In part 1 we laid a foundation for the visualization of Forney Factor Graphs (FFGs) when using RxInfer. In the current part (Part 2) we provide a satisfactory way to layout the graph in a grid format. We can also switch between using the raw variable names from RxInfer and the equivalent mathematical symbols.
In this notebook, we abandon the use of GraphViz in favor of using TikZ. We encountered certain limitations in the GraphViz package that turns out to be less ideal for our purpose. Here is a summary of the limitations:
GraphViz dot layout
posGraphViz neato layout
posGraphViz fdp layout
posOne of the distinguishing features of the RxInfer Julia package is that it uses reactive message passing (RMP). This means node updates in the factor graph happens asynchronously. A user usually tends to gloss over these details due to the increased complexity. When node updates happen in the more traditional way, i.e. synchronously (for example as with the PyMDP Python package), users tend to have the option of being aware of which node is currently being udpated. It is quite beneficial to conceptualize the workings of factor graphs in general and the visualization of the factor graph itself is often helpful. The existing visualization code is rather limited and that is the reason this project was undertaken. The ultimate goal is reach a visualization which conforms to the Constrained Forney Factor Graph (CFFG) as defined in
https://biaslab.github.io/pdf/arxiv/2306.08014.pdf
https://biaslab.github.io/pdf/arxiv/2306.02733.pdf
GraphPPL.jl exports the @model macro for model specification allowing the acceptance of a regular Julia function and then builds an FFG under the hood. This graph is bipartite where vertices belong to one of two sets: one for factors and one for variables. We will render these verices as follows:
For each of the examples in this project the following steps happen:
A @model is created
The @model is conditioned on some data
A RxInfer model is created (rxi_model)
A GraphPPL model is obtained (gppl_model)
A meta graph is obtained (meta_graph)
The graph is rendered by the existing implementation (GraphPlot.gplot())
Some vertex labels are inspected for the sake of interest
Setup global parameters to influence the behavior of generate_tikz()
_san_node_ids is provided for node names that needs to be sanitized_lup_enabled is set to true/false to enable lookup of math names_seqlup_enabled is set to true/false to enable lookup/sequential lookup of math names_raw_links_enabled is set to true/false to enable the drawing of raw links for reference_lup_dict is provided for all variable names needing math equivalentsThe TikZ string is generated (generate_tikz())
GraphPPL modelThe TikZ string is printed
The FFG is saved to a pdf file (show_tikz())
versioninfo() ## Julia versionJulia Version 1.10.0
Commit 3120989f39b (2023-12-25 18:01 UTC)
Build Info:
Official https://julialang.org/ release
Platform Info:
OS: Linux (x86_64-linux-gnu)
CPU: 12 × Intel(R) Core(TM) i7-8700B CPU @ 3.20GHz
WORD_SIZE: 64
LIBM: libopenlibm
LLVM: libLLVM-15.0.7 (ORCJIT, skylake)
Threads: 1 on 12 virtual cores
Environment:
JULIA_NUM_THREADS = import Pkg; Pkg.instantiate(); Pkg.activate()
Pkg.add(Pkg.PackageSpec(;name="RxInfer", version="3.0.0"))
Pkg.add(Pkg.PackageSpec(;name="MetaGraphsNext", version="0.7.0")) Activating project at `~/.julia/environments/v1.10`
Resolving package versions...
No Changes to `~/.julia/environments/v1.10/Project.toml`
No Changes to `~/.julia/environments/v1.10/Manifest.toml`
Resolving package versions...
No Changes to `~/.julia/environments/v1.10/Project.toml`
No Changes to `~/.julia/environments/v1.10/Manifest.toml`using RxInfer, MetaGraphsNextPkg.status()Status `~/.julia/environments/v1.10/Project.toml`
[86223c79] Graphs v1.11.2
[7073ff75] IJulia v1.25.0
[fa8bd995] MetaGraphsNext v0.7.0
[8314cec4] PGFPlotsX v1.6.1
⌃ [86711068] RxInfer v3.0.0
[b4f28e30] TikzGraphs v1.4.0
[37f6aa50] TikzPictures v3.5.0
Info Packages marked with ⌃ have new versions available and may be upgradable."""
Takes the tikz string given by generate_tikz() and
writes it to a .tex file to produce a TikZ visualisation.
"""
function show_tikz(tikz_code_graph::String)
## eval(Meta.parse(dot_code_graph)) ## for GraphViz
## see problem in ^v1 under TikzPictures section
## tikz_picture = TikzPicture(tikz_code_graph)
## return tikz_picture
file_path = "myoutput.tex" ## write to file rather than show in notebook
open(file_path, "w") do file
write(file, tikz_code_graph)
end
endshow_tikz##
# # If your PDF contains a TikZ picture (a vector graphic created using LaTeX),
# # you can still use the method I mentioned earlier to display it in a Julia notebook.
# # Here’s the method again for your reference:
# import Pkg; Pkg.add("PGFPlotsX")
# using PGFPlotsX
# # Create a struct that represents a PDF file
# struct PDF
# file::String
# end
# # Define a function to show the PDF as inline SVG
# function Base.show(io::IO, ::MIME"image/svg+xml", pdf::PDF)
# svg = first(splitext(pdf.file)) * ".svg"
# PGFPlotsX.convert_pdf_to_svg(pdf.file, svg)
# write(io, read(svg))
# try; rm(svg; force=true); catch e; end
# return nothing
# end
# # Now you can display a PDF file like this:
# display(PDF("myoutput.pdf"))
# # Internal Error: cairo context error: invalid matrix (not invertible)<0a>
# # cairo error: invalid matrix (not invertible)function retain_can(s::String) ## retain canonical chars of a label string
m = match(r"^[a-zA-Zγθs₀\*]*", s)
return m.match
end
function sanitized(vertex::String)
if haskey(_san_node_ids, vertex)
return _san_node_ids[vertex]
else
return vertex
end
end
function lup(label::String)
if _lup_enabled
lup_label = get(_lup_dict, label, replace(label, "_" => "\\_"))
else
return replace(label, "_" => "\\_")
end
end
function seqlup(label::String, i::Integer)
if _seqlup_enabled
lup_label = get(_lup_dict, label, split(label, '_')[1]*"_"*string(i))
return lup_label
else
return replace(label, "_" => "\\_")
end
end
function show_meta_graph(meta_graph) ## just for info
str = ""
for i in MetaGraphsNext.vertices(meta_graph)
label = MetaGraphsNext.label_for(meta_graph, i)
str *= " $(label);\n"
end
for edge in MetaGraphsNext.edges(meta_graph)
source_vertex = MetaGraphsNext.label_for(meta_graph, edge.src)
dest_vertex = MetaGraphsNext.label_for(meta_graph, edge.dst)
str *= " $(source_vertex) -- $(dest_vertex);\n"
end
print(str)
endshow_meta_graph (generic function with 1 method)"""
Given a user specified canonical factor label string,
returns all the GraphPPL associated labels from the context's factor_nodes.
"""
function str_facs(gppl_model, factor::String)
context = GraphPPL.getcontext(gppl_model)
vec = []
for (factor_ID, factor_label) in pairs(context.factor_nodes)
## println("$(factor_ID), $(factor_label)")
## println("$(typeof(factor_ID)), $(typeof(factor_label))")
node_data = gppl_model[factor_label]
## println("$(node_data.properties.fform)\n")
if retain_can(string(node_data.properties.fform)) == factor
append!(vec, factor_label)
end
end
result = string.(vec)
return result
end
"""
Given a user specified canonical variable label string,
returns all the GraphPPL associated labels from the context's individual_variables.
"""
function str_individual_vars(gppl_model, var::String)
context = GraphPPL.getcontext(gppl_model)
vec = []
for (node_ID, node_label) in pairs(context.individual_variables)
## println("$(node_ID), $(node_label)")
## println("$(typeof(node_ID)), $(typeof(node_label))")
if occursin(var, string(node_ID))
append!(vec, node_label)
end
end
result = string.(vec)
return result
end
"""
Given a user specified canonical variable label string,
returns all the GraphPPL associated labels from the context's vector_variables.
"""
function str_vector_vars(gppl_model, var::String)
context = GraphPPL.getcontext(gppl_model)
vec = []
for (node_ID, node_label) in pairs(context.vector_variables)
## println("$(node_ID), $(node_label)")
## println("$(typeof(node_ID)), $(typeof(node_label))")
if string(node_ID) == var
append!(vec, node_label)
end
end
result = string.(vec)
return result
endstr_vector_varsfunction spaces(n::Int)
d = 1/(n + 1)
return [i*d for i in 1:n]
end
function setup_divn(n)
divn = Dict()
for i in 1:n
divn[i] = spaces(i)
end
return divn
endsetup_divn (generic function with 1 method)_ytop = 15 ## grid y-value at the top of picture15function get_preamble_and_postamble(heading)
iob = IOBuffer() ## preamble
write(iob, "\\documentclass{standalone}\n")
write(iob, "\\usepackage{tikz}\n")
write(iob, "\\usepackage{amsmath}\n")
write(iob, "\\newcommand\\ns{10mm} %define node (minimum) size\n")
write(iob, "\\DeclareUnicodeCharacter{03B8}{\\theta}\n")
write(iob, "\\DeclareUnicodeCharacter{03B3}{\\gamma}\n")
## write(iob, "\\DeclareUnicodeCharacter{2080}{\\0}\n") ## theta_0
write(iob, "\\begin{document}\n")
write(iob, "\\begin{tikzpicture}[\n")
write(iob, " scale=1, \n")
write(iob, " draw=black, \n")
write(iob, " fac/.style={rectangle, draw=black!100, fill=black!0, minimum size=\\ns, inner sep=0pt},\n")
write(iob, " dlt/.style={rectangle, draw=black!100, fill=black!100, minimum size=.3*\\ns},\n")
write(iob, " var/.style={circle, draw=gray!100, fill=gray!100, minimum size=1mm, inner sep=0pt},\n")
write(iob, " bus/.style={rectangle, draw=black!100, fill=black!100, minimum width=30mm, minimum height=.5mm, inner sep=0pt},\n")
write(iob, " eql/.style={rectangle, draw=black!100, fill=black!0, minimum size=.5*\\ns},\n")
write(iob, " text=gray,\n")
write(iob, " ]\n")
write(iob, "\\node[font=\\Large] at (4,$(_ytop)) { };\n")
write(iob, "\\node[font=\\Large] at (4,$(_ytop-1)) {\\textbf{$(heading)}};\n")
## write(iob, "\\draw[lightgray] (0,0) grid (18,9);\n")
preamble = String(take!(iob))
print(preamble)
println("⋮"); println("⋮"); println("⋮") ## [\]vdots[tab]
iob = IOBuffer() ## postamble
write(iob, "\\end{tikzpicture}\n")
write(iob, "\\end{document}\n")
postamble = String(take!(iob))
print(postamble)
return preamble, postamble
endget_preamble_and_postamble (generic function with 1 method)function generate_tikz(;
heading::String,
Model::GraphPPL.Model,
layers::Vector{String},
iniparamB1_vars=nothing,
paramB1_var_uname=nothing,
iniparamB1_fac=nothing,
iniparamB2_vars=nothing,
paramB2_var_uname=nothing,
iniparamB2_fac=nothing,
inistate1_vars=nothing,
inistate1_fac=nothing,
state10_var=nothing,
state1_var_uname=nothing,
trans1_facs=nothing,
inistate2_vars=nothing,
inistate2_fac=nothing,
state20_var=nothing,
state2_var_uname=nothing,
trans2_facs=nothing,
trans2_pars=nothing,
inistate3_vars=nothing,
inistate3_fac=nothing,
state30_var=nothing,
state3_var_uname=nothing,
trans3_facs=nothing,
trans3_pars=nothing,
obser_var_uname=nothing,
obser_facs=nothing,
obser_pars=nothing,
iniparamA_vars=nothing,
iniparamA_fac=nothing,
paramA_var_uname=nothing
)
preamble, postamble = get_preamble_and_postamble(heading)
tikz = preamble
divn = setup_divn(15)
iob = IOBuffer() ## graph
if "paramB1" in layers
paramB1_vars = str_individual_vars(Model, paramB1_var_uname)
end
if "paramB2" in layers
paramB2_vars = str_individual_vars(Model, paramB2_var_uname)
end
if "state1" in layers
state1_vars = str_vector_vars(Model, state1_var_uname)
end
if "state2" in layers
if state2_var_uname != ""
state2_vars = str_vector_vars(Model, state2_var_uname)
else
state2_vars = Vector{String}()
end
end
if "state3" in layers
if state3_var_uname != ""
state3_vars = str_vector_vars(Model, state3_var_uname)
else
state3_vars = Vector{String}()
end
end
if "obser" in layers
obser_vars = str_vector_vars(Model, obser_var_uname)
end
if "paramA" in layers
paramA_vars = str_individual_vars(Model, paramA_var_uname)
end
ytop = _ytop; xleft = 0; ysep = 3; xsep = 2; y = ytop; x = xleft
write(iob, "%% --------------------------- NODES ---------------------------\n")
if "paramB1" in layers
y -= ysep; x = xleft
for (i,v) in enumerate(iniparamB1_vars)
write(iob, "\\node($(v))[var] at ($(x), $(y) - 0.5+$(divn[length(iniparamB1_vars)][i])) {};\n")
write(iob, "\\node[left] at ($(v)) {\$$(lup(v))\$};\n") ## label
end; x += xsep
write(iob, "\\node($(iniparamB1_fac))[fac] at ($(x), $(y)) {\$$(lup(iniparamB1_fac))\$};\n")
x += xsep
for (i,v) in enumerate(paramB1_vars)
write(iob, "\\node($(v))[eql] at ($(x), $(y)) {\$=\$};\n")
write(iob, "\\node[xshift=.4*\\ns, yshift=.4*\\ns] at ($(v)) {\$$(lup(v))\$};\n") ## label
end
end
if "paramB2" in layers
y -= ysep; x = xleft
for (i,v) in enumerate(iniparamB2_vars)
write(iob, "\\node($(v))[var] at ($(x), $(y) - 0.5+$(divn[length(iniparamB2_vars)][i])) {};\n")
write(iob, "\\node[left] at ($(v)) {\$$(lup(v))\$};\n") ## label
end; x += xsep
write(iob, "\\node($(iniparamB2_fac))[fac] at ($(x), $(y)) {\$$(lup(iniparamB2_fac))\$};\n")
x += xsep
for (i,v) in enumerate(paramB2_vars)
write(iob, "\\node($(v))[eql] at ($(x), $(y)) {\$=\$};\n")
write(iob, "\\node[xshift=.4*\\ns, yshift=.4*\\ns] at ($(v)) {\$$(lup(v))\$};\n") ## label
end
end
if "state1" in layers
y -= ysep; x = xleft
for (i,v) in enumerate(inistate1_vars)
write(iob, "\\node($(v))[var] at ($(x), $(y) - 0.5+$(divn[length(inistate1_vars)][i])) {};\n")
write(iob, "\\node[left] at ($(v)) {\$$(lup(v))\$};\n") ## label
end
x += xsep
write(iob, "\\node($(inistate1_fac))[fac] at ($(x), $(y)) {\$$(lup(inistate1_fac))\$};\n")
x += xsep
write(iob, "\\node($(state10_var))[var] at ($(x), $(y)) {};\n")
## write(iob, "\\node[above] at ($(state10_var)) {\$s_0\$};\n") ## label
write(iob, "\\node[above] at ($(state10_var)) {\$$(lup(state10_var))\$};\n") ## label
x += xsep
for (i,v) in enumerate(trans1_facs)
write(iob, "\\node($(v))[fac] at ($(x), $(y)) {\$$(lup(v))\$};\n")
x += 2*xsep
end
x = 4*xsep
for (i,v) in enumerate(state1_vars)
if i < length(state1_vars)
write(iob, "\\node($(v))[eql] at ($(x), $(y)) {\$=\$};\n")
write(iob, "\\node[xshift=.4*\\ns, yshift=.4*\\ns] at ($(v)) {\$$(seqlup(v, i))\$};\n") ## label
else
write(iob, "\\node($(v))[var] at ($(x), $(y)) {};\n")
write(iob, "\\node[above] at ($(v)) {\$$(seqlup(v, i))\$};\n") ## label
end
x += 2*xsep
end
end
if "state2" in layers
y -= ysep; x = xleft
x = 4*xsep
for (i,v) in enumerate(trans2_facs)
write(iob, "\\node($(v))[fac] at ($(x), $(y)) {\$$(lup(v))\$};\n")
x += 2*xsep
end
x = 4*xsep
for (i,v) in enumerate(trans2_pars)
write(iob, "\\node($(v))[var] at ($(x)-1, $(y)) {};\n")
write(iob, "\\node[left] at ($(v)) {\$$(lup(v))\$};\n") ## label
x += 2*xsep
end
x = 4*xsep
for (i,v) in enumerate(state2_vars)
if i < length(state2_vars)
write(iob, "\\node($(v))[eql] at ($(x), $(y)) {\$=\$};\n")
write(iob, "\\node[xshift=.4*\\ns, yshift=.4*\\ns] at ($(v)) {\$$(seqlup(v, i))\$};\n") ## label
else
write(iob, "\\node($(v))[var] at ($(x), $(y)) {};\n")
write(iob, "\\node[above] at ($(v)) {\$$(seqlup(v, i))\$};\n") ## label
end
x += 2*xsep
end
end
if "state3" in layers
y -= ysep; x = xleft
x = 4*xsep
for (i,v) in enumerate(trans3_facs)
write(iob, "\\node($(v))[fac] at ($(x), $(y)) {\$$(lup(v))\$};\n")
x += 2*xsep
end
x = 4*xsep
for (i,v) in enumerate(trans3_pars)
write(iob, "\\node($(v))[var] at ($(x)-1, $(y)) {};\n")
write(iob, "\\node[left] at ($(v)) {\$$(lup(v))\$};\n") ## label
x += 2*xsep
end
x = 4*xsep
for (i,v) in enumerate(state3_vars)
if i < length(state3_vars)
write(iob, "\\node($(v))[eql] at ($(x), $(y)) {\$=\$};\n")
write(iob, "\\node[xshift=.4*\\ns, yshift=.4*\\ns] at ($(v)) {\$$(seqlup(v, i))\$};\n") ## label
else
write(iob, "\\node($(v))[var] at ($(x), $(y)) {};\n")
write(iob, "\\node[above] at ($(v)) {\$$(seqlup(v, i))\$};\n") ## label
end
x += 2*xsep
end
end
if "obser" in layers
y -= ysep; x = 4*xsep
for (i,v) in enumerate(obser_facs)
write(iob, "\\node($(v))[fac] at ($(x), $(y)) {\$$(lup(v))\$};\n")
x += 2*xsep
end
x = 4*xsep
for (i,v) in enumerate(obser_pars)
write(iob, "\\node($(v))[var] at ($(x)-1, $(y)) {};\n")
write(iob, "\\node[left] at ($(v)) {\$$(lup(v))\$};\n") ## label
x += 2*xsep
end
y -= 2; x = 4*xsep
for (i,v) in enumerate(obser_vars)
write(iob, "\\node($(v))[var] at ($(x), $(y)) {};\n")
write(iob, "\\node[above right] at ($(v)) {\$$(seqlup(v, i))\$};\n") ## label
x += 2*xsep
end
end
if "paramA" in layers
y -= ysep; x = xleft
for (i,v) in enumerate(iniparamA_vars)
write(iob, "\\node($(v))[var] at (1, $(y) - 0.5+$(divn[length(iniparamA_vars)][i])) {};\n")
write(iob, "\\node[left] at ($(v)) {\$$(lup(v))\$};\n") ## label
end
x += xsep
write(iob, "\\node($(iniparamA_fac))[fac] at ($(x), $(y)) {\$$(lup(iniparamA_fac))\$};\n")
x = 4*xsep - .5*xsep ## last term is west-entry offset
## x += xsep
for (i,v) in enumerate(paramA_vars)
## write(iob, "\\node($(v))[bus, minimum width=30mm, minimum height=.5mm, inner sep=0pt] at (8, $(y)) {};\n")
write(iob, "\\node($(v))[eql] at ($(x), $(y)) {\$=\$};\n")
write(iob, "\\node[xshift=.4*\\ns, yshift=.4*\\ns] at ($(v)) {\$$(lup(v))\$};\n") ## label
end
end
write(iob, "%% --------------------------- LINKS ---------------------------\n")
y = ytop; x = xleft
if "paramB1" in layers
for (i,v) in enumerate(iniparamB1_vars)
write(iob, "\\draw ($(v)) -- ([shift={(0, $(divn[length(iniparamB1_vars)][i]))}]$(iniparamB1_fac).south west);\n")
end; x += xsep
write(iob, "\\draw ($(iniparamB1_fac)) -| ($(paramB1_vars[1]));\n"); x += 2*xsep
if "state1" in layers ## connect paramB1 layer to state1 layer
for (i,v) in enumerate(trans1_facs)
write(iob, "\\draw ($(paramB1_vars[1])) -| ([shift={(-.2*\\ns, 0)}]$(trans1_facs[i]).north east);\n")
end
end
end
if "paramB2" in layers
y -= ysep; x = xleft
for (i,v) in enumerate(iniparamB2_vars)
write(iob, "\\draw ($(v)) -- ([shift={(0, $(divn[length(iniparamB2_vars)][i]))}]$(iniparamB2_fac).south west);\n")
end; x += xsep
write(iob, "\\draw ($(iniparamB2_fac)) -| ($(paramB2_vars[1]));\n"); x += 2*xsep
if "state1" in layers ## connect paramB2 layer to state1 layer
for (i,v) in enumerate(trans1_facs)
write(iob, "\\draw ($(paramB2_vars[1])) -| ([shift={(.2*\\ns, 0)}]$(trans1_facs[i]).north west);\n")
end
end
end
if "state1" in layers ## state vars in this layer
for (i,v) in enumerate(inistate1_vars)
write(iob, "\\draw ($(v)) -- ([shift={(0, $(divn[length(inistate1_vars)][i]))}]$(inistate1_fac).south west);\n")
end
write(iob, "\\draw ($(inistate1_fac)) -| ($(state10_var));\n")
for (i,v) in enumerate(trans1_facs)
write(iob, "\\draw ($(v)) -- ($(state1_vars[i]).west);\n")
end
tmp = [state10_var; state1_vars]
for (i,v) in enumerate(trans1_facs)
write(iob, "\\draw ($(v).west) -- ($(tmp[i]).east);\n")
end
if "state2" in layers ## connect state1 layer to state2 layer
for (i,v) in enumerate(state1_vars)
write(iob, "\\draw ($(state1_vars[i])) -- ($(trans2_facs[i]));\n")
end
elseif "state3" in layers ## connect state1 layer to state2 layer
for (i,v) in enumerate(state1_vars)
write(iob, "\\draw ($(state1_vars[i])) -- ($(trans3_facs[i]));\n")
end
else
for (i,v) in enumerate(state1_vars)
write(iob, "\\draw ($(v)) -- ($(obser_facs[i]).north);\n")
end
end
end
if "state2" in layers
for (i,v) in enumerate(inistate2_vars)
write(iob, "\\draw ($(v)) -- ([shift={(0, $(divn[length(inistate2_vars)][i]))}]$(inistate2_fac).south west);\n")
end
if "state3" in layers ## connect state1 layer to state2 layer
for (i,v) in enumerate(trans2_facs)
write(iob, "\\draw ($(trans2_facs[i])) -- ($(trans3_facs[i]));\n")
end
end
end
if "state3" in layers
if "obser" in layers ## connect state1 layer to state2 layer
for (i,v) in enumerate(trans3_facs)
write(iob, "\\draw ($(trans3_facs[i])) -- ($(obser_facs[i]));\n")
end
end
end
if "obser" in layers
for (i,v) in enumerate(obser_vars)
write(iob, "\\draw ($(obser_facs[i])) -- ($(obser_vars[i]));\n")
end
end
if "paramA" in layers
for (i,v) in enumerate(iniparamA_vars)
## write(iob, "\\draw[blue, line width=3pt] ($(v)) -- ([shift={(0, $(divn[length(iniparamA_vars)][i]))}]$(iniparamA_fac).south west);\n")
write(iob, "\\draw ($(v)) -- ([shift={(0, $(divn[length(iniparamA_vars)][i]))}]$(iniparamA_fac).south west);\n")
end
write(iob, "\\draw ($(iniparamA_fac)) -| ($(paramA_vars[1]));\n")
for i in obser_facs
write(iob, "\\draw ($(paramA_vars[1])) -| ([shift={(-.5*\\ns,0)}]$(i).west) -- ($(i));\n")
end
end
## DRAW ALL RAW LINKS FOR REFERENCE
if _raw_links_enabled
G = Model.graph
for edge in MetaGraphsNext.edges(G)
source_vertex = MetaGraphsNext.label_for(G, edge.src)
dest_vertex = MetaGraphsNext.label_for(G, edge.dst)
write(iob, "\\draw[dotted, red, line width=1pt] ($(source_vertex)) -- ($(sanitized(string(dest_vertex))));\n")
end
end
## WRITE EQUAL NODES AGAIN
if "paramB1" in layers
for (i,v) in enumerate(paramB1_vars)
write(iob, "\\node($(v))[eql] at ($(v)) {\$=\$};\n")
end
end
if "paramB2" in layers
for (i,v) in enumerate(paramB2_vars)
write(iob, "\\node($(v))[eql] at ($(v)) {\$=\$};\n")
end
end
if "paramA" in layers
for (i,v) in enumerate(paramA_vars)
write(iob, "\\node($(v))[eql] at ($(v)) {\$=\$};\n")
end
end
graph = String(take!(iob))
tikz *= graph
tikz *= postamble
return tikz
endgenerate_tikz (generic function with 1 method)In this example, we are going to perform an exact inference for a coin-toss model that can be represented as:
\[\begin{aligned} p(\theta) &= \mathrm{Beta}(\theta|a, b),\\ p(y_i|\theta) &= \mathrm{Bern}(y_i|\theta),\\ \end{aligned}\]
where \(y_i \in \{0, 1\}\) is a binary observation induced by Bernoulli likelihood while \(\theta\) is a Beta prior distribution on the parameter of Bernoulli. We are interested in inferring the posterior distribution of \(\theta\).
The generative model is:
\[ \begin{aligned} p(\boldsymbol{y},\theta) &= p(\boldsymbol{y} \mid \theta) \cdot p(\theta) \\ &= \prod_{i=1}^N{p(y_i \mid \theta)} \cdot p(\theta) \\ &= \prod_{i=1}^N{\mathrm{Bern}(y_i \mid \theta)} \cdot \mathrm{Beta}(\theta \mid a,b) \end{aligned} \]
See Fig 4.1 in 2023_Bagaev_RPPfSBI_Thesis. So, \(N\) \(\delta\) factors, 1 Beta factor, \(N\) Ber factors.
@model function coin_model(y, a, b)
## We endow θ parameter of our model with some prior
θ ~ Beta(a, b)
## We assume that outcome of each coin flip is governed by the Bernoulli distribution
for i in eachindex(y)
y[i] ~ Bernoulli(θ)
end
endcoin_conditioned = coin_model(a = 2.0, b = 7.0) | (y = [ true, false, true ], )
coin_rxi_model = RxInfer.create_model(coin_conditioned)
coin_gppl_model = RxInfer.getmodel(coin_rxi_model)
coin_meta_graph = coin_gppl_model.graphMeta graph based on a Graphs.SimpleGraphs.SimpleGraph{Int64} with vertex labels of type GraphPPL.NodeLabel, vertex metadata of type GraphPPL.NodeData, edge metadata of type GraphPPL.EdgeLabel, graph metadata given by GraphPPL.Context(0, coin_model, "", nothing, {Beta = 1, Bernoulli = 3}, {}, {(Beta, 1) = Beta_6, (Bernoulli, 3) = Bernoulli_12, (Bernoulli, 1) = Bernoulli_8, (Bernoulli, 2) = Bernoulli_10}, {:constvar_2 = constvar_2_3, :θ = θ_1, :constvar_4 = constvar_4_5}, {:y = ResizableArray{GraphPPL.NodeLabel,1}(GraphPPL.NodeLabel[y_7, y_9, y_11])}, {}, {}, Base.RefValue{Any}(nothing)), and default weight 1.0for i in MetaGraphsNext.vertices(coin_meta_graph)
label = MetaGraphsNext.label_for(coin_meta_graph, i)
println("$i: $label")
end1: θ_1
2: constvar_2_3
3: constvar_4_5
4: Beta_6
5: y_7
6: Bernoulli_8
7: y_9
8: Bernoulli_10
9: y_11
10: Bernoulli_12##
## fieldnames(GraphPPL.Context)
coin_gppl_model_context = GraphPPL.getcontext(coin_gppl_model)
coin_gppl_model_context.individual_variables
coin_gppl_model_context.vector_variables
coin_gppl_model_context.factor_nodes4-element Dictionaries.UnorderedDictionary{GraphPPL.FactorID, GraphPPL.NodeLabel}
(Beta, 1) │ Beta_6
(Bernoulli, 3) │ Bernoulli_12
(Bernoulli, 1) │ Bernoulli_8
(Bernoulli, 2) │ Bernoulli_10##
str_facs(coin_gppl_model, "Bernoulli")
# str_individual_vars(coin_gppl_model, "θ")
# str_individual_vars(coin_gppl_model, "constvar_2")
# str_vector_vars(coin_gppl_model, "y")3-element Vector{String}:
"Bernoulli_12"
"Bernoulli_8"
"Bernoulli_10"show_meta_graph(coin_meta_graph) θ_1;
constvar_2_3;
constvar_4_5;
Beta_6;
y_7;
Bernoulli_8;
y_9;
Bernoulli_10;
y_11;
Bernoulli_12;
θ_1 -- Beta_6;
θ_1 -- Bernoulli_8;
θ_1 -- Bernoulli_10;
θ_1 -- Bernoulli_12;
constvar_2_3 -- Beta_6;
constvar_4_5 -- Beta_6;
y_7 -- Bernoulli_8;
y_9 -- Bernoulli_10;
y_11 -- Bernoulli_12;_san_node_ids = Dict("dummy" => "dummy")
_lup_enabled = true
_seqlup_enabled = true
_raw_links_enabled = false
_lup_dict = Dict{String, String}(
"constvar_2_3" => "a",
"constvar_4_5" => "b",
"Beta_6" => "\\mathcal{B}eta",
"Bernoulli_8" => "\\mathcal{B}er",
"Bernoulli_10" => "\\mathcal{B}er",
"Bernoulli_12" => "\\mathcal{B}er",
"θ_1" => "\\theta",
)
coin_tikz = generate_tikz(
heading = "Coin Toss",
Model = coin_gppl_model,
layers = [ ## fac layers, i.e. not var (vars are handled with assoced layer)
## "cntrl",
## "paramB1",
## "paramB2",
## "state1",
## "state2",
## "state3",
"obser",
## "prefr",
"paramA"
],
obser_var_uname = "y",
obser_facs = ["Bernoulli_8", "Bernoulli_10", "Bernoulli_12"],
obser_pars = [],
iniparamA_vars = ["constvar_2_3", "constvar_4_5"],
iniparamA_fac = "Beta_6",
paramA_var_uname="θ"
)
print(coin_tikz)
show_tikz(coin_tikz) ## write to file rather than show in notebook\documentclass{standalone}
\usepackage{tikz}
\usepackage{amsmath}
\newcommand\ns{10mm} %define node (minimum) size
\DeclareUnicodeCharacter{03B8}{\theta}
\DeclareUnicodeCharacter{03B3}{\gamma}
\begin{document}
\begin{tikzpicture}[
scale=1,
draw=black,
fac/.style={rectangle, draw=black!100, fill=black!0, minimum size=\ns, inner sep=0pt},
dlt/.style={rectangle, draw=black!100, fill=black!100, minimum size=.3*\ns},
var/.style={circle, draw=gray!100, fill=gray!100, minimum size=1mm, inner sep=0pt},
bus/.style={rectangle, draw=black!100, fill=black!100, minimum width=30mm, minimum height=.5mm, inner sep=0pt},
eql/.style={rectangle, draw=black!100, fill=black!0, minimum size=.5*\ns},
text=gray,
]
\node[font=\Large] at (4,15) { };
\node[font=\Large] at (4,14) {\textbf{Coin Toss}};
⋮
⋮
⋮
\end{tikzpicture}
\end{document}
\documentclass{standalone}
\usepackage{tikz}
\usepackage{amsmath}
\newcommand\ns{10mm} %define node (minimum) size
\DeclareUnicodeCharacter{03B8}{\theta}
\DeclareUnicodeCharacter{03B3}{\gamma}
\begin{document}
\begin{tikzpicture}[
scale=1,
draw=black,
fac/.style={rectangle, draw=black!100, fill=black!0, minimum size=\ns, inner sep=0pt},
dlt/.style={rectangle, draw=black!100, fill=black!100, minimum size=.3*\ns},
var/.style={circle, draw=gray!100, fill=gray!100, minimum size=1mm, inner sep=0pt},
bus/.style={rectangle, draw=black!100, fill=black!100, minimum width=30mm, minimum height=.5mm, inner sep=0pt},
eql/.style={rectangle, draw=black!100, fill=black!0, minimum size=.5*\ns},
text=gray,
]
\node[font=\Large] at (4,15) { };
\node[font=\Large] at (4,14) {\textbf{Coin Toss}};
%% --------------------------- NODES ---------------------------
\node(Bernoulli_8)[fac] at (8, 12) {$\mathcal{B}er$};
\node(Bernoulli_10)[fac] at (12, 12) {$\mathcal{B}er$};
\node(Bernoulli_12)[fac] at (16, 12) {$\mathcal{B}er$};
\node(y_7)[var] at (8, 10) {};
\node[above right] at (y_7) {$y_1$};
\node(y_9)[var] at (12, 10) {};
\node[above right] at (y_9) {$y_2$};
\node(y_11)[var] at (16, 10) {};
\node[above right] at (y_11) {$y_3$};
\node(constvar_2_3)[var] at (1, 7 - 0.5+0.3333333333333333) {};
\node[left] at (constvar_2_3) {$a$};
\node(constvar_4_5)[var] at (1, 7 - 0.5+0.6666666666666666) {};
\node[left] at (constvar_4_5) {$b$};
\node(Beta_6)[fac] at (2, 7) {$\mathcal{B}eta$};
\node(θ_1)[eql] at (7.0, 7) {$=$};
\node[xshift=.4*\ns, yshift=.4*\ns] at (θ_1) {$\theta$};
%% --------------------------- LINKS ---------------------------
\draw (Bernoulli_8) -- (y_7);
\draw (Bernoulli_10) -- (y_9);
\draw (Bernoulli_12) -- (y_11);
\draw (constvar_2_3) -- ([shift={(0, 0.3333333333333333)}]Beta_6.south west);
\draw (constvar_4_5) -- ([shift={(0, 0.6666666666666666)}]Beta_6.south west);
\draw (Beta_6) -| (θ_1);
\draw (θ_1) -| ([shift={(-.5*\ns,0)}]Bernoulli_8.west) -- (Bernoulli_8);
\draw (θ_1) -| ([shift={(-.5*\ns,0)}]Bernoulli_10.west) -- (Bernoulli_10);
\draw (θ_1) -| ([shift={(-.5*\ns,0)}]Bernoulli_12.west) -- (Bernoulli_12);
\node(θ_1)[eql] at (θ_1) {$=$};
\end{tikzpicture}
\end{document}2240
Our model for the Variational Bayesian Inference of a latent autoregressive model can be represented mathematically as follows:
\[\begin{aligned} p(\gamma) &= \mathcal{Gam}(\gamma|a, b)\\ p(\boldsymbol{\theta}) &= \mathcal{N}(\boldsymbol{\theta}|\mathbf{m}_{\theta}, \mathbf{V}_{\theta})\\ p(\mathbf{s}_t \mid \mathbf{s}_{t-1}, \boldsymbol{\theta}) &= \mathcal{N}\left(\mathbf{s}_t \mid \mathbf{B}\left(\boldsymbol{\theta}\right) \mathbf{s}_{t-1},\, \mathbf{V}(\gamma)\right)\\ p(x_t \mid \mathbf{s}_t) &= \mathcal{N}(x_t \mid \mathbf{s}_t, \tau^{-1}) \end{aligned}\]
where
\(M^{AR}\) is the order of the autoregression process
\(\boldsymbol{\theta}=(\theta_1, \theta_2, ..., \theta_{M^{AR}})^{\top}\) is a vector of transition coefficients
\(\mathbf{s}_{t-1} = (s_{t-1}, s_{t-2}, ..., s_{t-M^{AR}})^\top\) is the previous state
\(\mathbf{s}_t = (s_{t}, s_{t-1}, ..., s_{t-M^{AR}+1})^\top\) is the current state
\(\gamma\) is the transition precision
\(\tau\) is the observation precision
\(\mathbf{v}_u = (1,0,...,0)^\top\) is an \(M^{AR}\)-dimensional unit vector selecting the first component of the vector that follows
\(\mathbf{V}(\gamma) = (1/ \gamma)\mathbf{v}_u\mathbf{v}_u^\top\) is the transition covariance
\(\mathbf{B}(\boldsymbol{\theta}) = \begin{bmatrix} \boldsymbol{\qquad\theta}^\top \\ \mathbf{I}_{M^{AR}-1} & \mathbf{0} \end{bmatrix}\) is the transition matrix
The following diagram represents an autoregressive process:
@model function lar_model(
x, ##. data/observations
𝚃ᴬᴿ, ##. Uni/Multi variate
Mᴬᴿ, ##. AR order
vᵤ, ##. unit vector
τ) ##. observation precision
## Priors
γ ~ Gamma(α = 1.0, β = 1.0) ##. for transition precision
if 𝚃ᴬᴿ === Multivariate
θ ~ MvNormal(μ = zeros(Mᴬᴿ), Λ = diageye(Mᴬᴿ)) ##.kw μ,Λ only work inside macro
s₀ ~ MvNormal(μ = zeros(Mᴬᴿ), Λ = diageye(Mᴬᴿ)) ##.kw μ,Λ only work inside macro
else ## Univariate
θ ~ Normal(μ = 0.0, γ = 1.0)
s₀ ~ Normal(μ = 0.0, γ = 1.0)
end
sₜ₋₁ = s₀
for t in eachindex(x)
s[t] ~ AR(sₜ₋₁, θ, γ) #.Eq (2b)
if 𝚃ᴬᴿ === Multivariate
x[t] ~ Normal(μ = dot(vᵤ, s[t]), γ = τ) #.Eq (2c)
else
x[t] ~ Normal(μ = vᵤ*s[t], γ = τ) #.Eq (2c)
end
sₜ₋₁ = s[t]
end
end𝚃ᴬᴿ = Univariate
m = 1
τ̃ = 0.001 ## assumed observation precision
lar_conditioned = lar_model(
𝚃ᴬᴿ=𝚃ᴬᴿ,
Mᴬᴿ=m,
vᵤ=ReactiveMP.ar_unit(𝚃ᴬᴿ, m),
τ=τ̃
) | (x = [266.0, 145.0, 183.0],)lar_model(𝚃ᴬᴿ = Univariate, Mᴬᴿ = 1, vᵤ = 1.0, τ = 0.001) conditioned on:
x = [266.0, 145.0, 183.0]lar_rxi_model = RxInfer.create_model(lar_conditioned)
lar_gppl_model = RxInfer.getmodel(lar_rxi_model)
lar_meta_graph = lar_gppl_model.graphMeta graph based on a Graphs.SimpleGraphs.SimpleGraph{Int64} with vertex labels of type GraphPPL.NodeLabel, vertex metadata of type GraphPPL.NodeData, edge metadata of type GraphPPL.EdgeLabel, graph metadata given by GraphPPL.Context(0, lar_model, "", nothing, {AR = 3, GammaShapeRate = 1, NormalMeanPrecision = 5, * = 3}, {}, {(AR, 2) = AR_30, (NormalMeanPrecision, 2) = NormalMeanPrecision_18, (GammaShapeRate, 1) = GammaShapeRate_6, (*, 2) = *_34, (NormalMeanPrecision, 5) = NormalMeanPrecision_48, (NormalMeanPrecision, 3) = NormalMeanPrecision_28, (NormalMeanPrecision, 4) = NormalMeanPrecision_38, (NormalMeanPrecision, 1) = NormalMeanPrecision_12, (AR, 3) = AR_40, (*, 3) = *_44, (AR, 1) = AR_20, (*, 1) = *_24}, {:γ = γ_1, :constvar_42 = constvar_42_43, :constvar_14 = constvar_14_15, :constvar_16 = constvar_16_17, :anonymous_var_graphppl = anonymous_var_graphppl_41, :constvar_22 = constvar_22_23, :constvar_26 = constvar_26_27, :s₀ = s₀_13, :constvar_32 = constvar_32_33, :constvar_36 = constvar_36_37, :constvar_46 = constvar_46_47, :constvar_8 = constvar_8_9, :constvar_2 = constvar_2_3, :θ = θ_7, :constvar_4 = constvar_4_5, :constvar_10 = constvar_10_11}, {:s = ResizableArray{GraphPPL.NodeLabel,1}(GraphPPL.NodeLabel[s_19, s_29, s_39]), :x = ResizableArray{GraphPPL.NodeLabel,1}(GraphPPL.NodeLabel[x_25, x_35, x_45])}, {}, {}, Base.RefValue{Any}(nothing)), and default weight 1.0for i in MetaGraphsNext.vertices(lar_meta_graph)
label = MetaGraphsNext.label_for(lar_meta_graph, i)
println("$i: $label")
end1: γ_1
2: constvar_2_3
3: constvar_4_5
4: GammaShapeRate_6
5: θ_7
6: constvar_8_9
7: constvar_10_11
8: NormalMeanPrecision_12
9: s₀_13
10: constvar_14_15
11: constvar_16_17
12: NormalMeanPrecision_18
13: s_19
14: AR_20
15: anonymous_var_graphppl_21
16: constvar_22_23
17: *_24
18: x_25
19: constvar_26_27
20: NormalMeanPrecision_28
21: s_29
22: AR_30
23: anonymous_var_graphppl_31
24: constvar_32_33
25: *_34
26: x_35
27: constvar_36_37
28: NormalMeanPrecision_38
29: s_39
30: AR_40
31: anonymous_var_graphppl_41
32: constvar_42_43
33: *_44
34: x_45
35: constvar_46_47
36: NormalMeanPrecision_48##
## fieldnames(GraphPPL.Context)
lar_gppl_model_context = GraphPPL.getcontext(lar_gppl_model)
lar_gppl_model_context.individual_variables
lar_gppl_model_context.vector_variables
lar_gppl_model_context.factor_nodes12-element Dictionaries.UnorderedDictionary{GraphPPL.FactorID, GraphPPL.NodeLabel}
(AR, 2) │ AR_30
(NormalMeanPrecision, 2) │ NormalMeanPrecision_18
(GammaShapeRate, 1) │ GammaShapeRate_6
(*, 2) │ *_34
(NormalMeanPrecision, 5) │ NormalMeanPrecision_48
(NormalMeanPrecision, 3) │ NormalMeanPrecision_28
(NormalMeanPrecision, 4) │ NormalMeanPrecision_38
(NormalMeanPrecision, 1) │ NormalMeanPrecision_12
(AR, 3) │ AR_40
(*, 3) │ *_44
(AR, 1) │ AR_20
(*, 1) │ *_24##
str_facs(lar_gppl_model, "GammaShapeRate")
str_facs(lar_gppl_model, "AR")
str_facs(lar_gppl_model, "*")
str_individual_vars(lar_gppl_model, "γ")
# str_individual_vars(lar_gppl_model, "constvar_42")
# str_individual_vars(lar_gppl_model, "anonymous_var_graphppl")
# str_individual_vars(lar_gppl_model, "s₀")
# str_individual_vars(lar_gppl_model, "θ")
# str_vector_vars(lar_gppl_model, "s")
# str_vector_vars(lar_gppl_model, "x")1-element Vector{String}:
"γ_1"show_meta_graph(lar_meta_graph) γ_1;
constvar_2_3;
constvar_4_5;
GammaShapeRate_6;
θ_7;
constvar_8_9;
constvar_10_11;
NormalMeanPrecision_12;
s₀_13;
constvar_14_15;
constvar_16_17;
NormalMeanPrecision_18;
s_19;
AR_20;
anonymous_var_graphppl_21;
constvar_22_23;
*_24;
x_25;
constvar_26_27;
NormalMeanPrecision_28;
s_29;
AR_30;
anonymous_var_graphppl_31;
constvar_32_33;
*_34;
x_35;
constvar_36_37;
NormalMeanPrecision_38;
s_39;
AR_40;
anonymous_var_graphppl_41;
constvar_42_43;
*_44;
x_45;
constvar_46_47;
NormalMeanPrecision_48;
γ_1 -- GammaShapeRate_6;
γ_1 -- AR_20;
γ_1 -- AR_30;
γ_1 -- AR_40;
constvar_2_3 -- GammaShapeRate_6;
constvar_4_5 -- GammaShapeRate_6;
θ_7 -- NormalMeanPrecision_12;
θ_7 -- AR_20;
θ_7 -- AR_30;
θ_7 -- AR_40;
constvar_8_9 -- NormalMeanPrecision_12;
constvar_10_11 -- NormalMeanPrecision_12;
s₀_13 -- NormalMeanPrecision_18;
s₀_13 -- AR_20;
constvar_14_15 -- NormalMeanPrecision_18;
constvar_16_17 -- NormalMeanPrecision_18;
s_19 -- AR_20;
s_19 -- *_24;
s_19 -- AR_30;
anonymous_var_graphppl_21 -- *_24;
anonymous_var_graphppl_21 -- NormalMeanPrecision_28;
constvar_22_23 -- *_24;
x_25 -- NormalMeanPrecision_28;
constvar_26_27 -- NormalMeanPrecision_28;
s_29 -- AR_30;
s_29 -- *_34;
s_29 -- AR_40;
anonymous_var_graphppl_31 -- *_34;
anonymous_var_graphppl_31 -- NormalMeanPrecision_38;
constvar_32_33 -- *_34;
x_35 -- NormalMeanPrecision_38;
constvar_36_37 -- NormalMeanPrecision_38;
s_39 -- AR_40;
s_39 -- *_44;
anonymous_var_graphppl_41 -- *_44;
anonymous_var_graphppl_41 -- NormalMeanPrecision_48;
constvar_42_43 -- *_44;
x_45 -- NormalMeanPrecision_48;
constvar_46_47 -- NormalMeanPrecision_48;_san_node_ids = Dict("dummy" => "dummy")
_lup_enabled = true
_seqlup_enabled = true
_raw_links_enabled = true
_lup_dict = Dict{String, String}(
"θ_7" => "\\theta",
"constvar_8_9" => "\\mu",
"constvar_10_11" => "\\gamma",
## "NormalMeanPrecision_12" => "\\mathcal{N}\\_12",
"NormalMeanPrecision_12" => "\\mathcal{N}",
"constvar_2_3" => "\\alpha",
"constvar_4_5" => "\\beta",
"GammaShapeRate_6" => "\\mathcal{G}am",
"γ_1" => "\\gamma",
"constvar_14_15" => "\\mu",
"constvar_16_17" => "\\gamma",
"NormalMeanPrecision_18" => "\\mathcal{N}",
## "s₀_13" => "s_0", ## s₀ must always be in _lup_dict
"s₀_13" => "\\mathbf{s}_0",
"s_19" => "\\mathbf{s}_1",
"s_29" => "\\mathbf{s}_2",
"s_39" => "\\mathbf{s}_3",
"AR_20" => "AR",
"AR_30" => "AR",
"AR_40" => "AR",
"constvar_22_23" => "\\mathbf{B}",
"constvar_32_33" => "\\mathbf{B}",
"constvar_42_43" => "\\mathbf{B}",
"*_24" => "*",
"*_34" => "*",
"*_44" => "*",
"anonymous_var_graphppl_21" => "\\mathbf{v}_u",
"anonymous_var_graphppl_31" => "\\mathbf{v}_u",
"anonymous_var_graphppl_41" => "\\mathbf{v}_u",
"constvar_26_27" => "\\tau",
"constvar_36_37" => "\\tau",
"constvar_46_47" => "\\tau",
"NormalMeanPrecision_28" => "\\mathcal{N}",
"NormalMeanPrecision_38" => "\\mathcal{N}",
"NormalMeanPrecision_48" => "\\mathcal{N}",
)
lar_tikz = generate_tikz(
heading = "Time-Varying Autoregressive Model (Univariate)",
Model = lar_gppl_model,
layers = [ ## fac layers, i.e. not var (vars are handled with assoced layer)
## "cntrl",
"paramB1",
"paramB2",
"state1",
"state2",
"state3",
"obser",
## "prefr",
## "paramA"
],
iniparamB1_vars = ["constvar_8_9", "constvar_10_11"],
paramB1_var_uname="θ",
iniparamB1_fac = "NormalMeanPrecision_12",
iniparamB2_vars = ["constvar_2_3", "constvar_4_5"],
paramB2_var_uname="γ",
iniparamB2_fac = "GammaShapeRate_6",
inistate1_vars = ["constvar_14_15", "constvar_16_17"],
inistate1_fac = "NormalMeanPrecision_18",
state10_var = "s₀_13",
state1_var_uname="s",
trans1_facs = ["AR_20", "AR_30", "AR_40"],
inistate2_vars = [],
inistate2_fac = "",
state20_var = "",
state2_var_uname="",
trans2_facs = ["*_24", "*_34", "*_44", ],
trans2_pars = ["constvar_22_23", "constvar_32_33", "constvar_42_43"],
inistate3_vars = [],
inistate3_fac = "",
state30_var = "",
state3_var_uname="",
trans3_facs = ["anonymous_var_graphppl_21", "anonymous_var_graphppl_31", "anonymous_var_graphppl_41"],
trans3_pars = [],
obser_var_uname = "x",
obser_facs = ["NormalMeanPrecision_28", "NormalMeanPrecision_38", "NormalMeanPrecision_48"],
obser_pars = ["constvar_26_27", "constvar_36_37", "constvar_46_47"],
)
print(lar_tikz)
show_tikz(lar_tikz) ## write to file rather than show in notebook\documentclass{standalone}
\usepackage{tikz}
\usepackage{amsmath}
\newcommand\ns{10mm} %define node (minimum) size
\DeclareUnicodeCharacter{03B8}{\theta}
\DeclareUnicodeCharacter{03B3}{\gamma}
\begin{document}
\begin{tikzpicture}[
scale=1,
draw=black,
fac/.style={rectangle, draw=black!100, fill=black!0, minimum size=\ns, inner sep=0pt},
dlt/.style={rectangle, draw=black!100, fill=black!100, minimum size=.3*\ns},
var/.style={circle, draw=gray!100, fill=gray!100, minimum size=1mm, inner sep=0pt},
bus/.style={rectangle, draw=black!100, fill=black!100, minimum width=30mm, minimum height=.5mm, inner sep=0pt},
eql/.style={rectangle, draw=black!100, fill=black!0, minimum size=.5*\ns},
text=gray,
]
\node[font=\Large] at (4,15) { };
\node[font=\Large] at (4,14) {\textbf{Time-Varying Autoregressive Model (Univariate)}};
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\end{tikzpicture}
\end{document}
\documentclass{standalone}
\usepackage{tikz}
\usepackage{amsmath}
\newcommand\ns{10mm} %define node (minimum) size
\DeclareUnicodeCharacter{03B8}{\theta}
\DeclareUnicodeCharacter{03B3}{\gamma}
\begin{document}
\begin{tikzpicture}[
scale=1,
draw=black,
fac/.style={rectangle, draw=black!100, fill=black!0, minimum size=\ns, inner sep=0pt},
dlt/.style={rectangle, draw=black!100, fill=black!100, minimum size=.3*\ns},
var/.style={circle, draw=gray!100, fill=gray!100, minimum size=1mm, inner sep=0pt},
bus/.style={rectangle, draw=black!100, fill=black!100, minimum width=30mm, minimum height=.5mm, inner sep=0pt},
eql/.style={rectangle, draw=black!100, fill=black!0, minimum size=.5*\ns},
text=gray,
]
\node[font=\Large] at (4,15) { };
\node[font=\Large] at (4,14) {\textbf{Time-Varying Autoregressive Model (Univariate)}};
%% --------------------------- NODES ---------------------------
\node(constvar_8_9)[var] at (0, 12 - 0.5+0.3333333333333333) {};
\node[left] at (constvar_8_9) {$\mu$};
\node(constvar_10_11)[var] at (0, 12 - 0.5+0.6666666666666666) {};
\node[left] at (constvar_10_11) {$\gamma$};
\node(NormalMeanPrecision_12)[fac] at (2, 12) {$\mathcal{N}$};
\node(θ_7)[eql] at (4, 12) {$=$};
\node[xshift=.4*\ns, yshift=.4*\ns] at (θ_7) {$\theta$};
\node(constvar_2_3)[var] at (0, 9 - 0.5+0.3333333333333333) {};
\node[left] at (constvar_2_3) {$\alpha$};
\node(constvar_4_5)[var] at (0, 9 - 0.5+0.6666666666666666) {};
\node[left] at (constvar_4_5) {$\beta$};
\node(GammaShapeRate_6)[fac] at (2, 9) {$\mathcal{G}am$};
\node(γ_1)[eql] at (4, 9) {$=$};
\node[xshift=.4*\ns, yshift=.4*\ns] at (γ_1) {$\gamma$};
\node(constvar_14_15)[var] at (0, 6 - 0.5+0.3333333333333333) {};
\node[left] at (constvar_14_15) {$\mu$};
\node(constvar_16_17)[var] at (0, 6 - 0.5+0.6666666666666666) {};
\node[left] at (constvar_16_17) {$\gamma$};
\node(NormalMeanPrecision_18)[fac] at (2, 6) {$\mathcal{N}$};
\node(s₀_13)[var] at (4, 6) {};
\node[above] at (s₀_13) {$\mathbf{s}_0$};
\node(AR_20)[fac] at (6, 6) {$AR$};
\node(AR_30)[fac] at (10, 6) {$AR$};
\node(AR_40)[fac] at (14, 6) {$AR$};
\node(s_19)[eql] at (8, 6) {$=$};
\node[xshift=.4*\ns, yshift=.4*\ns] at (s_19) {$\mathbf{s}_1$};
\node(s_29)[eql] at (12, 6) {$=$};
\node[xshift=.4*\ns, yshift=.4*\ns] at (s_29) {$\mathbf{s}_2$};
\node(s_39)[var] at (16, 6) {};
\node[above] at (s_39) {$\mathbf{s}_3$};
\node(*_24)[fac] at (8, 3) {$*$};
\node(*_34)[fac] at (12, 3) {$*$};
\node(*_44)[fac] at (16, 3) {$*$};
\node(constvar_22_23)[var] at (8-1, 3) {};
\node[left] at (constvar_22_23) {$\mathbf{B}$};
\node(constvar_32_33)[var] at (12-1, 3) {};
\node[left] at (constvar_32_33) {$\mathbf{B}$};
\node(constvar_42_43)[var] at (16-1, 3) {};
\node[left] at (constvar_42_43) {$\mathbf{B}$};
\node(anonymous_var_graphppl_21)[fac] at (8, 0) {$\mathbf{v}_u$};
\node(anonymous_var_graphppl_31)[fac] at (12, 0) {$\mathbf{v}_u$};
\node(anonymous_var_graphppl_41)[fac] at (16, 0) {$\mathbf{v}_u$};
\node(NormalMeanPrecision_28)[fac] at (8, -3) {$\mathcal{N}$};
\node(NormalMeanPrecision_38)[fac] at (12, -3) {$\mathcal{N}$};
\node(NormalMeanPrecision_48)[fac] at (16, -3) {$\mathcal{N}$};
\node(constvar_26_27)[var] at (8-1, -3) {};
\node[left] at (constvar_26_27) {$\tau$};
\node(constvar_36_37)[var] at (12-1, -3) {};
\node[left] at (constvar_36_37) {$\tau$};
\node(constvar_46_47)[var] at (16-1, -3) {};
\node[left] at (constvar_46_47) {$\tau$};
\node(x_25)[var] at (8, -5) {};
\node[above right] at (x_25) {$x_1$};
\node(x_35)[var] at (12, -5) {};
\node[above right] at (x_35) {$x_2$};
\node(x_45)[var] at (16, -5) {};
\node[above right] at (x_45) {$x_3$};
%% --------------------------- LINKS ---------------------------
\draw (constvar_8_9) -- ([shift={(0, 0.3333333333333333)}]NormalMeanPrecision_12.south west);
\draw (constvar_10_11) -- ([shift={(0, 0.6666666666666666)}]NormalMeanPrecision_12.south west);
\draw (NormalMeanPrecision_12) -| (θ_7);
\draw (θ_7) -| ([shift={(-.2*\ns, 0)}]AR_20.north east);
\draw (θ_7) -| ([shift={(-.2*\ns, 0)}]AR_30.north east);
\draw (θ_7) -| ([shift={(-.2*\ns, 0)}]AR_40.north east);
\draw (constvar_2_3) -- ([shift={(0, 0.3333333333333333)}]GammaShapeRate_6.south west);
\draw (constvar_4_5) -- ([shift={(0, 0.6666666666666666)}]GammaShapeRate_6.south west);
\draw (GammaShapeRate_6) -| (γ_1);
\draw (γ_1) -| ([shift={(.2*\ns, 0)}]AR_20.north west);
\draw (γ_1) -| ([shift={(.2*\ns, 0)}]AR_30.north west);
\draw (γ_1) -| ([shift={(.2*\ns, 0)}]AR_40.north west);
\draw (constvar_14_15) -- ([shift={(0, 0.3333333333333333)}]NormalMeanPrecision_18.south west);
\draw (constvar_16_17) -- ([shift={(0, 0.6666666666666666)}]NormalMeanPrecision_18.south west);
\draw (NormalMeanPrecision_18) -| (s₀_13);
\draw (AR_20) -- (s_19.west);
\draw (AR_30) -- (s_29.west);
\draw (AR_40) -- (s_39.west);
\draw (AR_20.west) -- (s₀_13.east);
\draw (AR_30.west) -- (s_19.east);
\draw (AR_40.west) -- (s_29.east);
\draw (s_19) -- (*_24);
\draw (s_29) -- (*_34);
\draw (s_39) -- (*_44);
\draw (*_24) -- (anonymous_var_graphppl_21);
\draw (*_34) -- (anonymous_var_graphppl_31);
\draw (*_44) -- (anonymous_var_graphppl_41);
\draw (anonymous_var_graphppl_21) -- (NormalMeanPrecision_28);
\draw (anonymous_var_graphppl_31) -- (NormalMeanPrecision_38);
\draw (anonymous_var_graphppl_41) -- (NormalMeanPrecision_48);
\draw (NormalMeanPrecision_28) -- (x_25);
\draw (NormalMeanPrecision_38) -- (x_35);
\draw (NormalMeanPrecision_48) -- (x_45);
\draw[dotted, red, line width=1pt] (γ_1) -- (GammaShapeRate_6);
\draw[dotted, red, line width=1pt] (γ_1) -- (AR_20);
\draw[dotted, red, line width=1pt] (γ_1) -- (AR_30);
\draw[dotted, red, line width=1pt] (γ_1) -- (AR_40);
\draw[dotted, red, line width=1pt] (constvar_2_3) -- (GammaShapeRate_6);
\draw[dotted, red, line width=1pt] (constvar_4_5) -- (GammaShapeRate_6);
\draw[dotted, red, line width=1pt] (θ_7) -- (NormalMeanPrecision_12);
\draw[dotted, red, line width=1pt] (θ_7) -- (AR_20);
\draw[dotted, red, line width=1pt] (θ_7) -- (AR_30);
\draw[dotted, red, line width=1pt] (θ_7) -- (AR_40);
\draw[dotted, red, line width=1pt] (constvar_8_9) -- (NormalMeanPrecision_12);
\draw[dotted, red, line width=1pt] (constvar_10_11) -- (NormalMeanPrecision_12);
\draw[dotted, red, line width=1pt] (s₀_13) -- (NormalMeanPrecision_18);
\draw[dotted, red, line width=1pt] (s₀_13) -- (AR_20);
\draw[dotted, red, line width=1pt] (constvar_14_15) -- (NormalMeanPrecision_18);
\draw[dotted, red, line width=1pt] (constvar_16_17) -- (NormalMeanPrecision_18);
\draw[dotted, red, line width=1pt] (s_19) -- (AR_20);
\draw[dotted, red, line width=1pt] (s_19) -- (*_24);
\draw[dotted, red, line width=1pt] (s_19) -- (AR_30);
\draw[dotted, red, line width=1pt] (anonymous_var_graphppl_21) -- (*_24);
\draw[dotted, red, line width=1pt] (anonymous_var_graphppl_21) -- (NormalMeanPrecision_28);
\draw[dotted, red, line width=1pt] (constvar_22_23) -- (*_24);
\draw[dotted, red, line width=1pt] (x_25) -- (NormalMeanPrecision_28);
\draw[dotted, red, line width=1pt] (constvar_26_27) -- (NormalMeanPrecision_28);
\draw[dotted, red, line width=1pt] (s_29) -- (AR_30);
\draw[dotted, red, line width=1pt] (s_29) -- (*_34);
\draw[dotted, red, line width=1pt] (s_29) -- (AR_40);
\draw[dotted, red, line width=1pt] (anonymous_var_graphppl_31) -- (*_34);
\draw[dotted, red, line width=1pt] (anonymous_var_graphppl_31) -- (NormalMeanPrecision_38);
\draw[dotted, red, line width=1pt] (constvar_32_33) -- (*_34);
\draw[dotted, red, line width=1pt] (x_35) -- (NormalMeanPrecision_38);
\draw[dotted, red, line width=1pt] (constvar_36_37) -- (NormalMeanPrecision_38);
\draw[dotted, red, line width=1pt] (s_39) -- (AR_40);
\draw[dotted, red, line width=1pt] (s_39) -- (*_44);
\draw[dotted, red, line width=1pt] (anonymous_var_graphppl_41) -- (*_44);
\draw[dotted, red, line width=1pt] (anonymous_var_graphppl_41) -- (NormalMeanPrecision_48);
\draw[dotted, red, line width=1pt] (constvar_42_43) -- (*_44);
\draw[dotted, red, line width=1pt] (x_45) -- (NormalMeanPrecision_48);
\draw[dotted, red, line width=1pt] (constvar_46_47) -- (NormalMeanPrecision_48);
\node(θ_7)[eql] at (θ_7) {$=$};
\node(γ_1)[eql] at (γ_1) {$=$};
\end{tikzpicture}
\end{document}8179
Note that the option was chosen to draw the raw links as well for this FFG.