y = F.slice(xzy, begin=(None, px + pz),
end=(None, px + pz + 1)).squeeze()
linear = self.fe(x).squeeze() + F.sum(z * u[0], axis=1)
linear = F.clip(linear, -10.0, 10.0)
log_pdf = y * linear - F.exp(linear) - F.gammaln(y + 1.0)
return log_pdf
# Model
np.random.seed(123)
mx.random.seed(123)
dim_all = px + pz + 1
model = LatentModel(GLMMLogLik(px, pz),
encoder=VAEEncoder([dim_all, 256, 128],
latent_dim=pz,
act="softrelu"),
decoder=VAEDecoder([128, 256, pz],
latent_dim=pz,
npar=1,
act="softrelu"),
sim_z=10,
nchain=30,
ctx=ctx)
model.init(lr=0.0001, lr_bc=0.0001)
# Model fitting
batch_size = 1000
est_nsamp = 100000
bhat = model.module.log_cond_pdf.fe.weight
t1 = time.time()
mu0, _ = gen_mu_mixture_prior(est_nsamp, **mix_par)
# Data
mu, x = gen_mu_mixture_prior(n, **mix_par)
xt = mx.nd.array(x).reshape(-1, 1)
# Empirical Bayes estimation
eb_mu = np.mean(x)
eb_var = np.var(x) - 1.0
mu_est_eb = np.random.normal(eb_mu, math.sqrt(eb_var), est_nsamp)
# Model
model = LatentModel(ConditionalNormal(dimu=1),
encoder=VAEEncoder([1, 50, 100, 50], latent_dim=1),
decoder=VAEDecoder([50, 100, 50, 1], latent_dim=1, npar=1),
sim_z=100, nchain=nchain, ctx=ctx)
model.init(lr=0.01, lr_bc=0.01)
# Model fitting
logger.log(" => VAE")
model.fit(xt, epochs=1000, batch_size=batch_size, eval_nll=False, verbose=False)
mu_est_vae = model.simulate_prior(est_nsamp)[0].squeeze()
ks = stats.kstest(mu_est_vae, true_dist)
w = stats.wasserstein_distance(mu0, mu_est_vae)
logger.log(" => KS = {}, p-val = {}".format(ks.statistic, ks.pvalue))
logger.log(" => W = {}\n".format(w))
mu = np.random.exponential(scale=scale, size=n)
x = mu + np.random.randn(n)
return mu, x
# Data
np.random.seed(123)
mx.random.seed(123)
n = 1000
exp_scale = 2.0
mu, x = gen_mu_exp_prior(n, exp_scale)
xt = mx.nd.array(x).reshape(-1, 1)
# Model
model = LatentModel(ConditionalNormal(dimu=1),
encoder=VAEEncoder([1, 10], latent_dim=1),
decoder=VAEDecoder([10, 1], latent_dim=1, npar=1),
sim_z=10, nchain=100, ctx=ctx)
model.init(lr=0.01, lr_bc=0.01)
# Model fitting
batch_size = n # mini-batch size
est_nsamp = 10000 # size of Monte Carlo sample to approximate the density
epochs_vae = 1000 # pre-train model using VAE
epochs_bc = 1000 # bias correction step
# VAE
model.fit(xt, epochs=epochs_vae, batch_size=batch_size)
mu_est_vae = model.simulate_prior(est_nsamp)[0].squeeze()
# ALMOND bias correction