def compare_algorithms():
x = np.ones((10, 10))
x[:, 5:] = -1
x_noisy = x + np.random.normal(0, 1.8, size=x.shape)
inds = np.arange(x.size).reshape(x.shape).astype(np.int64)
horz = np.c_[inds[:, :-1].ravel(), inds[:, 1:].ravel()]
vert = np.c_[inds[:-1, :].ravel(), inds[1:, :].ravel()]
edges = np.vstack([horz, vert])
#unaries = 2 * x_thresh.astype(np.float).ravel() - 1
unaries = x_noisy.ravel()
unaries = np.c_[np.exp(-unaries), np.exp(unaries)]
pairwise = np.exp(np.eye(2) * 4.1)
# repeat pairwise for each edge
pairwise = np.repeat(pairwise[np.newaxis, :, :], len(edges), axis=0)
algorithms = ["maxprod", "gibbs", "jt", "trw", "treeep"]
fix, axes = plt.subplots(1, len(algorithms))
for ax, alg in zip(axes, algorithms):
result_mrf = mrf(unaries, edges, pairwise, verbose=1, alg=alg)
ax.matshow(result_mrf.reshape(x.shape))
ax.set_title(alg)
ax.set_xticks(())
ax.set_yticks(())
plt.show()
def compare_algorithms():
x = np.ones((10, 10))
x[:, 5:] = -1
x_noisy = x + np.random.normal(0, 1.8, size=x.shape)
inds = np.arange(x.size).reshape(x.shape).astype(np.int64)
horz = np.c_[inds[:, :-1].ravel(), inds[:, 1:].ravel()]
vert = np.c_[inds[:-1, :].ravel(), inds[1:, :].ravel()]
edges = np.vstack([horz, vert])
#unaries = 2 * x_thresh.astype(np.float).ravel() - 1
unaries = x_noisy.ravel()
unaries = np.c_[np.exp(-unaries), np.exp(unaries)]
pairwise = np.exp(np.eye(2) * 4.1)
# repeat pairwise for each edge
pairwise = np.repeat(pairwise[np.newaxis, :, :], len(edges), axis=0)
algorithms = ["maxprod", "gibbs", "jt", "trw", "treeep"]
fix, axes = plt.subplots(1, len(algorithms))
for ax, alg in zip(axes, algorithms):
result_mrf = mrf(unaries, edges, pairwise, verbose=1, alg=alg)
ax.matshow(result_mrf.reshape(x.shape))
ax.set_title(alg)
ax.set_xticks(())
ax.set_yticks(())
plt.show()
def predict(self, X_prob, blocks):
"""
X_prob: X_prob[i,j] is the probability that phone i has label j.
blocks: X_prob[blocks == i] is sentence i
Returns X_decoded which is a (1d) label vector where X_decoded[i] is
the label assigned to phone i by viterbi decoding.
The model used for decoding a sentence with n phones is a CRF with the
following structure:
/-------+-------+------------ Edge potentials from language model (this object)
| | |
v v v
X_1 --- X_2 --- ... --- X_n <-- P(X_n=j | Y_n) provided in X_prob
^ ^ ^
| | |
P_1 P_2 P_n <-- Phone observations (never seen by this model)
Decoding is done separately for each sentence. The potentials for each
X_i -- X_{i+1} edge are the same.
"""
# upper bound on sentence length, +10 because I'm too lazy to think about off-by-1 errors.
max_sentence_length = np.max(np.diff(
np.nonzero(np.diff(blocks) != 0))) + 10
# Construct the edges and pairwise potentials for a chain CRF.
# We construct the largest CRF we'll need here, and use sections of the chain for shorter sentences.
edges = np.arange(max_sentence_length)
edges = np.c_[edges[:-1], edges[1:]]
pairwise = np.repeat(self.Q[np.newaxis, :, :],
max_sentence_length,
axis=0)
decoded_labels = []
for X_prob_sent in iterator.blocks(X_prob, blocks):
sentence_length = X_prob_sent.shape[0]
decoded = daicrf.mrf(X_prob_sent.astype(np.float),
edges[:sentence_length - 1],
pairwise[:sentence_length - 1, :, ],
verbose=0,
alg='jt')
decoded_labels.append(decoded)
X_decoded = np.concatenate(decoded_labels)
return X_decoded
def predict(self, X_prob, blocks):
"""
X_prob: X_prob[i,j] is the probability that phone i has label j.
blocks: X_prob[blocks == i] is sentence i
Returns X_decoded which is a (1d) label vector where X_decoded[i] is
the label assigned to phone i by viterbi decoding.
The model used for decoding a sentence with n phones is a CRF with the
following structure:
/-------+-------+------------ Edge potentials from language model (this object)
| | |
v v v
X_1 --- X_2 --- ... --- X_n <-- P(X_n=j | Y_n) provided in X_prob
^ ^ ^
| | |
P_1 P_2 P_n <-- Phone observations (never seen by this model)
Decoding is done separately for each sentence. The potentials for each
X_i -- X_{i+1} edge are the same.
"""
# upper bound on sentence length, +10 because I'm too lazy to think about off-by-1 errors.
max_sentence_length = np.max(np.diff(np.nonzero(np.diff(blocks) != 0))) + 10
# Construct the edges and pairwise potentials for a chain CRF.
# We construct the largest CRF we'll need here, and use sections of the chain for shorter sentences.
edges = np.arange(max_sentence_length)
edges = np.c_[edges[:-1], edges[1:]]
pairwise = np.repeat(self.Q[np.newaxis,:,:], max_sentence_length, axis=0)
decoded_labels = []
for X_prob_sent in iterator.blocks(X_prob, blocks):
sentence_length = X_prob_sent.shape[0]
decoded = daicrf.mrf(
X_prob_sent.astype(np.float),
edges[:sentence_length-1],
pairwise[:sentence_length-1,:,],
verbose=0,
alg='jt')
decoded_labels.append(decoded)
X_decoded = np.concatenate(decoded_labels)
return X_decoded
def example_binary():
x = np.ones((10, 10))
x[:, 5:] = -1
x_noisy = x + np.random.normal(0, .8, size=x.shape)
x_thresh = x_noisy > .0
fig, axes = plt.subplots(1, 5)
axes[0].set_title("Original")
axes[0].matshow(x)
axes[1].set_title("binary")
axes[1].matshow(x_noisy)
axes[2].set_title("thresholded")
axes[2].matshow(x_thresh)
inds = np.arange(x.size).reshape(x.shape).astype(np.int64)
horz = np.c_[inds[:, :-1].ravel(), inds[:, 1:].ravel()]
vert = np.c_[inds[:-1, :].ravel(), inds[1:, :].ravel()]
edges = np.vstack([horz, vert])
#unaries = 2 * x_thresh.astype(np.float).ravel() - 1
unaries = x_noisy.ravel()
unaries = np.c_[np.exp(-unaries), np.exp(unaries)]
axes[3].set_title("Potts MRF")
result = potts_mrf(unaries, edges, 1.1, verbose=1)
axes[3].matshow(result.reshape(x.shape))
# repeat pairwise for each edge
pairwise = np.exp(np.eye(2) * 1.1)
pairwise = np.repeat(pairwise[np.newaxis, :, :], len(edges), axis=0)
result_mrf = mrf(unaries, edges, pairwise, verbose=1, alg="trw")
axes[4].set_title("MRF")
axes[4].matshow(result_mrf.reshape(x.shape))
for ax in axes:
ax.set_xticks(())
ax.set_yticks(())
plt.show()
def example_binary():
x = np.ones((10, 10))
x[:, 5:] = -1
x_noisy = x + np.random.normal(0, .8, size=x.shape)
x_thresh = x_noisy > .0
fig, axes = plt.subplots(1, 5)
axes[0].set_title("Original")
axes[0].matshow(x)
axes[1].set_title("binary")
axes[1].matshow(x_noisy)
axes[2].set_title("thresholded")
axes[2].matshow(x_thresh)
inds = np.arange(x.size).reshape(x.shape).astype(np.int64)
horz = np.c_[inds[:, :-1].ravel(), inds[:, 1:].ravel()]
vert = np.c_[inds[:-1, :].ravel(), inds[1:, :].ravel()]
edges = np.vstack([horz, vert])
#unaries = 2 * x_thresh.astype(np.float).ravel() - 1
unaries = x_noisy.ravel()
unaries = np.c_[np.exp(-unaries), np.exp(unaries)]
axes[3].set_title("Potts MRF")
result = potts_mrf(unaries, edges, 1.1, verbose=1)
axes[3].matshow(result.reshape(x.shape))
# repeat pairwise for each edge
pairwise = np.exp(np.eye(2) * 1.1)
pairwise = np.repeat(pairwise[np.newaxis, :, :], len(edges), axis=0)
result_mrf = mrf(unaries, edges, pairwise, verbose=1, alg="trw")
axes[4].set_title("MRF")
axes[4].matshow(result_mrf.reshape(x.shape))
for ax in axes:
ax.set_xticks(())
ax.set_yticks(())
plt.show()
def example_multinomial():
np.random.seed(45)
unaries = np.zeros((10, 12, 3))
unaries[:, :4, 0] = 1
unaries[:, 4:8, 1] = 1
unaries[:, 8:, 2] = 1
x = np.argmax(unaries, axis=2)
unaries_noisy = unaries + np.random.normal(size=unaries.shape)
x_thresh = np.argmax(unaries_noisy, axis=2)
unaries_noisy = np.exp(unaries_noisy).reshape(-1, 3)
inds = np.arange(x.size).reshape(x.shape).astype(np.int64)
horz = np.c_[inds[:, :-1].ravel(), inds[:, 1:].ravel()]
vert = np.c_[inds[:-1, :].ravel(), inds[1:, :].ravel()]
edges = np.vstack([horz, vert])
result = potts_mrf(unaries_noisy, edges, 1.1)
pairwise = np.eye(3) + np.ones((1, 1))
pairwise[-1, 0] = 0
pairwise[0, -1] = 0
print(pairwise)
# repeat pairwise for each edge
pairwise = np.repeat(pairwise[np.newaxis, :, :], len(edges), axis=0)
result_mrf = mrf(unaries_noisy, edges, np.exp(pairwise), alg="jt")
plot, axes = plt.subplots(1, 4)
axes[0].set_title("original")
axes[0].matshow(x)
axes[1].set_title("thresholded")
axes[1].matshow(x_thresh)
axes[1].set_title("Potts MRF")
axes[2].matshow(result.reshape(x.shape))
axes[1].set_title("MRF")
axes[3].matshow(result_mrf.reshape(x.shape))
for ax in axes:
ax.set_xticks(())
ax.set_yticks(())
plt.show()
def example_multinomial():
np.random.seed(45)
unaries = np.zeros((10, 12, 3))
unaries[:, :4, 0] = 1
unaries[:, 4:8, 1] = 1
unaries[:, 8:, 2] = 1
x = np.argmax(unaries, axis=2)
unaries_noisy = unaries + np.random.normal(size=unaries.shape)
x_thresh = np.argmax(unaries_noisy, axis=2)
unaries_noisy = np.exp(unaries_noisy).reshape(-1, 3)
inds = np.arange(x.size).reshape(x.shape).astype(np.int64)
horz = np.c_[inds[:, :-1].ravel(), inds[:, 1:].ravel()]
vert = np.c_[inds[:-1, :].ravel(), inds[1:, :].ravel()]
edges = np.vstack([horz, vert])
result = potts_mrf(unaries_noisy, edges, 1.1)
pairwise = np.eye(3) + np.ones((1, 1))
pairwise[-1, 0] = 0
pairwise[0, -1] = 0
print(pairwise)
# repeat pairwise for each edge
pairwise = np.repeat(pairwise[np.newaxis, :, :], len(edges), axis=0)
result_mrf = mrf(unaries_noisy, edges, np.exp(pairwise), alg="jt")
plot, axes = plt.subplots(1, 4)
axes[0].set_title("original")
axes[0].matshow(x)
axes[1].set_title("thresholded")
axes[1].matshow(x_thresh)
axes[1].set_title("Potts MRF")
axes[2].matshow(result.reshape(x.shape))
axes[1].set_title("MRF")
axes[3].matshow(result_mrf.reshape(x.shape))
for ax in axes:
ax.set_xticks(())
ax.set_yticks(())
plt.show()
def example():
img1 = np.asarray(Image.open("scene1.row3.col1.ppm")) / 255.
img2 = np.asarray(Image.open("scene1.row3.col2.ppm")) / 255.
img1 = img1[180:220, 80:120]
img2 = img2[180:220, 80:120]
unaries = (stereo_unaries(img1, img2) * 100).astype(np.int32)
n_disps = unaries.shape[2]
pairwise = .10 * np.eye(n_disps)
newshape = unaries.shape[:2]
x, y = np.ogrid[:n_disps, :n_disps]
#one_d_topology = 5 * np.abs(x - y).astype(np.int32).copy("C")
# libdai works in exp space
pairwise_exp = np.exp(pairwise)
# build edges for max product inference:
inds = np.arange(np.prod(newshape)).reshape(newshape).astype(np.int64)
horz = np.c_[inds[:, :-1].ravel(), inds[:, 1:].ravel()]
vert = np.c_[inds[:-1, :].ravel(), inds[1:, :].ravel()]
edges = np.vstack([horz, vert]).copy()
#asdf = np.random.permutation(len(edges))
#edges = edges[asdf]
start = time()
max_product = mrf(np.exp(-unaries.reshape(-1, n_disps)),
edges,
pairwise_exp,
alg='maxprod')
time_maxprod = time() - start
energy_max_prod = energy(unaries, max_product.reshape(newshape), -pairwise)
start = time()
trw = mrf(np.exp(-unaries.reshape(-1, n_disps)),
edges,
pairwise_exp,
alg='trw')
time_trw = time() - start
energy_trw = energy(unaries, trw, -pairwise)
start = time()
treeep = mrf(np.exp(-unaries.reshape(-1, n_disps)),
edges,
pairwise,
alg='treeep')
time_treeep = time() - start
energy_treeep = energy(unaries, treeep.reshape(newshape), -pairwise)
start = time()
gibbs = mrf(np.exp(-unaries.reshape(-1, n_disps)),
edges,
pairwise_exp,
alg='gibbs')
time_gibbs = time() - start
energy_gibbs = energy(unaries, gibbs.reshape(newshape), -pairwise)
fix, axes = plt.subplots(3, 3, figsize=(16, 8))
energy_argmax = energy(unaries, np.argmin(unaries, axis=2), -pairwise)
#energies = np.array([energy_argmax, energy_gibbs, energy_max_prod,
#energy_treeep, energy_trw])
#(energy_argmax, energy_gibbs, energy_qpbo,
#energy_max_prod, energy_treep, energy_trw) = energies - energy_gc
axes[0, 0].imshow(img1)
axes[0, 1].imshow(img2)
axes[0, 2].set_title("unaries only e=%f" % (energy_argmax))
axes[0, 2].matshow(np.argmin(unaries, axis=2), vmin=0, vmax=8)
axes[1, 0].set_title("treeep %.2fs, e=%f" % (time_treeep, energy_treeep))
axes[1, 0].matshow(treeep.reshape(newshape), vmin=0, vmax=8)
axes[1, 2].set_title("max-product %.2fs, e=%f" %
(time_maxprod, energy_max_prod))
axes[1, 2].matshow(max_product.reshape(newshape), vmin=0, vmax=8)
axes[2, 0].set_title("trw %.2fs, e=%f" % (time_trw, energy_trw))
axes[2, 0].matshow(trw.reshape(newshape), vmin=0, vmax=8)
axes[2, 2].set_title("gibbs %.2fs, e=%f" % (time_gibbs, energy_gibbs))
axes[2, 2].matshow(gibbs.reshape(newshape), vmin=0, vmax=8)
for ax in axes.ravel():
ax.set_xticks(())
ax.set_yticks(())
plt.tight_layout()
plt.show()
edges = np.arange(max_sentence_length)
edges = np.c_[edges[:-1], edges[1:]]
pairwise = np.repeat(bigram.Q[np.newaxis,:,:], max_sentence_length, axis=0) + 1e-6
def _block_iterator(X, blocks):
for i in xrange(blocks.max()+1):
yield X[blocks == i]
decoded_labels = []
for Y_sent in _block_iterator(Y, timit_test.sentence_ids):
#print Y_sent.sum()
#print ".",
sentence_length = Y_sent.shape[0]
decoded = daicrf.mrf(
Y_sent.astype(np.float),
edges[:sentence_length-1],
pairwise[:sentence_length-1,:,],
verbose=0,
alg='jt')
decoded_labels.append(decoded)
#if len(decoded_labels) > 5:
# break
print ""
Y_decoded = np.equal.outer(
np.concatenate(decoded_labels),
np.arange(timit_test.y.shape[1]))
Y_decoded_folded = np.equal.outer(
np.argmax(np.dot(Y_decoded, F), axis=1),
np.arange(F.shape[1]))
def example():
img1 = np.asarray(Image.open("scene1.row3.col1.ppm")) / 255.
img2 = np.asarray(Image.open("scene1.row3.col2.ppm")) / 255.
img1 = img1[180:220, 80:120]
img2 = img2[180:220, 80:120]
unaries = (stereo_unaries(img1, img2) * 100).astype(np.int32)
n_disps = unaries.shape[2]
pairwise = .10 * np.eye(n_disps)
newshape = unaries.shape[:2]
x, y = np.ogrid[:n_disps, :n_disps]
#one_d_topology = 5 * np.abs(x - y).astype(np.int32).copy("C")
# libdai works in exp space
pairwise_exp = np.exp(pairwise)
# build edges for max product inference:
inds = np.arange(np.prod(newshape)).reshape(newshape).astype(np.int64)
horz = np.c_[inds[:, :-1].ravel(), inds[:, 1:].ravel()]
vert = np.c_[inds[:-1, :].ravel(), inds[1:, :].ravel()]
edges = np.vstack([horz, vert]).copy()
#asdf = np.random.permutation(len(edges))
#edges = edges[asdf]
start = time()
max_product = mrf(np.exp(-unaries.reshape(-1, n_disps)),
edges, pairwise_exp, alg='maxprod')
time_maxprod = time() - start
energy_max_prod = energy(unaries, max_product.reshape(newshape), -pairwise)
start = time()
trw = mrf(np.exp(-unaries.reshape(-1, n_disps)),
edges, pairwise_exp, alg='trw')
time_trw = time() - start
energy_trw = energy(unaries, trw, -pairwise)
start = time()
treeep = mrf(np.exp(-unaries.reshape(-1, n_disps)),
edges, pairwise, alg='treeep')
time_treeep = time() - start
energy_treeep = energy(unaries, treeep.reshape(newshape), -pairwise)
start = time()
gibbs = mrf(np.exp(-unaries.reshape(-1, n_disps)),
edges, pairwise_exp, alg='gibbs')
time_gibbs = time() - start
energy_gibbs = energy(unaries, gibbs.reshape(newshape), -pairwise)
fix, axes = plt.subplots(3, 3, figsize=(16, 8))
energy_argmax = energy(unaries, np.argmin(unaries, axis=2), -pairwise)
#energies = np.array([energy_argmax, energy_gibbs, energy_max_prod,
#energy_treeep, energy_trw])
#(energy_argmax, energy_gibbs, energy_qpbo,
#energy_max_prod, energy_treep, energy_trw) = energies - energy_gc
axes[0, 0].imshow(img1)
axes[0, 1].imshow(img2)
axes[0, 2].set_title("unaries only e=%f" % (energy_argmax))
axes[0, 2].matshow(np.argmin(unaries, axis=2), vmin=0, vmax=8)
axes[1, 0].set_title("treeep %.2fs, e=%f" % (time_treeep, energy_treeep))
axes[1, 0].matshow(treeep.reshape(newshape), vmin=0, vmax=8)
axes[1, 2].set_title("max-product %.2fs, e=%f"
% (time_maxprod, energy_max_prod))
axes[1, 2].matshow(max_product.reshape(newshape), vmin=0, vmax=8)
axes[2, 0].set_title("trw %.2fs, e=%f" % (time_trw, energy_trw))
axes[2, 0].matshow(trw.reshape(newshape), vmin=0, vmax=8)
axes[2, 2].set_title("gibbs %.2fs, e=%f" % (time_gibbs, energy_gibbs))
axes[2, 2].matshow(gibbs.reshape(newshape), vmin=0, vmax=8)
for ax in axes.ravel():
ax.set_xticks(())
ax.set_yticks(())
plt.tight_layout()
plt.show()
