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fix and-node update
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@ThijsvdLaar
ThijsvdLaar committed May 25, 2022
1 parent 005a16c commit 3a502a7
Showing 1 changed file with 80 additions and 69 deletions.
149 changes: 80 additions & 69 deletions demo/implementing_additional_nodes.ipynb
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Expand Up @@ -59,15 +59,17 @@
"Note that the combination $y=1, z=0$ is disallowed by the truth table, and therefore $f(y=1, x, z=0)=0$ for both $x$. Furthermore, note that the combination $y=0, z=0$ appears twice, such that $f(y=0, x, z=0)=1$ for both $x$. This leads to\n",
"\\begin{align*} \n",
" \\overleftarrow{\\mu}_x(x) &= (1 - p_y)(1 - p_z) + 0 + (1 - p_y)p_z f(y=0, x, z=1) + p_y p_z f(y=1, x, z=1)\\\\\n",
" &= \\begin{cases}(1-p_y)(1-p_z) &\\text{ if } x=1\\\\\n",
" (1-p_y)(1-p_z) + p_z &\\text{ if } x=0 \\end{cases}\\\\\n",
" &\\propto \\mathcal{B}er\\left(x \\bigg| \\frac{a}{2a + p_z}\\right)\\,, \\text{ with } a=(1-p_y)(1-p_z).\n",
" &= \\begin{cases}(1-p_y)(1-p_z) + p_y p_z &\\text{ if } x=1\\\\\n",
" (1-p_y)(1-p_z) + p_z - p_y p_x &\\text{ if } x=0 \\end{cases}\\\\\n",
" &= \\begin{cases}1 - p_y - p_z + 2 p_y p_z &\\text{ if } x=1\\\\\n",
" 1-p_y &\\text{ if } x=0 \\end{cases}\\\\\n",
" &\\propto \\mathcal{B}er\\left(x \\bigg| \\frac{1 - p_y - p_z + 2 p_y p_z}{2 - 2 p_y - p_z + 2 p_y p_z}\\right)\\,.\n",
"\\end{align*}\n",
"\n",
"### Backward message for $z$\n",
"From symmerty, the backward message for $z$ follows as\n",
"\\begin{align*}\n",
" \\overleftarrow{\\mu}_z(z) \\propto \\mathcal{B}er\\left(z \\bigg| \\frac{a}{2a + p_x}\\right)\\,, \\text{ with } a=(1-p_y)(1-p_x)\\,.\n",
" \\overleftarrow{\\mu}_z(z) \\propto \\mathcal{B}er\\left(z \\bigg| \\frac{1 - p_y - p_x + 2 p_y p_x}{2 - 2 p_y - p_x + 2 p_y p_x}\\right)\\,.\n",
"\\end{align*}\n",
"\n",
"## Unit Tests\n",
Expand All @@ -76,7 +78,7 @@
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Expand Down Expand Up @@ -144,7 +146,7 @@
" @test isApplicable(SPAndIn1BNB, [Message{Bernoulli}, Nothing, Message{Bernoulli}]) \n",
" @test !isApplicable(SPAndIn1BNB, [Message{Bernoulli}, Message{Bernoulli}, Nothing]) \n",
"\n",
" @test ruleSPAndIn1BNB(Message(Univariate, Bernoulli, p=0.1), nothing, Message(Univariate, Bernoulli, p=0.25)) == Message(Univariate, Bernoulli, p=0.421875)\n",
" @test ruleSPAndIn1BNB(Message(Univariate, Bernoulli, p=0.1), nothing, Message(Univariate, Bernoulli, p=0.25)) == Message(Univariate, Bernoulli, p=0.4375)\n",
"end\n",
"\n",
"@testset \"SPAndIn2BBN\" begin\n",
Expand All @@ -153,7 +155,7 @@
" @test isApplicable(SPAndIn2BBN, [Message{Bernoulli}, Message{Bernoulli}, Nothing]) \n",
" @test !isApplicable(SPAndIn2BBN, [Nothing, Message{Bernoulli}, Message{Bernoulli}]) \n",
"\n",
" @test ruleSPAndIn2BBN(Message(Univariate, Bernoulli, p=0.1), Message(Univariate, Bernoulli, p=0.25), nothing) == Message(Univariate, Bernoulli, p=0.421875)\n",
" @test ruleSPAndIn2BBN(Message(Univariate, Bernoulli, p=0.1), Message(Univariate, Bernoulli, p=0.25), nothing) == Message(Univariate, Bernoulli, p=0.4375)\n",
"end\n",
"\n",
"end"
Expand All @@ -169,7 +171,7 @@
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Expand Down Expand Up @@ -233,7 +235,7 @@
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Expand Down Expand Up @@ -265,7 +267,7 @@
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Expand All @@ -279,17 +281,19 @@
"function ruleSPAndIn1BNB(msg_out::Message{Bernoulli}, msg_in1::Nothing, msg_in2::Message{Bernoulli})\n",
" p_out = msg_out.dist.params[:p]\n",
" p_in2 = msg_in2.dist.params[:p]\n",
" a = (1 - p_out)*(1 - p_in2)\n",
" a = 1 - p_out - p_in2 + 2*p_out*p_in2\n",
" b = 1 - p_out\n",
"\n",
" return Message(Univariate, Bernoulli, p=a/(2*a + p_in2))\n",
" return Message(Univariate, Bernoulli, p=a/(a + b))\n",
"end\n",
"\n",
"function ruleSPAndIn1BNB(msg_out::Message{Bernoulli}, msg_in1::Message{Bernoulli}, msg_in2::Nothing)\n",
" p_out = msg_out.dist.params[:p]\n",
" p_in1 = msg_in1.dist.params[:p]\n",
" a = (1 - p_out)*(1 - p_in1)\n",
" a = 1 - p_out - p_in1 + 2*p_out*p_in1\n",
" b = 1 - p_out\n",
"\n",
" return Message(Univariate, Bernoulli, p=a/(2*a + p_in1))\n",
" return Message(Univariate, Bernoulli, p=a/(a + b))\n",
"end\n",
";"
]
Expand All @@ -305,7 +309,7 @@
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Expand All @@ -321,7 +325,7 @@
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Expand All @@ -338,99 +342,99 @@
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Expand All @@ -446,7 +450,7 @@
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Expand All @@ -459,7 +463,7 @@
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Expand All @@ -481,7 +485,14 @@
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Expand All @@ -491,13 +502,13 @@
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