def test_ais_with_dbn(self):
dbn = DBN(RBM(10, 10))
dbn.add_layer(RBM(10, 20))
hidden_states = utils.binary_numbers(dbn[0].Y.shape[0])
ais = Estimator(dbn)
ais_logz = ais.estimate_log_partition_function(
100, np.sqrt(np.arange(0, 1, 0.001)))
brf_logz = utils.logsumexp(dbn[1]._ulogprob_vis(hidden_states))
brf_probs = []
dbn_probs = []
dbn_bound = []
for i in range(50):
sample = np.matrix(np.random.rand(10, 1)) > 0.5
prob, bound = ais.estimate_log_probability(sample, 200)
brf_probs.append(
utils.logsumexp(
dbn[1]._ulogprob_vis(hidden_states) +
dbn[0]._clogprob_vis_hid(sample, hidden_states), 1) -
brf_logz)
dbn_probs.append(prob)
dbn_bound.append(bound)
self.assertTrue(np.mean(dbn_bound) < np.mean(dbn_probs))
self.assertTrue(np.abs(np.mean(dbn_probs) - np.mean(brf_probs)) < 0.1)
def test_ais_with_dbn(self): dbn = DBN(RBM(10, 10)) dbn.add_layer(RBM(10, 20)) hidden_states = utils.binary_numbers(dbn[0].Y.shape[0]) ais = Estimator(dbn) ais_logz = ais.estimate_log_partition_function(100, np.sqrt(np.arange(0, 1, 0.001))) brf_logz = utils.logsumexp(dbn[1]._ulogprob_vis(hidden_states)) brf_probs = [] dbn_probs = [] dbn_bound = [] for i in range(50): sample = np.matrix(np.random.rand(10, 1)) > 0.5 prob, bound = ais.estimate_log_probability(sample, 200) brf_probs.append(utils.logsumexp(dbn[1]._ulogprob_vis(hidden_states) + dbn[0]._clogprob_vis_hid(sample, hidden_states), 1) - brf_logz) dbn_probs.append(prob) dbn_bound.append(bound) self.assertTrue(np.mean(dbn_bound) < np.mean(dbn_probs)) self.assertTrue(np.abs(np.mean(dbn_probs) - np.mean(brf_probs)) < 0.1)
def test_ais_with_dbn_sanity_check(self):
dbn = DBN(RBM(5, 20))
dbn.add_layer(RBM(20, 5))
dbn.add_layer(RBM(5, 20))
dbn[0].W = np.matrix(np.random.randn(5, 20))
dbn[0].b = np.matrix(np.random.rand(5, 1) - 0.5)
dbn[0].c = np.matrix(np.random.rand(20, 1) - 0.5)
dbn[1].W = dbn[0].W.T
dbn[1].b = dbn[0].c
dbn[1].c = dbn[0].b
dbn[2].W = dbn[0].W
dbn[2].b = dbn[0].b
dbn[2].c = dbn[0].c
samples = dbn.sample(100)
ais = Estimator(dbn[0])
rbm_logz = ais.estimate_log_partition_function(
100, np.sqrt(np.arange(0, 1, 0.001)))
rbm_probs = ais.estimate_log_probability(samples)
ais = Estimator(dbn)
dbn_logz = ais.estimate_log_partition_function(
100, np.sqrt(np.arange(0, 1, 0.001)))
dbn_probs = ais.estimate_log_probability(samples)
self.assertTrue(abs(dbn_logz - rbm_logz) / rbm_logz < 0.02)
self.assertTrue((np.exp(dbn_probs) - np.exp(rbm_probs)).mean() < 0.02)
def test_ais_with_semirbm_sanity_check(self):
grbm = GaussianRBM(15, 50)
grbm.b = np.random.randn(grbm.b.shape[0], 1)
grbm.c = np.random.randn(grbm.c.shape[0], 1)
srbm = SemiRBM(50, 20)
srbm.W = srbm.W * 0.
srbm.c = srbm.c * 0.
srbm.L = grbm.W.T * grbm.W
srbm.b = grbm.W.T * grbm.b + grbm.c + 0.5 * np.matrix(np.diag(
srbm.L)).T
srbm.L = srbm.L - np.matrix(np.diag(np.diag(srbm.L)))
ais = Estimator(grbm)
ais.estimate_log_partition_function(num_ais_samples=100,
beta_weights=np.arange(0, 1, 1E-3))
ais = Estimator(srbm)
ais.estimate_log_partition_function(num_ais_samples=100,
beta_weights=np.arange(0, 1, 1E-2))
glogz = grbm._ais_logz + srbm.Y.shape[0] * np.log(2)
slogz = srbm._ais_logz + grbm.X.shape[0] * np.log(np.sqrt(2 * np.pi))
self.assertTrue(np.abs(glogz - slogz) < 1.)
def test_ais_with_rbm(self): rbm = RBM(5, 20) rbm.W = np.matrix(np.random.randn(5, 20)) rbm.b = np.matrix(np.random.randn(5, 1)) rbm.c = np.matrix(np.random.randn(20, 1)) ais = Estimator(rbm) ais_logz = ais.estimate_log_partition_function(100, np.arange(0, 1, 0.001)) brf_logz = utils.logsumexp(rbm._ulogprob_vis(utils.binary_numbers(rbm.X.shape[0]))) lower = np.log(np.exp(ais_logz) - 4. * np.sqrt(rbm._ais_var)) upper = np.log(np.exp(ais_logz) + 4. * np.sqrt(rbm._ais_var)) self.assertTrue(upper - lower < 1.) self.assertTrue(lower < brf_logz and brf_logz < upper)
def test_ais_with_gaussianrbm(self): rbm = GaussianRBM(30, 10) rbm.c = np.matrix(np.random.randn(10, 1)) rbm.W = np.matrix(np.random.randn(30, 10)) rbm.b = np.matrix(np.random.rand(30, 1)) ais = Estimator(rbm) ais_logz = ais.estimate_log_partition_function(100, np.arange(0., 1., 1E-4)) brf_logz = utils.logsumexp(rbm._ulogprob_hid(utils.binary_numbers(rbm.Y.shape[0]))) lower = np.log(np.exp(ais_logz) - 4 * np.sqrt(rbm._ais_var)) upper = np.log(np.exp(ais_logz) + 4 * np.sqrt(rbm._ais_var)) self.assertTrue(upper - lower < 1.5) self.assertTrue(lower < brf_logz and brf_logz < upper)
def test_ais_with_semirbm(self): rbm = SemiRBM(5, 20) rbm.L = np.matrix(np.random.randn(5, 5)) rbm.L = np.triu(rbm.L) + np.triu(rbm.L).T - 2 * np.diag(np.diag(rbm.L)) rbm.num_lateral_updates = 5 rbm.sampling_method = SemiRBM.GIBBS ais = Estimator(rbm) ais_logz = ais.estimate_log_partition_function(100, np.arange(0, 1, 0.001)) brf_logz = np.log(np.sum(np.exp(rbm._ulogprob_vis(utils.binary_numbers(rbm.X.shape[0]))))) lower = np.log(np.exp(ais_logz) - 4 * np.sqrt(rbm._ais_var)) upper = np.log(np.exp(ais_logz) + 4 * np.sqrt(rbm._ais_var)) self.assertTrue(upper - lower < 1.) self.assertTrue(lower < brf_logz and brf_logz < upper)
def test_ais_with_semirbm_dbn(self):
dbn = DBN(RBM(5, 5))
dbn.add_layer(SemiRBM(5, 5))
ais = Estimator(dbn)
ais.estimate_log_partition_function(100,
np.arange(0, 1, 1E-3),
layer=0)
ais.estimate_log_partition_function(10, np.arange(0, 1, 1E-3), layer=1)
dbn[0]._brf_logz = utils.logsumexp(dbn[0]._ulogprob_vis(
utils.binary_numbers(dbn[0].X.shape[0])))
dbn[1]._brf_logz = utils.logsumexp(dbn[1]._ulogprob_vis(
utils.binary_numbers(dbn[1].X.shape[0])))
samples = np.concatenate(
[dbn.sample(25, 100, 20),
np.matrix(np.random.rand(5, 25) > 0.5)], 1)
Y = utils.binary_numbers(dbn[0].Y.shape[0])
X = utils.binary_numbers(dbn[0].X.shape[0])
logRy = dbn[1]._ulogprob_vis(Y)
logQy = utils.logsumexp(dbn[0]._ulogprob(X, Y, all_pairs=True), 0)
log_sum = utils.logsumexp(
dbn[0]._clogprob_hid_vis(samples, Y, all_pairs=True) - logQy +
logRy, 1)
logPx = log_sum + dbn[0]._ulogprob_vis(samples) - dbn[1]._brf_logz
logPx_ = ais.estimate_log_probability(samples)[0]
self.assertTrue(np.abs(logPx_.mean() - logPx.mean()) < 0.1)
def test_ais_with_gaussianrbm(self):
rbm = GaussianRBM(30, 10)
rbm.c = np.matrix(np.random.randn(10, 1))
rbm.W = np.matrix(np.random.randn(30, 10))
rbm.b = np.matrix(np.random.rand(30, 1))
ais = Estimator(rbm)
ais_logz = ais.estimate_log_partition_function(100,
np.arange(0., 1., 1E-4))
brf_logz = utils.logsumexp(
rbm._ulogprob_hid(utils.binary_numbers(rbm.Y.shape[0])))
lower = np.log(np.exp(ais_logz) - 4 * np.sqrt(rbm._ais_var))
upper = np.log(np.exp(ais_logz) + 4 * np.sqrt(rbm._ais_var))
self.assertTrue(upper - lower < 1.5)
self.assertTrue(lower < brf_logz and brf_logz < upper)
def test_ais_with_rbm(self):
rbm = RBM(5, 20)
rbm.W = np.matrix(np.random.randn(5, 20))
rbm.b = np.matrix(np.random.randn(5, 1))
rbm.c = np.matrix(np.random.randn(20, 1))
ais = Estimator(rbm)
ais_logz = ais.estimate_log_partition_function(100,
np.arange(0, 1, 0.001))
brf_logz = utils.logsumexp(
rbm._ulogprob_vis(utils.binary_numbers(rbm.X.shape[0])))
lower = np.log(np.exp(ais_logz) - 4. * np.sqrt(rbm._ais_var))
upper = np.log(np.exp(ais_logz) + 4. * np.sqrt(rbm._ais_var))
self.assertTrue(upper - lower < 1.)
self.assertTrue(lower < brf_logz and brf_logz < upper)
def test_ais_with_semirbm(self):
rbm = SemiRBM(5, 20)
rbm.L = np.matrix(np.random.randn(5, 5))
rbm.L = np.triu(rbm.L) + np.triu(rbm.L).T - 2 * np.diag(np.diag(rbm.L))
rbm.num_lateral_updates = 5
rbm.sampling_method = SemiRBM.GIBBS
ais = Estimator(rbm)
ais_logz = ais.estimate_log_partition_function(100,
np.arange(0, 1, 0.001))
brf_logz = np.log(
np.sum(
np.exp(rbm._ulogprob_vis(utils.binary_numbers(
rbm.X.shape[0])))))
lower = np.log(np.exp(ais_logz) - 4 * np.sqrt(rbm._ais_var))
upper = np.log(np.exp(ais_logz) + 4 * np.sqrt(rbm._ais_var))
self.assertTrue(upper - lower < 1.)
self.assertTrue(lower < brf_logz and brf_logz < upper)
def test_ais_with_dbn_sanity_check(self): dbn = DBN(RBM(5, 20)) dbn.add_layer(RBM(20, 5)) dbn.add_layer(RBM(5, 20)) dbn[0].W = np.matrix(np.random.randn(5, 20)) dbn[0].b = np.matrix(np.random.rand(5, 1) - 0.5) dbn[0].c = np.matrix(np.random.rand(20, 1) - 0.5) dbn[1].W = dbn[0].W.T dbn[1].b = dbn[0].c dbn[1].c = dbn[0].b dbn[2].W = dbn[0].W dbn[2].b = dbn[0].b dbn[2].c = dbn[0].c samples = dbn.sample(100) ais = Estimator(dbn[0]) rbm_logz = ais.estimate_log_partition_function(100, np.sqrt(np.arange(0, 1, 0.001))) rbm_probs = ais.estimate_log_probability(samples) ais = Estimator(dbn) dbn_logz = ais.estimate_log_partition_function(100, np.sqrt(np.arange(0, 1, 0.001))) dbn_probs = ais.estimate_log_probability(samples) self.assertTrue(abs(dbn_logz - rbm_logz) / rbm_logz < 0.02) self.assertTrue((np.exp(dbn_probs) - np.exp(rbm_probs)).mean() < 0.02)
def test_ais_with_semirbm_sanity_check(self): grbm = GaussianRBM(15, 50) grbm.b = np.random.randn(grbm.b.shape[0], 1) grbm.c = np.random.randn(grbm.c.shape[0], 1) srbm = SemiRBM(50, 20) srbm.W = srbm.W * 0. srbm.c = srbm.c * 0. srbm.L = grbm.W.T * grbm.W srbm.b = grbm.W.T * grbm.b + grbm.c + 0.5 * np.matrix(np.diag(srbm.L)).T srbm.L = srbm.L - np.matrix(np.diag(np.diag(srbm.L))) ais = Estimator(grbm) ais.estimate_log_partition_function(num_ais_samples=100, beta_weights=np.arange(0, 1, 1E-3)) ais = Estimator(srbm) ais.estimate_log_partition_function(num_ais_samples=100, beta_weights=np.arange(0, 1, 1E-2)) glogz = grbm._ais_logz + srbm.Y.shape[0] * np.log(2) slogz = srbm._ais_logz + grbm.X.shape[0] * np.log(np.sqrt(2 * np.pi)) self.assertTrue(np.abs(glogz - slogz) < 1.)
def test_ais_with_semirbm_dbn(self): dbn = DBN(RBM(5, 5)) dbn.add_layer(SemiRBM(5, 5)) ais = Estimator(dbn) ais.estimate_log_partition_function(100, np.arange(0, 1, 1E-3), layer=0) ais.estimate_log_partition_function(10, np.arange(0, 1, 1E-3), layer=1) dbn[0]._brf_logz = utils.logsumexp(dbn[0]._ulogprob_vis(utils.binary_numbers(dbn[0].X.shape[0]))) dbn[1]._brf_logz = utils.logsumexp(dbn[1]._ulogprob_vis(utils.binary_numbers(dbn[1].X.shape[0]))) samples = np.concatenate([dbn.sample(25, 100, 20), np.matrix(np.random.rand(5, 25) > 0.5)], 1) Y = utils.binary_numbers(dbn[0].Y.shape[0]) X = utils.binary_numbers(dbn[0].X.shape[0]) logRy = dbn[1]._ulogprob_vis(Y) logQy = utils.logsumexp(dbn[0]._ulogprob(X, Y, all_pairs=True), 0) log_sum = utils.logsumexp(dbn[0]._clogprob_hid_vis(samples, Y, all_pairs=True) - logQy + logRy, 1) logPx = log_sum + dbn[0]._ulogprob_vis(samples) - dbn[1]._brf_logz logPx_ = ais.estimate_log_probability(samples)[0] self.assertTrue(np.abs(logPx_.mean() - logPx.mean()) < 0.1)