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Asia example

release/4.3a0
p-zach 2025-04-16 16:29:11 -04:00
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gtsam/inference/doc/BayesNet.ipynb
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@ -15,7 +15,7 @@
"id": "bayesnet_desc_md"
},
"source": [
"A `BayesNet` in GTSAM represents a directed graphical model, specifically the result of running sequential variable elimination (like Cholesky or QR factorization) on a `FactorGraph`.\n",
"A `BayesNet` in GTSAM represents a directed graphical model, created by running sequential variable elimination (like Cholesky or QR factorization) on a `FactorGraph` or constructing from scratch.\n",
"\n",
"It is essentially a collection of `Conditional` objects, ordered according to the elimination order. Each conditional represents $P(\\text{variable} | \\text{parents})$, where the parents are variables that appear later in the elimination ordering.\n",
"\n",
@ -57,7 +57,7 @@
},
{
"cell_type": "code",
"execution_count": 13,
"execution_count": 44,
"metadata": {
"id": "bayesnet_import_code"
},
@ -69,6 +69,8 @@
"\n",
"# We need concrete graph types and elimination to get a BayesNet\n",
"from gtsam import GaussianFactorGraph, Ordering, GaussianBayesNet\n",
"# For the Asia example\n",
"from gtsam import DiscreteBayesNet, DiscreteConditional, DiscreteKeys, DiscreteValues, symbol\n",
"from gtsam import symbol_shorthand\n",
"\n",
"X = symbol_shorthand.X\n",
@ -88,7 +90,7 @@
},
{
"cell_type": "code",
"execution_count": 14,
"execution_count": 45,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
@ -144,7 +146,7 @@
},
{
"cell_type": "code",
"execution_count": 15,
"execution_count": 46,
"metadata": {},
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{
@ -199,7 +201,7 @@
},
{
"cell_type": "code",
"execution_count": 10,
"execution_count": 47,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
@ -250,7 +252,7 @@
},
{
"cell_type": "code",
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"execution_count": 48,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
@ -297,7 +299,7 @@
},
{
"cell_type": "code",
"execution_count": 12,
"execution_count": 49,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
@ -353,10 +355,10 @@
"</svg>\n"
],
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"<graphviz.sources.Source at 0x18b7818a990>"
"<graphviz.sources.Source at 0x18b7757b020>"
]
},
"execution_count": 12,
"execution_count": 49,
"metadata": {},
"output_type": "execute_result"
}
@ -364,6 +366,364 @@
"source": [
"graphviz.Source(bayes_net.dot())"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "bayesnet_discrete_md"
},
"source": [
"## Example: DiscreteBayesNet (Asia Network)\n",
"\n",
"While the previous examples focused on `GaussianBayesNet`, GTSAM also supports `DiscreteBayesNet` for representing probability distributions over discrete variables. Here we construct the classic 'Asia' network example directly by adding `DiscreteConditional` objects."
]
},
{
"cell_type": "code",
"execution_count": 50,
"metadata": {
"id": "bayesnet_discrete_imports_code"
},
"outputs": [],
"source": [
"# Define keys for the Asia network variables\n",
"A = symbol('A', 8) # Visit to Asia?\n",
"S = symbol('S', 7) # Smoker?\n",
"T = symbol('T', 6) # Tuberculosis?\n",
"L = symbol('L', 5) # Lung Cancer?\n",
"B = symbol('B', 4) # Bronchitis?\n",
"E = symbol('E', 3) # Tuberculosis or Lung Cancer?\n",
"X = symbol('X', 2) # Positive X-Ray?\n",
"D = symbol('D', 1) # Dyspnea (Shortness of breath)?\n",
"\n",
"# Define cardinalities (all are binary in this case)\n",
"cardinalities = { A: 2, S: 2, T: 2, L: 2, B: 2, E: 2, X: 2, D: 2 }\n",
"\n",
"# Helper to create DiscreteKeys object\n",
"def make_keys(keys_list):\n",
" dk = DiscreteKeys()\n",
" for k in keys_list:\n",
" dk.push_back((k, cardinalities[k]))\n",
" return dk"
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "bayesnet_discrete_build_code",
"outputId": "456789ab-cdef-0123-4567-89abcdef0123"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Asia Bayes Net:\n",
"DiscreteBayesNet\n",
" \n",
"size: 8\n",
"conditional 0: P( D1 | E3 B4 ):\n",
" Choice(E3) \n",
" 0 Choice(D1) \n",
" 0 0 Choice(B4) \n",
" 0 0 0 Leaf 0.9\n",
" 0 0 1 Leaf 0.2\n",
" 0 1 Choice(B4) \n",
" 0 1 0 Leaf 0.1\n",
" 0 1 1 Leaf 0.8\n",
" 1 Choice(D1) \n",
" 1 0 Choice(B4) \n",
" 1 0 0 Leaf 0.3\n",
" 1 0 1 Leaf 0.1\n",
" 1 1 Choice(B4) \n",
" 1 1 0 Leaf 0.7\n",
" 1 1 1 Leaf 0.9\n",
"\n",
"conditional 1: P( X2 | E3 ):\n",
" Choice(X2) \n",
" 0 Choice(E3) \n",
" 0 0 Leaf 0.95\n",
" 0 1 Leaf 0.02\n",
" 1 Choice(E3) \n",
" 1 0 Leaf 0.05\n",
" 1 1 Leaf 0.98\n",
"\n",
"conditional 2: P( E3 | T6 L5 ):\n",
" Choice(T6) \n",
" 0 Choice(L5) \n",
" 0 0 Choice(E3) \n",
" 0 0 0 Leaf 1\n",
" 0 0 1 Leaf 0\n",
" 0 1 Choice(E3) \n",
" 0 1 0 Leaf 0\n",
" 0 1 1 Leaf 1\n",
" 1 Choice(L5) \n",
" 1 0 Choice(E3) \n",
" 1 0 0 Leaf 0\n",
" 1 0 1 Leaf 1\n",
" 1 1 Choice(E3) \n",
" 1 1 0 Leaf 0\n",
" 1 1 1 Leaf 1\n",
"\n",
"conditional 3: P( B4 | S7 ):\n",
" Choice(S7) \n",
" 0 Choice(B4) \n",
" 0 0 Leaf 0.7\n",
" 0 1 Leaf 0.3\n",
" 1 Choice(B4) \n",
" 1 0 Leaf 0.4\n",
" 1 1 Leaf 0.6\n",
"\n",
"conditional 4: P( L5 | S7 ):\n",
" Choice(S7) \n",
" 0 Choice(L5) \n",
" 0 0 Leaf 0.99\n",
" 0 1 Leaf 0.01\n",
" 1 Choice(L5) \n",
" 1 0 Leaf 0.9\n",
" 1 1 Leaf 0.1\n",
"\n",
"conditional 5: P( T6 | A8 ):\n",
" Choice(T6) \n",
" 0 Choice(A8) \n",
" 0 0 Leaf 0.99\n",
" 0 1 Leaf 0.95\n",
" 1 Choice(A8) \n",
" 1 0 Leaf 0.01\n",
" 1 1 Leaf 0.05\n",
"\n",
"conditional 6: P( S7 ):\n",
" Leaf 0.5\n",
"\n",
"conditional 7: P( A8 ):\n",
" Choice(A8) \n",
" 0 Leaf 0.99\n",
" 1 Leaf 0.01\n",
"\n"
]
}
],
"source": [
"# Create the DiscreteBayesNet\n",
"asia_net = DiscreteBayesNet()\n",
"\n",
"# Helper function to create parent list in correct format\n",
"def make_parent_tuples(parent_keys):\n",
" return [(pk, cardinalities[pk]) for pk in parent_keys]\n",
"\n",
"# P(D | E, B) - Dyspnea given Either and Bronchitis\n",
"asia_net.add(DiscreteConditional((D, cardinalities[D]), make_parent_tuples([E, B]), \"9/1 2/8 3/7 1/9\"))\n",
"\n",
"# P(X | E) - X-Ray result given Either\n",
"asia_net.add(DiscreteConditional((X, cardinalities[X]), make_parent_tuples([E]), \"95/5 2/98\"))\n",
"\n",
"# P(E | T, L) - Either Tub. or Lung Cancer (OR gate)\n",
"# \"F T T T\" means P(E=1|T=0,L=0)=0, P(E=1|T=0,L=1)=1, P(E=1|T=1,L=0)=1, P(E=1|T=1,L=1)=1\n",
"asia_net.add(DiscreteConditional((E, cardinalities[E]), make_parent_tuples([T, L]), \"F T T T\"))\n",
"\n",
"# P(B | S) - Bronchitis given Smoker\n",
"asia_net.add(DiscreteConditional((B, cardinalities[B]), make_parent_tuples([S]), \"70/30 40/60\"))\n",
"\n",
"# P(L | S) - Lung Cancer given Smoker\n",
"asia_net.add(DiscreteConditional((L, cardinalities[L]), make_parent_tuples([S]), \"99/1 90/10\"))\n",
"\n",
"# P(T | A) - Tuberculosis given Asia\n",
"asia_net.add(DiscreteConditional((T, cardinalities[T]), make_parent_tuples([A]), \"99/1 95/5\"))\n",
"\n",
"# P(S) - Prior on Smoking\n",
"asia_net.add(DiscreteConditional((S, cardinalities[S]), [], \"1/1\")) # or \"50/50\"\n",
"\n",
"# Add conditional probability tables (CPTs) using C++ sugar syntax\n",
"# P(A) - Prior on Asia\n",
"asia_net.add(DiscreteConditional((A, cardinalities[A]), [], \"99/1\"))\n",
"\n",
"print(\"Asia Bayes Net:\")\n",
"asia_net.print()"
]
},
{
"cell_type": "code",
"execution_count": 58,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "bayesnet_discrete_viz_eval_code",
"outputId": "56789abc-def0-1234-5678-9abcdef01234"
},
"outputs": [
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"text": [
"Log Probability of all zeros: -1.2366269421045588\n",
"Sampled Values (basic print):\n",
"DiscreteValues{4683743612465315848: 0, 4755801206503243780: 1, 4899916394579099649: 1, 4971973988617027587: 0, 5476377146882523141: 0, 5980780305148018695: 1, 6052837899185946630: 0, 6341068275337658370: 0}\n",
"Sampled Values (pretty print):\n",
" A8: 0\n",
" B4: 1\n",
" D1: 1\n",
" E3: 0\n",
" L5: 0\n",
" S7: 1\n",
" T6: 0\n",
" X2: 0\n"
]
}
],
"source": [
"# Visualize the network structure\n",
"dot_string = asia_net.dot()\n",
"display(graphviz.Source(dot_string))\n",
"\n",
"# Evaluate the log probability of a specific assignment\n",
"# Example: Calculate P(A=0, S=0, T=0, L=0, B=0, E=0, X=0, D=0)\n",
"values = DiscreteValues()\n",
"for key, card in cardinalities.items():\n",
" values[key] = 0 # Assign 0 to all variables to start\n",
"\n",
"log_prob_zeros = asia_net.logProbability(values)\n",
"print(f\"Log Probability of all zeros: {log_prob_zeros}\")\n",
"\n",
"# Sample from the Bayes Net\n",
"sample = asia_net.sample()\n",
"print(\"Sampled Values (basic print):\")\n",
"print(sample)\n",
"\n",
"# --- Pretty Print ---\n",
"print(\"Sampled Values (pretty print):\")\n",
"# Create a reverse mapping from integer key to string like 'A8'\n",
"# We defined A=symbol('A',8), S=symbol('S',7), etc. above\n",
"symbol_map = { A: 'A8', S: 'S7', T: 'T6', L: 'L5', B: 'B4', E: 'E3', X: 'X2', D: 'D1' }\n",
"# Iterate through the sampled values and print nicely\n",
"# Sort items by the symbol string for consistent order (optional)\n",
"for key, value in sorted(sample.items(), key=lambda item: symbol_map.get(item[0], str(item[0]))):\n",
" symbol_str = symbol_map.get(key, f\"UnknownKey({key})\") # Get 'A8' from key A\n",
" print(f\" {symbol_str}: {value}\")"
]
}
],
"metadata": {