def svi_example(true_model, true_data):
X, mask = true_data.X, true_data.mask
# Fit a test model
model = FactorAnalysis(
D_obs, D_latent,
# W=true_model.W, sigmasq=true_model.sigmasq
)
# Add the data in minibatches
minibatchsize = 250
for start in range(0, N, minibatchsize):
end = min(start + minibatchsize, N)
model.add_data(X[start:end], mask=mask[start:end])
lps = []
angles = []
N_iters = 100
delay = 10.0
forgetting_rate = 0.75
stepsize = (np.arange(N_iters) + delay)**(-forgetting_rate)
for itr in progprint_xrange(N_iters):
lps.append(model.meanfield_sgdstep(stepsize[itr]))
E_W, _, _, _ = model.regression.mf_expectations
angles.append(principal_angle(true_model.W, E_W))
Z_inf = model.data_list[0].E_Z
Z_true = true_data.Z[:Z_inf.shape[0]]
plot_results(lps, angles, Z_true, Z_inf)
def svi_example(true_model, X, Z_true, mask):
# Fit a test model
model = FactorAnalysis(
D_obs, D_latent,
# W=true_model.W, sigmasq=true_model.sigmasq
)
# Add the data in minibatches
N = X.shape[0]
minibatchsize = 200
prob = minibatchsize / float(N)
lps = []
angles = []
N_iters = 100
delay = 10.0
forgetting_rate = 0.75
stepsize = (np.arange(N_iters) + delay)**(-forgetting_rate)
for itr in progprint_xrange(N_iters):
minibatch = np.random.permutation(N)[:minibatchsize]
X_mb, mask_mb = X[minibatch], mask[minibatch]
lps.append(model.meanfield_sgdstep(X_mb, prob, stepsize[itr], masks=mask_mb))
E_W, _, _, _ = model.regression.mf_expectations
angles.append(principal_angle(true_model.W, E_W))
# Compute the expected states for the first minibatch of data
model.add_data(X, mask)
statesobj = model.data_list.pop()
statesobj.meanfieldupdate()
Z_inf = statesobj.E_Z
plot_results(lps, angles, Z_true, Z_inf)
def svi_example(true_model, true_data):
X, mask = true_data.X, true_data.mask
# Fit a test model
model = FactorAnalysis(
D_obs, D_latent,
# W=true_model.W, sigmasq=true_model.sigmasq
)
# Add the data in minibatches
N = X.shape[0]
minibatchsize = 200
prob = minibatchsize / float(N)
lps = []
angles = []
N_iters = 100
delay = 10.0
forgetting_rate = 0.75
stepsize = (np.arange(N_iters) + delay)**(-forgetting_rate)
for itr in progprint_xrange(N_iters):
minibatch = np.random.permutation(N)[:minibatchsize]
X_mb, mask_mb = X[minibatch], mask[minibatch]
lps.append(model.meanfield_sgdstep(X_mb, prob, stepsize[itr], masks=mask_mb))
E_W, _, _, _ = model.regression.mf_expectations
angles.append(principal_angle(true_model.W, E_W))
# Compute the expected states for the first minibatch of data
model.add_data(X[:minibatchsize], mask[:minibatchsize])
statesobj = model.data_list.pop()
statesobj.meanfieldupdate()
Z_inf = statesobj.E_Z
Z_true = true_data.Z[:minibatchsize]
plot_results(lps, angles, Z_true, Z_inf)
def em_example(true_model, X, Z_true, mask):
# Fit a test model
model = FactorAnalysis(
D_obs, D_latent,
# W=true_model.W, sigmasq=true_model.sigmasq
)
inf_data = model.add_data(X, mask=mask)
model.set_empirical_mean()
lps = []
angles = []
N_iters = 100
for _ in progprint_xrange(N_iters):
model.EM_step()
lps.append(model.log_likelihood())
angles.append(principal_angle(true_model.W, model.W))
plot_results(lps, angles, Z_true, inf_data.E_Z)
def gibbs_example(true_model, true_data):
X, mask = true_data.X, true_data.mask
# Fit a test model
model = FactorAnalysis(
D_obs, D_latent,
# W=true_model.W, sigmasq=true_model.sigmasq
)
inf_data = model.add_data(X, mask=mask)
lps = []
angles = []
N_iters = 100
for _ in progprint_xrange(N_iters):
model.resample_model()
lps.append(model.log_likelihood())
angles.append(principal_angle(true_model.W, model.W))
plot_results(lps, angles, true_data.Z, inf_data.Z)
def meanfield_example(true_model, X, Z_true, mask):
# Fit a test model
model = FactorAnalysis(
D_obs, D_latent,
# W=true_model.W, sigmasq=true_model.sigmasq
)
inf_data = model.add_data(X, mask=mask)
model.set_empirical_mean()
lps = []
angles = []
N_iters = 100
for _ in progprint_xrange(N_iters):
model.meanfield_coordinate_descent_step()
lps.append(model.expected_log_likelihood())
E_W, _, _, _ = model.regression.mf_expectations
angles.append(principal_angle(true_model.W, E_W))
plot_results(lps, angles, Z_true, inf_data.Z)
def em_example(true_model, true_data):
X, mask = true_data.X, true_data.mask
# Fit a test model
model = FactorAnalysis(
D_obs, D_latent,
# W=true_model.W, sigmasq=true_model.sigmasq
)
inf_data = model.add_data(X, mask=mask)
lps = []
angles = []
N_iters = 100
for _ in progprint_xrange(N_iters):
model.EM_step()
lps.append(model.log_likelihood())
angles.append(principal_angle(true_model.W, model.W))
plot_results(lps, angles, true_data.Z, inf_data.E_Z)
def gibbs_example(true_model, X, Z_true, mask):
# Fit a test model
model = FactorAnalysis(
D_obs,
D_latent,
# W=true_model.W, sigmasq=true_model.sigmasq
)
inf_data = model.add_data(X, mask=mask)
model.set_empirical_mean()
lps = []
angles = []
N_iters = 100
for _ in progprint_xrange(N_iters):
model.resample_model()
lps.append(model.log_likelihood())
angles.append(principal_angle(true_model.W, model.W))
plot_results(lps, angles, Z_true, inf_data.Z)
def meanfield_example(true_model, true_data):
X, mask = true_data.X, true_data.mask
# Fit a test model
model = FactorAnalysis(
D_obs, D_latent,
# W=true_model.W, sigmasq=true_model.sigmasq
)
inf_data = model.add_data(X, mask=mask)
lps = []
angles = []
N_iters = 100
for _ in progprint_xrange(N_iters):
model.meanfield_coordinate_descent_step()
lps.append(model.expected_log_likelihood())
E_W, _, _, _ = model.regression.mf_expectations
angles.append(principal_angle(true_model.W, E_W))
plot_results(lps, angles, true_data.Z, inf_data.Z)