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Changed waterballoon factory function name.
PiperOrigin-RevId: 343283244
This commit is contained in:
Pedro A. Ortega
committed by
Saran Tunyasuvunakool
Saran Tunyasuvunakool
parent
cecb85baa5
commit
e574fb42a9
@@ -40,11 +40,13 @@
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"that causal Bayesian networks can’t. Even so, they have received little\n",
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"attention from the AI and ML community.\n",
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"\n",
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"For instance, we can describe a scenario where the weather is the cause and the barometer reading the effect, or viceversa, depending on whether we're on Earth or on some alien planet with different physics:\n",
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"For instance, we can describe a scenario where the weather is the cause and the\n",
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"barometer reading the effect, or viceversa, depending on whether we're on Earth\n",
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"or on some alien planet with different physics:\n",
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"\n",
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"\u003cimg src=\"http://www.adaptiveagents.org/_media/wiki/probtrees.png\" alt=\"Probability Trees\" width=\"700\"/\u003e\n",
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"\n",
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"Causal dependencies like these are naturally represented as a tree. We will see later that they allow us representing causal induction.\n",
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"Causal dependencies like these are naturally represented as a tree.\n",
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"\n",
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"In this tutorial we present new algorithms for causal reasoning in discrete\n",
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"probability trees that cover the entire causal hierarchy (association,\n",
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@@ -3214,11 +3216,18 @@
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"source": [
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"## Water Balloon Squad (a.k.a. Firing Squad)\n",
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"\n",
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"The following is a classical example used for illustrating counterfactual reasoning. There are two children (A and B) holding a water balloon, waiting for a signal from their friend (the \"captain\"). Upon the captain's signal, they both throw their water balloon at a single target simultaneously and accurately. The causal dependencies are as shown next:\n",
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"The following is a classical example used for illustrating counterfactual\n",
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"reasoning. There are two children (A and B) holding a water balloon, waiting\n",
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"for a signal from their friend (the \"captain\"). Upon the captain's signal,\n",
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"they both throw their water balloon at a single target simultaneously and\n",
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"accurately. The causal dependencies are as shown next:\n",
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"\n",
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"\u003cimg src=\"http://www.adaptiveagents.org/_media/wiki/waterballoon.png\" alt=\"Water Balloon Squad\" width=\"200\"/\u003e\n",
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"\n",
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"This situation can also be described using a probability tree constructed below. Note that in order to avoid problems due to conditioning on zero-probability transitions, we assign a tiny value (`eps`) to the nearly-impossible transitions.\n",
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"This situation can also be described using a probability tree constructed\n",
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"below. Note that in order to avoid problems due to conditioning on\n",
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"zero-probability transitions, we assign a tiny value (`eps`) to the\n",
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"nearly-impossible transitions.\n",
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"\n"
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]
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},
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@@ -3232,7 +3241,7 @@
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"source": [
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"#@title Water Balloon Squad factory function.\n",
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"\n",
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"def waterballon(bvar, eps=0.0001):\n",
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"def waterballoon(bvar, eps=0.0001):\n",
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" # Root: defined.\n",
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" # Define the captain's signal.\n",
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" if 'Captain' not in bvar:\n",
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@@ -3301,7 +3310,8 @@
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"id": "OfgAR3u0zASo"
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},
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"source": [
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"Let's ask our first question. Assume A throws the water balloon. What is the probability of B having thrown the balloon too?"
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"Let's ask our first question. Assume A throws the water balloon.\n",
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"What is the probability of B having thrown the balloon too?"
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]
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},
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{
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@@ -3312,7 +3322,7 @@
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},
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"outputs": [],
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"source": [
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"# Condition on having A throwing the water balloon.\n",
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"# Condition on A throwing the water balloon.\n",
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"wbs_see = wbs.see(cut_A)\n",
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"\n",
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"# Print the probability of B throwing the water balloon.\n",
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@@ -3329,9 +3339,12 @@
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"id": "IALdewe2zWVy"
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},
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"source": [
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"Notice how conditioning changed the transition probabilities, which then allow us to identify the pathways leading up to the event in which B throws the balloon. \n",
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"Notice how conditioning changed the transition probabilities, which then \n",
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"allow us to identify the pathways leading up to the event in which B throws\n",
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"the balloon. \n",
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"\n",
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"Assume now that A decides to act on their own and throws the balloon. What is the probability of B having thrown the balloon too?"
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"Assume now that A decides to act on their own and throws the balloon.\n",
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"What is the probability of B having thrown the balloon too?"
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]
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},
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{
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@@ -3359,9 +3372,15 @@
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"id": "okJ6csZNz-C7"
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},
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"source": [
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"Notice the difference between the two results above. If A acts on their own will, then this alters the conclusions we can draw.\n",
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"Notice the difference between the two results above. If A acts on their own\n",
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"will, then this alters the conclusions we can draw.\n",
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"\n",
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"Let's ask a more complex question. **Assume A or B throw the balloon on their own will.** That is, we do not know precisely whether A acted by themself, B acted by themself, or both acted toghether. Intuitively, in this situation it is more likely that B threw the balloon. What is the probability?"
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"Let's ask a more complex question. **Assume A or B throw the balloon on their\n",
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"own will.** That is, we do not know precisely whether A acted by themself,\n",
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"B acted by themself, or both acted together. \n",
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"Intuitively, B (or A for that matter) is more likely to having thrown\n",
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"the water balloon in this situation than when they were waiting for\n",
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"the captain's signal. What is the probability?"
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]
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},
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{
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@@ -3389,11 +3408,14 @@
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"id": "U6AUPwU8wSoc"
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},
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"source": [
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"The above result shows that it is indeed more likely that B has thrown their water balloon. \n",
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"The above result shows that it is indeed more likely (%75) that B has \n",
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"thrown their balloon than when they were waiting for the signal (50%). \n",
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"\n",
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"Now we will ask counterfactual questions. Let us start with an easy one first. \n",
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"Now we will ask counterfactual questions. Let's start with an easy one first. \n",
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"\n",
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"Assume you observe that the target is wet. Then, **had the captain not given the signal**, what is the probability that B threw the water balloon at the target?"
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"Assume you observe that the target is wet. Then, **had the captain not given\n",
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"the signal**, what is the probability that B would have thrown their water\n",
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"balloon at the target?"
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]
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},
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{
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@@ -3421,9 +3443,11 @@
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"id": "0gifSRkYxDMA"
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},
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"source": [
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"The result shows that B would not have thrown the water balloon, which makes sense, as we assumed that the captain had not given the signal.\n",
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"The result shows that B would not have thrown the water balloon.\n",
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"This makes sense, as we assumed that B did not get the captain's signal.\n",
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"\n",
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"Now, assume again you observe that the target is wet. **Had A not thrown the water balloon, would B have thrown it?**"
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"Now, assume again you observe that the target is wet. \n",
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"**Had A not thrown the water balloon, would B have thrown it?**"
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]
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},
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{
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@@ -3451,7 +3475,10 @@
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"id": "Jl6rVmjcxqUY"
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},
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"source": [
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"As is shown above, the answer is yes. This is because observing the wet target allows us to conclude that the captain has given the signal. Hence, had A not thrown the water balloon, B must have thrown it."
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"As is shown above, the answer is yes. This is because from observing the wet\n",
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"target we can conclude that the captain has given the signal. \n",
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"Hence, had A not thrown the water balloon, B must have thrown it\n",
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"instead. You can verify the causal pathways by inspecting the tree."
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]
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},
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{
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@@ -4085,13 +4112,65 @@
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],
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