpdf(value, loc=loc, scale=scale))
def main(argv):
### PLOT BASIS VECTOR NORMS
subplot(0, 0, spacing=1.)
legend_entries = []
for model in models:
results = Experiment(model['path'])
isa = results['model'].model[1].model
dct = results['model'].transforms[0]
# basis in whitened pixel space
A = dot(dct.A[1:].T, isa.A)
# basis vector norms
norms = sort(sqrt(sum(square(A), 0)))[::-1]
plot(norms,
color=model['color'],
line_width=1.2)
plot([len(norms), len(norms) + 1, 255], [norms[-1], 0, 0],
color=model['color'],
line_style='densely dashed',
line_width=1.2,
pgf_options=['forget plot'])
legend_entries.append(model['legend'])
xlabel('Basis coefficient, $i$')
ylabel('Basis vector norm, $||a_i||$')
legend(*legend_entries, location='north east')
axis(width=5, height=4)
axis([0, 256, 0, 1])
xtick([64, 128, 192, 256])
grid()
### VISUALIZE BASIS
subplot(0, 1)
results = Experiment(model['path'])
isa = results['model'].model[1].model
dct = results['model'].transforms[0]
# basis in whitened pixel space
A = dot(dct.A[1:].T, isa.A)
indices = argsort(sqrt(sum(square(A), 0)))[::-1]
A = A[:, indices]
# adjust intensity range
a = percentile(abs(A).ravel(), PERC)
A = (A + a) / (2. * a) * 255. + 0.5
A[A < 0.] = 0.5
A[A > 256.] = 255.5
A = asarray(A, 'uint8')
# stitch together into a single image
patch_size = int(sqrt(A.shape[0]) + 0.5)
patches = stitch(A.T.reshape(-1, patch_size, patch_size), num_cols=NUM_COLS)
patches = repeat(repeat(patches, RES, 0), RES, 1)
imshow(patches, dpi=75 * RES)
rectangle(72 * RES, 80.8 * RES, 64 * RES, 55.2 * RES,
color=RGB(1.0, 0.8, 0.5),
line_width=1.,
line_style='densely dashed')
axis(
height=4,
width=4,
ticks='none',
axis_on_top=False,
clip=False,
pgf_options=['xlabel style={yshift=-0.47cm}', 'clip=false'])
savefig('results/vanhateren/overcompleteness.tex')
draw()
### MARGINAL SOURCE DISTRIBUTIONS
figure()
samples = []
for gsm in isa.subspaces:
samples.append(gsm.sample(1000))
perc = percentile(hstack(samples), 99.5)
xvals = linspace(-perc, perc, 100)
for i in range(1, 7):
for j in range(8, 15):
try:
gsm = isa.subspaces[indices[i * NUM_COLS + j]]
except:
pass
else:
subplot(7 - i, j, spacing=0)
plot(xvals, laplace.logpdf(xvals, scale=sqrt(0.5)).ravel(), line_width=0.8, color=RGB(0.1, 0.6, 1.0))
plot(xvals, gsm.loglikelihood(xvals.reshape(1, -1)).ravel(), 'k', line_width=1.)
gca().width = 4. / 6.
gca().height = 4. / 6.
axis([-perc, perc, -6., 2.])
xtick([])
ytick([])
savefig('results/vanhateren/marginals.tex')
draw()
return 0
def main(argv):
experiment = Experiment(argv[1])
isa = experiment['model'].model[1].model
dct = experiment['model'].transforms[0]
### BASIS
# basis in pixel space
A = dot(dct.A[1:].T, isa.A)
# sort by norm
norms = sqrt(sum(square(A), 0))
indices = argsort(norms)[::-1]
# A = A[:, indices]
# adjust intensity range
a = percentile(abs(A).ravel(), PERC)
A = (A + a) / (2. * a) * 255. + 0.5
A[A < 0.] = 0.5
A[A > 256.] = 255.5
A = asarray(A, 'uint8')
# stitch together into a single image
patch_size = int(sqrt(A.shape[0]) + 0.5)
patches = stitch(A.T.reshape(-1, patch_size, patch_size), num_cols=NUM_COLS)
patches = repeat(repeat(patches, RES, 0), RES, 1)
imshow(patches, dpi=75 * RES)
axis('off')
draw()
### SAMPLES
samples = experiment['model'].sample(128)
a = percentile(abs(samples).ravel(), PERC)
samples = (samples + a) / (2. * a) * 255. + 0.5
samples[samples < 0.] = 0.5
samples[samples > 256.] = 255.5
samples = asarray(samples, 'uint8')
samples = stitch(samples.T.reshape(-1, patch_size, patch_size))
samples = repeat(repeat(samples, RES, 0), RES, 1)
# visualize samples
figure()
imshow(samples, dpi=75 * RES)
title('Samples')
axis('off')
draw()
### MARGINAL SOURCE DISTRIBUTIONS
figure()
samples = []
for gsm in isa.subspaces:
samples.append(gsm.sample(1000))
perc = percentile(hstack(samples), 99.5)
xvals = linspace(-perc, perc, 100)
for i in range(0, 8):
for j in range(0, 16):
try:
gsm = isa.subspaces[indices[i * NUM_COLS + j]]
except:
pass
else:
subplot(7 - i, j, spacing=0)
plot(xvals, laplace.logpdf(xvals, scale=sqrt(0.5)).ravel(), 'k', opacity=0.5)
plot(xvals, gsm.loglikelihood(xvals.reshape(1, -1)).ravel(), 'b-', line_width=1.)
gca().width = 0.8
gca().height = 0.8
axis([-perc, perc, -6., 2.])
xtick([])
ytick([])
draw()
return 0
def main(argv):
### PLOT BASIS VECTOR NORMS
subplot(0, 0, spacing=1.)
legend_entries = []
for model in models:
results = Experiment(model['path'])
isa = results['model'].model[1].model
dct = results['model'].transforms[0]
# basis in whitened pixel space
A = dot(dct.A[1:].T, isa.A)
# basis vector norms
norms = sort(sqrt(sum(square(A), 0)))[::-1]
plot(norms, color=model['color'], line_width=1.2)
plot([len(norms), len(norms) + 1, 255], [norms[-1], 0, 0],
color=model['color'],
line_style='densely dashed',
line_width=1.2,
pgf_options=['forget plot'])
legend_entries.append(model['legend'])
xlabel('Basis coefficient, $i$')
ylabel('Basis vector norm, $||a_i||$')
legend(*legend_entries, location='north east')
axis(width=5, height=4)
axis([0, 256, 0, 1])
xtick([64, 128, 192, 256])
grid()
### VISUALIZE BASIS
subplot(0, 1)
results = Experiment(model['path'])
isa = results['model'].model[1].model
dct = results['model'].transforms[0]
# basis in whitened pixel space
A = dot(dct.A[1:].T, isa.A)
indices = argsort(sqrt(sum(square(A), 0)))[::-1]
A = A[:, indices]
# adjust intensity range
a = percentile(abs(A).ravel(), PERC)
A = (A + a) / (2. * a) * 255. + 0.5
A[A < 0.] = 0.5
A[A > 256.] = 255.5
A = asarray(A, 'uint8')
# stitch together into a single image
patch_size = int(sqrt(A.shape[0]) + 0.5)
patches = stitch(A.T.reshape(-1, patch_size, patch_size),
num_cols=NUM_COLS)
patches = repeat(repeat(patches, RES, 0), RES, 1)
imshow(patches, dpi=75 * RES)
rectangle(72 * RES,
80.8 * RES,
64 * RES,
55.2 * RES,
color=RGB(1.0, 0.8, 0.5),
line_width=1.,
line_style='densely dashed')
axis(height=4,
width=4,
ticks='none',
axis_on_top=False,
clip=False,
pgf_options=['xlabel style={yshift=-0.47cm}', 'clip=false'])
savefig('results/vanhateren/overcompleteness.tex')
draw()
### MARGINAL SOURCE DISTRIBUTIONS
figure()
samples = []
for gsm in isa.subspaces:
samples.append(gsm.sample(1000))
perc = percentile(hstack(samples), 99.5)
xvals = linspace(-perc, perc, 100)
for i in range(1, 7):
for j in range(8, 15):
try:
gsm = isa.subspaces[indices[i * NUM_COLS + j]]
except:
pass
else:
subplot(7 - i, j, spacing=0)
plot(xvals,
laplace.logpdf(xvals, scale=sqrt(0.5)).ravel(),
line_width=0.8,
color=RGB(0.1, 0.6, 1.0))
plot(xvals,
gsm.loglikelihood(xvals.reshape(1, -1)).ravel(),
'k',
line_width=1.)
gca().width = 4. / 6.
gca().height = 4. / 6.
axis([-perc, perc, -6., 2.])
xtick([])
ytick([])
savefig('results/vanhateren/marginals.tex')
draw()
return 0