Construct a factor graph with normal distributed observations, a normal prior for the mean and a gamma prior for the precision parameter.
def construct_fg(data):
data = map(lambda x: [x], data)
fg = factor_graph_t()
fg += normal_fnode_t("normal1")
fg += normal_vnode_t("x")
fg += normal_fnode_t("normal2", 0, 0.01)
fg += normal_vnode_t("mu")
fg += gamma_fnode_t ("gamma", 1, 2)
fg += gamma_vnode_t ("tau")
fg.link("normal1:output", "x")
fg.link("normal2:output", "mu")
fg.link("gamma:output", "tau")
fg.link("normal1:mean", "mu")
fg.link("normal1:precision", "tau")
fg.variable_node("x").condition(data)
return fg
Generate some data and run the factor graph
mu = 1
sigma = 0.1
data = np.random.normal(mu, sigma, 1000)
fg = construct_fg(data)
fg()
Instead of having a product normal distribution it is also possible to construct a variable and factor node for each observation.
def construct_fg(data):
data = map(lambda x: [x], data)
fg = factor_graph_t()
# factor graph inside the plate
fg += normal_fnode_t("normal1")
fg += normal_vnode_t("x")
fg.link("normal1:output", "x")
# replicate this graph n-1 times
fg.replicate(len(data)-1)
# construct graph outside the plate
fg += normal_fnode_t("normal2", 0, 0.01)
fg += normal_vnode_t("mu")
fg += gamma_fnode_t ("gamma", 1, 2)
fg += gamma_vnode_t ("tau")
fg.link("normal2:output", "mu")
fg.link("gamma:output", "tau")
# connect v2 and v3 to all factors f1
# within the plate
fg.link("normal1:mean", "mu")
fg.link("normal1:precision", "tau")
# loop over all variable nodes v1
for i, d in enumerate(data):
fg.variable_node("x", i).condition([d])
return fg
def construct_fg(data):
data = map(lambda x: [x], data)
fg = factor_graph_t()
fg += categorical_fnode_t("categorical", 3)
fg += categorical_vnode_t("x", 3)
fg += dirichlet_fnode_t ("dirichlet", [2,1,2])
fg += dirichlet_vnode_t ("theta", 3)
fg.link("categorical:output", "x")
fg.link("categorical:theta", "theta")
fg.link("dirichlet:output", "theta")
fg.variable_node("x").condition(data)
return fg
data = [0,0,0,1,1,2,1,1,2,0]
fg = construct_fg(data)
fg()
def construct_fg(data):
# prepare the mixture node
m = mixture_fnode_t("mixture")
m += normal_fnode_t("normal1", 0, 100)
m += normal_fnode_t("normal2", 0, 100)
# construct graph inside the plate
fg = factor_graph_t()
fg += m
fg += normal_vnode_t("x")
fg += categorical_fnode_t("categorical", 2)
fg += categorical_vnode_t("z", 2)
fg.link("mixture:indicator", "z")
fg.link("mixture:output", "x")
fg.link("categorical:output", "z")
fg.replicate(len(data)-1)
# construct the remaining graph
fg += normal_vnode_t("mu1")
fg += normal_vnode_t("mu2")
fg += normal_fnode_t("normal1", 0.0, 0.01)
fg += normal_fnode_t("normal2", 0.0, 0.01)
fg += dirichlet_fnode_t("dirichlet", [1,1])
fg += dirichlet_vnode_t("theta", 2)
fg.link("dirichlet:output", "theta")
fg.link("categorical:theta", "theta")
fg.link("normal1:output", "mu1")
fg.link("normal2:output", "mu2")
fg.link("mixture:normal1:mean", "mu1")
fg.link("mixture:normal2:mean", "mu2")
for i, x in enumerate(data):
fg.variable_node("x", i).condition([[x]])
return fg
Create two normal distributions with different mean and variance. The two distributions are multiplied and the resulting distribution is shown after renormalization.
n0 = normal_distribution_t()
n1 = normal_distribution_t(1,2)
n2 = normal_distribution_t(2,3)
n0 *= n1
n0 *= n2
n0.renormalize()
Construct a bivariate normal distribution
d = binormal_distribution_t(2, 2, 1, 0.9, 0.8)
