def ice_cream_n_group_pgm():
G = PGM()
G.add_node("alpha", content=r"$\alpha$", x=-1, y=1, scale=1.2, fixed=True)
G.add_node("beta", content=r"$\beta$", x=1, y=1, scale=1.2, fixed=True)
G.add_node("p", content=r"$p_{i}$", x=0, y=1, scale=1.2)
G.add_node("likes", content=r"$l_{i}$", x=0, y=0, scale=1.2, observed=True)
G.add_edge("alpha", "p")
G.add_edge("beta", "p")
G.add_edge("p", "likes")
G.add_plate([-0.5, -0.8, 1, 2.3], label=r"shop $i$")
G.show()
def convoluted_hierarchical_p():
G = PGM()
G.add_node("likes",
content="$l_{j, i}$",
x=1,
y=1,
scale=1.2,
observed=True)
G.add_node("p_shop", content="$p_{j, i}$", x=1, y=2, scale=1.2)
G.add_node("alpha_owner", content=r"$\alpha_{j}$", x=0, y=3, scale=1.2)
G.add_node("beta_owner", content=r"$\beta_{j}$", x=2, y=3, scale=1.2)
G.add_node("lambda_a_pop",
content=r"$\lambda_{\alpha}$",
x=0,
y=4,
scale=1.2)
G.add_node("lambda_b_pop",
content=r"$\lambda_{\beta}$",
x=2,
y=4,
scale=1.2)
G.add_node(
"tau_lambda_a",
content=r"$\tau_{\lambda_{\alpha}}$",
x=0,
y=5,
fixed=True,
)
G.add_node(
"tau_lambda_b",
content=r"$\tau_{\lambda_{\beta}}$",
x=2,
y=5,
fixed=True,
)
G.add_edge("alpha_owner", "p_shop")
G.add_edge("beta_owner", "p_shop")
G.add_edge("p_shop", "likes")
G.add_edge("lambda_a_pop", "alpha_owner")
G.add_edge("lambda_b_pop", "beta_owner")
G.add_edge("tau_lambda_a", "lambda_a_pop")
G.add_edge("tau_lambda_b", "lambda_b_pop")
G.add_plate(plate=[0.5, 0.2, 1, 2.3], label=r"shop $i$")
G.add_plate(plate=[-0.5, 0, 3, 3.5], label=r"owner $j$")
G.render()
def hierarchical_p():
"""A naive representation of the hierarchical p that we desire."""
G = PGM()
G.add_node("p_shop", content=r"$p_{j, i}$", x=1, y=2, scale=1.2)
G.add_node("likes",
content="$l_{j, i}$",
x=1,
y=1,
scale=1.2,
observed=True)
G.add_node("p_owner", content=r"$p_{j}$", x=1, y=3, scale=1.2)
G.add_node("p_pop", content=r"$p$", x=1, y=4, scale=1.2)
G.add_edge("p_pop", "p_owner")
G.add_edge("p_owner", "p_shop")
G.add_edge("p_shop", "likes")
G.add_plate(plate=[0.3, 0.3, 1.5, 2.2], label=r"shop $i$")
G.add_plate(plate=[0, -0.1, 2.1, 3.6], label=r"owner $j$")
G.render()
#pgm.add_edge("Transmission","Counts")
#pgm.add_edge("Transmission","Counts_g")
#pgm.add_edge("Transmission","Zeropoints")
pgm.add_edge("Type","Spars")
pgm.add_edge("G_i","Spars")
#pgm.add_edge("Counts_g","^Counts")
#pgm.add_edge("Detected","^Counts")
# Big Plate: Galaxy
pgm.add_plate(Plate([1.5, 0.5, 4.2, 3],
label=r"SNe $i = 1, \cdots, N_{SN}$",
shift=-0.1))
# Render and save.
pgm.render()
# pgm.figure.text(0.2,0.98,r'\underline{UNIVERSE}',size='large')
# pgm.figure.text(0.45,0.98,r'\underline{OBSERVATORY}',size='large')
# pgm.figure.text(0.72,0.98,r'\underline{DATA}',size='large')
pgm.figure.savefig("../results/toy_pgm.pdf")
def hierarchical_pgm():
G = PGM()
tfm_plot_params = {"ec": "red"}
G.add_node("likes",
content=r"$l_{j,i}$",
x=0,
y=0,
scale=1.2,
observed=True)
G.add_node(
"p_shop",
content=r"$p_{j,i}$",
x=0,
y=1,
scale=1.2,
plot_params=tfm_plot_params,
)
G.add_node("mu_shop", content=r"$\mu_{j,i}$", x=1, y=1, scale=1.2)
G.add_node("mu_owner", content=r"$\mu_{j}$", x=1, y=2, scale=1.2)
G.add_node("sigma_owner", content=r"$\sigma_{j}$", x=2, y=2, scale=1.2)
G.add_node(
"p_owner",
content=r"$p_{j}$",
x=0,
y=2,
scale=1.2,
plot_params=tfm_plot_params,
)
G.add_node("mu_population", content=r"$\mu$", x=1, y=3, scale=1.2)
G.add_node(
"sigma_population",
content=r"$\sigma$",
x=2,
y=3,
scale=1.2,
fixed=True,
)
G.add_node(
"p_population",
content="p",
x=0,
y=3,
scale=1.2,
plot_params=tfm_plot_params,
)
G.add_node("lambda", content=r"$\lambda$", x=3, y=2, scale=1.2, fixed=True)
G.add_node("mean_population",
content="mean",
x=1,
y=4,
scale=1.2,
fixed=True)
G.add_node(
"variance_population",
content="variance",
x=2,
y=4,
scale=1.2,
fixed=True,
)
G.add_edge("mu_shop", "p_shop")
G.add_edge("p_shop", "likes")
G.add_edge("mu_owner", "mu_shop")
G.add_edge("sigma_owner", "mu_shop")
G.add_edge("mu_owner", "p_owner")
G.add_edge("mu_population", "mu_owner")
G.add_edge("sigma_population", "mu_owner")
G.add_edge("mu_population", "p_population")
G.add_edge("lambda", "sigma_owner")
G.add_edge("mean_population", "mu_population")
G.add_edge("variance_population", "mu_population")
G.add_plate([-0.5, -0.5, 2, 2], label="shop $i$", position="bottom right")
G.add_plate([-0.7, -0.7, 3.2, 3.2],
label="owner $j$",
position="bottom right")
G.render()
def pgm():
from daft import PGM, Node, Plate
from matplotlib import rc
rc("font", family="serif", size=8)
rc("text", usetex=True)
pgm = PGM([9.5, 8.5], origin=[0., 0.2], observed_style='inner')
#pgm.add_node(Node('dispersion',r"\center{$\sigma_{Ia}$ \newline $\sigma_{!Ia}$}", 1,6,scale=1.2,aspect=1.8))
pgm.add_node(Node('Rate_Ia', r"{SNIa Rate}", 1, 8, fixed=1))
pgm.add_node(Node('Rate_II', r"{SNII Rate}", 2, 8, scale=1.6, aspect=1.2))
pgm.add_node(Node('L_Ia', r"{SNIa L, $\sigma_L$}", 3, 8, scale=1.6, aspect=1.2))
pgm.add_node(Node('L_II', r"{SNII L, $\sigma_L$}", 4, 8, scale=1.6, aspect=1.2))
pgm.add_node(Node('Cosmology', r"Cosmology", 7, 8, scale=1.6, aspect=1.2))
pgm.add_node(Node('Calibration', r"Calibration", 8, 8, scale=1.6, aspect=1.2))
# pgm.add_node(Node('Neighbors',r"\centering{Neighbor \newline Redshifts}", 5,7, scale=1.6,aspect=1.2))
pgm.add_node(Node('Redshift', r"{Redshift}", 6, 7, scale=1.6, aspect=1.2))
pgm.add_node(Node('Type_prob', r"Type prob", 1, 6, fixed=1, offset=(20, -10)))
pgm.add_node(Node('Distance', r"$L_D$", 7, 6, fixed=1, offset=(10, 10)))
pgm.add_node(Node('Type', r"Type", 1, 5, scale=1.6, aspect=1.2))
pgm.add_node(Node('Luminosity', r"Luminosity", 4, 4, scale=1.6, aspect=1.2))
pgm.add_node(Node('Flux', r"Flux", 7, 3, scale=1.2, fixed=True, offset=(-20, -20)))
pgm.add_node(Node('Obs_Type', r"Obs type", 1, 1, scale=1.6, aspect=1.2, observed=1))
pgm.add_node(Node('Obs_Redshift', r"Obs redshift", 6, 1, scale=1.6, aspect=1.2, observed=1))
pgm.add_node(Node('Counts', r"Counts", 8, 1, scale=1.2, observed=1))
pgm.add_edge("Rate_Ia","Type_prob")
pgm.add_edge("Rate_II","Type_prob")
pgm.add_edge("Cosmology","Distance")
pgm.add_edge("Redshift","Distance")
pgm.add_edge("Type_prob", "Type")
pgm.add_edge("Type","Luminosity")
pgm.add_edge("L_Ia", "Luminosity")
pgm.add_edge("L_II", "Luminosity")
pgm.add_edge("Luminosity","Flux")
pgm.add_edge("Redshift","Flux")
pgm.add_edge("Distance","Flux")
pgm.add_edge("Type","Obs_Type")
# pgm.add_edge("Neighbors","Obs_Redshift")
pgm.add_edge("Redshift","Obs_Redshift")
pgm.add_edge("Flux","Counts")
pgm.add_edge("Calibration","Counts")
# Big Plate: Galaxy
pgm.add_plate(Plate([0.4, 0.5, 8.2, 7.],
label=r"SNe $i = 1, \cdots, N_{SN}$",
shift=-0.2,label_offset=[20,2]))
pgm.add_plate(Plate([0.5, 3.5, 4., 2.],
label=r"Type $\in \{Ia, II\}$",
shift=-0.2,label_offset=[20,2]))
# Render and save.
pgm.render()
# pgm.figure.text(0.01,0.9,r'\underline{UNIVERSAL}',size='large')
# pgm.figure.text(0.01,0.55,r'{\centering \underline{INDIVIDUAL} \newline \underline{SN}}',size='large')
# pgm.figure.text(0.01,0.2,r'\underline{OBSERVATORY}',size='large')
# pgm.figure.text(0.01,0.1,r'\underline{DATA}',size='large')
pgm.figure.savefig("../results/nodes_pgm.pdf")
pgm.add_edge("G_i","Type")
pgm.add_edge("G_i","theta_Ti")
pgm.add_edge("Type","Luminosity")
pgm.add_edge("Luminosity","Flux")
pgm.add_edge("Type","Stheta")
pgm.add_edge("theta_T","Luminosity")
pgm.add_edge("theta_Ti","Luminosity")
pgm.add_edge("Flux","^Counts")
#pgm.add_edge("Flux_g","Counts_g")
#pgm.add_edge("Counts","^Counts")
#pgm.add_edge("Counts_g","^Counts")
pgm.add_edge("Transmission","^Counts")
#pgm.add_edge("Transmission","Counts_g")
pgm.add_edge("Type","ST")
pgm.add_edge("theta_Ti","Stheta")
#pgm.add_edge("Counts_g","^Counts")
# Big Plate: Galaxy
pgm.add_plate(Plate([0.5, 0.5, 7.2, 5.],
label=r"SNe $i = 1, \cdots, N_{SN}$",
shift=-0.2,label_offset=[10,2]))
# Render and save.
pgm.render()
# pgm.figure.text(0.2,0.98,r'\underline{UNIVERSE}',size='large')
# pgm.figure.text(0.45,0.98,r'\underline{OBSERVATORY}',size='large')
# pgm.figure.text(0.72,0.98,r'\underline{DATA}',size='large')
pgm.figure.savefig("../results/hdpgm.pdf")
# pgm.add_edge("Type","Stheta")
pgm.add_edge("theta_T", "Luminosity")
# pgm.add_edge("theta_Ti","Luminosity")
pgm.add_edge("Flux", "^Counts")
# pgm.add_edge("Flux_g","Counts_g")
# pgm.add_edge("Counts","^Counts")
# pgm.add_edge("Counts_g","^Counts")
pgm.add_edge("Global Transmission", "Transmission")
pgm.add_edge("Transmission", "^Counts")
# pgm.add_edge("Transmission","Counts_g")
pgm.add_edge("Type", "ST")
# pgm.add_edge("theta_Ti","Stheta")
# pgm.add_edge("Counts_g","^Counts")
# Big Plate: Galaxy
pgm.add_plate(Plate([1.4, 0.5, 7.2, 7.0], label=r"SNe $i = 1, \cdots, N_{SN}$", shift=-0.2, label_offset=[20, 2]))
pgm.add_plate(
Plate(
[4.5, 0.6, 4, 4.0],
label=r"{\centering LC Point $j = 1, \cdots, N_{band}$, $k = 1, \cdots, N_{date}$}",
shift=-0.2,
label_offset=[2, 2],
)
)
# Render and save.
pgm.render()
pgm.figure.text(0.01, 0.9, r"\underline{UNIVERSAL}", size="large")
pgm.add_node(Node("citrue", r"$c_i^\mathrm{true}$", 5, 3))
# Per-SN parameters: second line in the plate
pgm.add_node(Node("x0itrue", r"$x_{0,i}^\mathrm{true}$", 3, 2))
#pgm.add_node(Node("mui", r"$\mu_i$", 2, 2))
# Per-SN parameters: third line in the plate
pgm.add_node(Node("zi", r"$z_i$", 2, 1, observed=True))
# Observed photometry
pgm.add_node(Node("fij", r"$f_{i,j}$", 4, 1, observed=True))
pgm.add_node(Node("t0true", r"$t_0^{\mathrm{true}}$", 5, 1))
# Big Plate: SNe
pgm.add_plate(
Plate([1.5, 0.5, 4, 3.], label=r"SNe $i = 1, \cdots, N_{SN}$", shift=-0.1))
# Cosmological parameters
pgm.add_node(Node("cosmology", r"$\Omega$", 1, 2))
# nuisance parameters
pgm.add_node(Node("nuisance", r"$\alpha, \beta, x_{00}$", 0.7, 3, aspect=2.0))
# Add in the edges.
pgm.add_edge("x1dist", "x1itrue")
pgm.add_edge("cdist", "citrue")
pgm.add_edge("sigdist", "x0itrue")
pgm.add_edge("x1itrue", "x0itrue")
pgm.add_edge("citrue", "x0itrue")
