Lecture10-PoS1

Lecture10-PoS1 - About Language Psych 215L: Language...

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Unformatted text preview: About Language Psych 215L: Language Acquisition Lecture 9 Poverty of the Stimulus About Language One way to think about how to classify the knowledge that you have when you know a language: You know what items (sounds, words, sentences, questions, etc.) are part of the language. You can tell whether or not a given item is grammatical in the language. Hoggle is definitely an ornery dwarf. [grammatical] * Hoggle an dwarf definitely ornery is. [ungrammatical] About Language One way to think about how to classify the knowledge that you have when you know a language: One way to think about how to classify the knowledge that you have when you know a language: You know what items (sounds, words, sentences, questions, etc.) are part of the language. You can tell whether or not a given item is grammatical in the language. You know what items (sounds, words, sentences, questions, etc.) are part of the language. You can tell whether or not a given item is grammatical in the language. Hoggle is definitely an ornery dwarf. [part of English] * Hoggle an dwarf definitely ornery is. [not part of English] The reason you can do this is because you know the rules & patterns that generate the items that are part of the language. (mental grammar) About Children Learning Language Adult knowledge: grammar that generates the items that are part of the language. The child’s job: figure out the rules that generate the items that belong in the language and that don’t generate items that don’t. For example, the child wants rules to generate “Hoggle is definitely an ornery dwarf.” but not “Hoggle an dwarf definitely ornery is. ” Not in English Hoggle an dwarf ornery is Bite adventurers fairies Can the girl who summon the Goblin King can solve the Labyrinth? Want to learn rules that generate this set of items… …and exclude this set of items Not in English Hoggle an dwarf ornery is Bite adventurers fairies In English Fairies bite Hoggle is an ornery adventurers dwarf Can the girl who can summon the Goblin King solve the Labyrinth? Can the girl who summon the Goblin King can solve the Labyrinth? In English Fairies bite Hoggle is an ornery adventurers dwarf Can the girl who can summon the Goblin King solve the Labyrinth? Not in English Hoggle an dwarf ornery is Bite adventurers fairies In English Fairies bite Hoggle is an ornery adventurers dwarf Can the girl who can summon the Goblin King solve the Labyrinth? Can the girl who summon the Goblin King can solve the Labyrinth? So what’s the problem? Fairies bite It’s not clear that children encounter all the items that are part of the language. So what’s the problem? One solution: children generalize Fairies bite But how do they generalize? If they only encounter a subset of the language’s items, how do they know everything that belongs in the language? To here? Items in English Items not in English Items in English Items Encountered Items Encountered So what’s the problem? One solution: children generalize Items not in English Fairies bite But how do they generalize? So what’s the problem? One solution: children generalize Fairies bite But how do they generalize? To here? To here? Items in English Items Encountered Items not in English Items in English Items Encountered Items not in English So what’s the problem? One solution: children generalize Fairies bite But how do they generalize? So what’s the problem? Fairies bite The problem is that children must make the right generalization from data that are compatible with multiple generalizations. In this sense, the data encountered are impoverished. They do not single out the correct generalization by themselves. To here? Items in English Items not in English Items not in English Items in English Items Encountered Items Encountered So what’s the problem? Fairies bite This is sometimes called the “poverty of the stimulus”, the “induction problem”, or the “no negative evidence problem”. A numerical analogy Items encountered: 3, 5, 7 What set are these numbers drawn from? That is, what is the right “number rule” for this language that will allow you to predict what numbers will appear in the future? Numbers less than 20 9 Odd numbers Items in English Items Encountered Prime numbers 15 Items not in English 18 3 4 13 5 7 11 12 2 6 Poverty of the Stimulus: Logic Fairies bite Children encounter data that are compatible with many hypotheses about the correct rules and patterns of the language. Items in English Items not in English Items Encountered Fairies bite A rational learner would consider all compatible hypotheses, and perhaps make errors before choosing the correct hypothesis. Items Encountered Fairies bite Specifically, the data encountered are compatible with both the correct hypothesis and other, incorrect hypotheses about the rules and patterns of the language. Items in English Items not in English Items Encountered Poverty of the Stimulus: Logic Items in English Poverty of the Stimulus: Logic Items not in English Poverty of the Stimulus: Logic Fairies bite Expectation for rational learners: errors in performance. Children will behave as if they think ungrammatical items are part of the language at some point. Items in English Items Encountered Items not in English Argument for Prior Knowledge Fairies bite But what if children never behave as if they consider the incorrect hypotheses? That is, they never produce errors compatible with the incorrect hypotheses or accept items that are compatible with the incorrect hypotheses. Items in English Items not in English Items Encountered Argument for Prior Knowledge Argument for Prior Knowledge Fairies bite Conclusion: children have some learning bias that causes them never to consider the incorrect hypotheses. Instead, they only consider the correct hypothesis for what the rules and patterns of the language might be. Learning bias restricts children’s hypothesis to this as the set of items allowed in the language Items in English Items not in English Items Encountered Specific Example: Yes/No Question Formation Fairies bite Nativist conclusion: the learning bias children have is specific to language (domain-specific) and is innate (not derivable from the child’s experience). This kind of learning bias is sometimes called “Universal Grammar”. Domain-specific, innate learning bias restricts children’s hypothesis to this as the set of items allowed in the language Jareth can alter time. To turn the sentence into a yes/no question, move the auxiliary verb (“can”) to the front. Can Jareth alter time? Items in English Items Encountered Items not in English The child’s task: figure out a rule that will form yes/no questions from their corresponding sentences. Specific Example: Yes/No Question Formation Jareth can alter time. Can Jareth alter time? Rule? Specific Example: Yes/No Question Formation Jareth can alter time. Can Jareth alter time? Rule: Move first auxiliary? Specific Example: Yes/No Question Formation Jareth can alter time. Can Jareth alter time? Rule: Move first auxiliary? Specific Example: Yes/No Question Formation Jareth can alter time. Can Jareth alter time? Rule: Move first auxiliary? Rule? Anyone who can wish away their brother would be tempted to do it. Would anyone who can wish away their brother be tempted to do it? Anyone who can wish away their brother would be tempted to do it. Would anyone who can wish away their brother be tempted to do it? Specific Example: Yes/No Question Formation Jareth can alter time. Can Jareth alter time? Rule: Move first auxiliary? Specific Example: Yes/No Question Formation Jareth can alter time. Can Jareth alter time? Rule: Move last auxiliary? Anyone who can wish away their brother would be tempted to do it. Would anyone who can wish away their brother be tempted to do it? Rule: Move first auxiliary? Rule: Move last auxiliary? Anyone who can wish away their brother would be tempted to do it. Would anyone who can wish away their brother be tempted to do it? Someone who can solve the labyrinth can show someone else who can’t how. Can someone who can solve the labyrinth show someone else who can’t how? Specific Example: Yes/No Question Formation Jareth can alter time. Can Jareth alter time? Rule: Move first auxiliary? Rule: Move last auxiliary? Anyone who can wish away their brother would be tempted to do it. Would anyone who can wish away their brother be tempted to do it? Rule??? Someone who can solve the labyrinth can show someone else who can’t how. Can someone who can solve the labyrinth show someone else who can’t how? Specific Example: Yes/No Question Formation Jareth can alter time. Can Jareth alter time? Rule: Move first auxiliary? Rule: Move last auxiliary? Anyone who can wish away their brother would be tempted to do it. Would anyone who can wish away their brother be tempted to do it? Rule??? Someone who can solve the labyrinth can show someone else who can’t how. Can someone who can solve the labyrinth show someone else who can’t how? Need a rule that is compatible with all of these, since they’re all grammatical English questions. Specific Example: Yes/No Question Formation Specific Example: Yes/No Question Formation embedded clauses = additional descriptive sentences that are not part of the main clause Jareth can alter time. Can Jareth alter time? Jareth can alter time. Can Jareth alter time? Anyone who can wish away their brother would be tempted to do it. Would anyone who can wish away their brother be tempted to do it? Anyone who can wish away their brother would be tempted to do it. Would anyone who can wish away their brother be tempted to do it? Someone who can solve the labyrinth can show someone else who can’t how. Can someone who can solve the labyrinth show someone else who can’t how? Someone who can solve the labyrinth can show someone else who can’t how. Can someone who can solve the labyrinth show someone else who can’t how? Idea: Try looking at the sentence structure, not just the linear order of the words in the sentences. Idea: Try looking at the sentence structure, not just the linear order of the words in the sentences. Specific Example: Yes/No Question Formation Specific Example: Yes/No Question Formation Jareth can alter time. Can Jareth alter time? embedded clauses = additional descriptive sentences that are not part of the main clause Jareth can alter time. Can Jareth alter time? Anyone who can wish away their brother would be tempted to do it. Would anyone who can wish away their brother be tempted to do it? Anyone would be tempted to do it. Would anyone be tempted to do it? Someone who can solve the labyrinth can show someone else who can’t how. Can someone who can solve the labyrinth show someone else who can’t how? Someone can show someone else how. Can someone show someone else how? Let’s look just at the main clauses in these examples Let’s look just at the main clauses in these examples Specific Example: Yes/No Question Formation Jareth can alter time. Can Jareth alter time? Children’s Knowledge Children seem to know this rule by the age of 3. (Crain & Nakayama 1987) Anyone would be tempted to do it. Would anyone be tempted to do it? Learning problem: Children don’t encounter all the examples we saw. They encounter a subset of the possible yes/no questions in English. Someone can show someone else how. Can someone show someone else how? Rule that works for all of these examples (and all English examples): Move the auxiliary verb in the main clause to make a yes/no question. Most of the data they encounter (particularly before the age of 3) are simple yes/no questions. Jareth can alter time. Can Jareth alter time? This is a rule dependent on the structure of the sentences. Learning Difficulties: Yes/No Questions The problem is that these simple yes/no questions are compatible with a lot of different rules. Rule: Move first auxiliary? Jareth can alter time. Can Jareth alter time? Learning Difficulties: Yes/No Questions Rational learner prediction: if children considered all these hypotheses, they should make mistakes on more complex yes/no questions. Let’s look at two hypotheses in detail. Rule: Move first auxiliary? Rule: Move last auxiliary? Rule: Move main clause auxiliary? Rule: Move auxiliary in even-numbered position in sentence? Rule: Move auxiliary closest to a noun? Rule: Move main clause auxiliary? Learning Difficulties: Yes/No Questions Learning Difficulties: Yes/No Questions The girl who can solve the labyrinth is happy. The girl who can solve the labyrinth is happy. Predictions of questions generated Predictions of questions generated Rule: Move first auxiliary? Rule: Move first auxiliary? * Can the girl who solve the labyrinth is happy? * Can the girl who solve the labyrinth is happy? Rule: Move main clause auxiliary? Correct rule = grammatical question Is the girl who can solve the labyrinth happy? Learning Difficulties: Yes/No Questions Crain & Nakayama (1987) showed that children as young as 3 years old don’t make these mistakes. They use the right rule for this complex yes/no question. Predictions of questions generated Learning Difficulties: Yes/No Questions But the simple questions they see are compatible with both of these hypotheses (along with many others). How do children choose the right rule from all the possible rules that are compatible? That is, how do they generalize the right way from the subset of the data they encounter? Rule: Move first auxiliary? Items in English * Can the girl who solve the labyrinth is happy? Items Encountered Rule: Move main clause auxiliary? Is the girl who can solve the labyrinth happy? Rule: Move main clause auxiliary? Is the girl who can solve the labyrinth happy? Learning Difficulties: Yes/No Questions Learning Difficulties: Yes/No Questions Nativist position: Children have an innate bias to look for rules that make use of sentence structure. Specifically, they only consider rules that are structure-dependent. Rule: Move first auxiliary? Rule: Move last auxiliary? Rule: Move auxiliary in evennumbered position in sentence? Rule: Move auxiliary closest to a noun? Items in English Items Encountered It is this structure-dependent learning bias that allows children to generalize the correct way from “impoverished” data. Items in English Items Encountered Rule: Move main clause auxiliary? Is the girl who can solve the labyrinth happy? Another example of children’s constrained generalization Another example of children’s constrained generalization Crain & McKee (1985): pronoun interpretation Crain & McKee (1985): pronoun interpretation While he danced around the throne room, Jareth smiled. (Adults: he = Jareth) (Children: he = Jareth) While he danced around the throne room, Jareth smiled. (he = Jareth) Jareth smiled while he danced around the throne room. Another example of children’s constrained generalization Crain & McKee (1985): pronoun interpretation While he danced around the throne room, Jareth smiled. (he = Jareth) Another example of children’s constrained generalization Crain & McKee (1985): pronoun interpretation While Jareth danced around the throne room, he smiled. (Adults: he = Jareth) (Children: he = Jareth) Jareth smiled while he danced around the throne room. (Adults: he = Jareth) (Children: he = Jareth) Possible generalization: Can put pronoun before name or name before pronoun Another example of children’s constrained generalization Crain & McKee (1985): pronoun interpretation Another example of children’s constrained generalization Crain & McKee (1985): pronoun interpretation While Jareth danced around the throne room, he smiled. (he = Jareth) While Jareth danced around the throne room, he smiled. (he = Jareth) He smiled while Jareth danced around the throne room. He smiled while Jareth danced around the throne room. (Adults: he cannot be Jareth) Another example of children’s constrained generalization Crain & McKee (1985): pronoun interpretation Another example of children’s constrained generalization Crain & McKee (1985): pronoun interpretation While Jareth danced around the throne room, he smiled. (he = Jareth) While Jareth danced around the throne room, he smiled. (he = Jareth) He smiled while Jareth danced around the throne room. (Adults: he cannot be Jareth) (Children: he cannot be Jareth) He smiled while Jareth danced around the throne room. (Adults: he cannot be Jareth) (Children: he cannot be Jareth) Possible generalization fails: Order of pronoun and name matters. Why? Answer: Constraint on pronoun interpretation. This constraint (c-command) is structure-dependent, it turns out. Another example of children’s constrained generalization Another example of children’s constrained generalization Crain & McKee (1985): pronoun interpretation While he danced around the throne room, Jareth smiled. (he = Jareth) Jareth smiled while he danced around the throne room. (he = Jareth) While Jareth danced around the throne room, he smiled. (he = Jareth) He smiled while Jareth danced around the throne room. (he ≠ Jareth) Crain & McKee (1985): pronoun interpretation The point: Children generalize only in a very specific way. In particular, they don’t just generalize everything that they can. Their generalizations appear to be constrained. Nativist idea for how their generalizations/hypotheses are constrained: innate learning bias about language = Universal Grammar. Poverty of the Stimulus leads to Innate Knowledge about Language: Summary of Logic Hypothesis = Generalization 1) Suppose there are some data. 1) Suppose there are some data. 2) Suppose there is an incorrect hypothesis compatible with the data. 2) Suppose there are multiple generalizations compatible with the data. 3) Suppose children behave as if they never entertain the incorrect hypothesis. 3) Suppose children behave as if they only make one generalization. Conclusion: Children possess prior (innate) learning biases ruling out the incorrect hypothesis from the hypotheses they do actually consider. Conclusion: Children possess prior (innate) learning biases that bias them away from the incorrect generalizations. Making generalizations that are underdetermined by the data Making generalizations that are underdetermined by the data Items in English Items not in English Items Encountered Children encounter a subset of the language’s data, and have to decide how to generalize from that data Here’s a question (Gerken 2006): is there any way to check what kinds of generalizations children prefer to make? Example: Suppose they’re given a data set that is compatible with two generalizations: a less-general one and a moregeneral one. data less general more general Generalization = predictions about what data are in the language x x Do children think this generalization is the right one? data less general x x x x x x x xx x x x x x x x x x x x x x more general x x x x Data children encounter x x x x x Choosing generalizations x x x Or do children think this generalization is the right one? How can we tell? x x x x x x xx x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x xx x x x x x x x x x x x x x x x They will not think that data that are in the more-general hypothesis are in the language. x x x x If children think the lessgeneral hypothesis is correct, they will think data covered by that hypothesis are in the language - in addition to the data they encountered. x x x x x x x x x Choosing generalizations: the more general hypothesis x Choosing generalizations: the less general hypothesis x If children think the more-general hypothesis is correct, they will think data covered by that hypothesis are in the language - in addition to the data they encountered and the data in the less-general hypothesis. Potential child responses when multiple generalizations are possible Reality check What do these correspond to in a real language learning scenario? Data: Simple yes/no questions in English x x xx x x x x x x x x x x x x x x x “Is the dwarf laughing?” more-general x x x “Can the goblin king sing?” x x x x x x x x x x x less-general x x x x x x x x xx x x x x x x x x x x “Will Sarah solve the Labyrinth?” x x x x x x x x Reality check What do these correspond to in a real language learning scenario? x x x x x x x x x x x x x x x x x x x x x x Reality check What do these correspond to in a real language learning scenario? less-general hypothesis: Some complex grammatical yes-no questions “Is the dwarf laughing about the fairies he sprayed?” “Can the goblin king sing whenever he wants?” x x x x x x x x x x x x x x x x x x x x x x xx x x x x x x x x x x x x x x x x x x more-general hypothesis: Full range of complex grammatical yes-no questions “Can the girl who ate the peach and forgot everything save her brother?” “Will the dwarf who deserted Sarah help her reach the castle that’s beyond the goblin city?” Experimental Study: Gerken (2006) Artificial language: AAB/ABA pattern How can we tell what generalizations children actually make? Let’s try an artificial language learning study. Marcus et al. (1999) found that very young infants will notice that words made up of 3 syllables follow a pattern that can be represented as AAB or ABA. Children will be trained on data from an artificial language. This language will consist of words that follow a certain pattern. Example: The child’s job: determine what the pattern is that allows a word to be part of the artificial language. ABA language words: ledile, lejele, widiwi, wijewi Artificial language: AAB/ABA pattern A syllables = le, wi B syllables = di, je AAB language words: leledi, leleje, wiwidi, wiwije Words in the AAB pattern artificial language. di li we le Gerken (2006) decided to test what kind of generalization children would make if they were given particular kinds of data from this same artificial language. je leledi leleje leleli lelewe wi wiwidi wiwije wiwili wiwiwe ji jijidi jijije jijili jijiwe de dededi dedeje dedeli dedewe What if children were only trained on a certain subset of the words in the language? Words in the AAB pattern artificial language. di je li we le leledi leleje leleli lelewe wi wiwidi wiwije wiwili wiwiwe ji jijidi jijije jijili jijiwe de dededi dedeje dedeli dedewe Question: If children are given this subset of the data that is compatible with both generalizations, which generalization will they make (AAdi or AAB)? (Experimental Condition) Training on four word types: leledi, wiwidi, jijidi, dededi (Experimental Condition) Training on four word types: leledi, wiwidi, jijidi, dededi These data are consistent with a less-general pattern (AAdi) as well as the more-general pattern of the language (AAB) These data are consistent with a less-general pattern (AAdi) as well as the more-general pattern of the language (AAB) Words in the AAB pattern artificial language. di je li we le leledi leleje leleli lelewe wi wiwidi wiwije wiwili wiwiwe ji jijidi jijije jijili jijiwe de dededi dedeje dedeli dedewe This control condition is used to see what children’s behavior is when the data are only consistent with one of the generalizations (the more general AAB one). If children fail to make the generalization in the control condition, then the results in the experimental condition will not be informative. (Perhaps the task was too hard for children.) (Control Condition) Training on four word types: leledi, wiwije, jijili, dedewe (Control Condition) Training on four word types: leledi, wiwije, jijili, dedewe These data are only consistent with the more-general pattern of the language (AAB) These data are only consistent with the more-general pattern of the language (AAB) Experiment 1 Experiment 1 Predictions Task type: Head Turn Preference Procedure Experimental: leledi…wiwidi…jijidi…dededi Control: leledi…wiwije…jijili…dedewe Children: 9-month-olds Stimuli: 2 minutes of artificial language words. Control: leledi…wiwije…jijili…dedewe If children learn the more-general pattern (AAB), they will prefer to listen to an AAB pattern word even if it doesn’t end in di - like kokoba, over a word that does not follow the AAB pattern, like kobako. Test condition words: AAB pattern words using syllables the children had never encountered before in the language. Ex: kokoba (novel syllables: ko, ba) Experiment 1 Predictions Experimental: leledi…wiwidi…jijidi…dededi If children learn the less-general pattern (AAdi), they will not prefer to listen to an AAB pattern word that does not end in di, like kokoba, over a word that does not follow the AAB pattern, like kobako. If children learn the more-general pattern (AAB), they will prefer to listen to an AAB pattern word even if it doesn’t end in di - like kokoba, over a word that does not follow the AAB pattern, like kobako. Experiment 1 Results Control: leledi…wiwije…jijili…dedewe Children listened longer on average to test items consistent with the AAB pattern (like kokoba) [13.51 sec], as opposed to items inconsistent with it (like kobako) [10.14]. Implication: They can notice the AAB pattern and make the generalization from this artificial language data. Experimental: leledi…wiwidi…jijidi…dededi Experiment 1 Results Control: leledi…wiwije…jijili…dedewe Experiment 1 Results Control: leledi…wiwije…jijili…dedewe They can notice the AAB pattern and make the generalization from this artificial language data. Experimental: leledi…wiwidi…jijidi…dededi Children did not listen longer on average to test items consistent with the AAB pattern (like kokoba) [10.74 sec], as opposed to items inconsistent with it (like kobako) [10.18]. Implication: They do not make the more-general generalization (AAB). Experiment 2 They can notice the AAB pattern and make the generalization from this artificial language data. Experimental: leledi…wiwidi…jijidi…dededi Implication: They do not make the more-general generalization (AAB) from this data Question: Do they make the less-general generalization (AAdi), or do they just fail completely to make a generalization? Experiment 2 Predictions Task type: Head Turn Preference Procedure Experimental: leledi…wiwidi…jijidi…dededi Children: 9-month-olds Experimental: leledi…wiwidi…jijidi…dededi If children learn the less-general pattern (AAdi), they will prefer to listen to an AAdi pattern word, like kokodi, over a word that does not follow the AAdi pattern, like kodiko. Stimuli: 2 minutes of artificial language words. Test condition words: novel AAdi pattern words using syllables the children had never encountered before in the language. Ex: kokodi (novel syllable: ko) If children don’t learn any pattern, they will not prefer to listen to an AAdi pattern word, like kokodi, over a word that does not follow the AAdi pattern, like kodiko. Experiment 2 Results Children prefer to listen to novel words that follow the lessgeneral AAdi pattern, like kokodi [9.33 sec] over novel words that do not follow the AAdi pattern, like kodiko [6.25 sec]. When children are given data that is compatible with a lessgeneral and a more-general generalization, they prefer to be conservative and make the less-general generalization. prefer this one x Implication: They make the less-general generalization (AAdi) from this data. It is not the case that they fail to make any generalization at all. x x x x x x x x x x x x x x x x x x x x x x x x x Why would a preference for the less-general generalization be a sensible preference to have? What if children preferred this one… x x x x Specifically for the artificial language study conducted, children prefer not to make unnecessary abstractions about the data. They prefer the AAdi pattern over a more abstract AAB pattern when the AAdi pattern fits the data they have encountered. x x x x x x x x x x x x x x x x x x x x x x x x x x x x When children are given data that is compatible with a lessgeneral and a more-general generalization, they prefer to be conservative and make the less-general generalization. x x x x x Gerken (2006) Results x x x x x Experimental: leledi…wiwidi…jijidi…dededi Gerken (2006) Results x x x x …but the language really was this one? Problem: There are no data the child could receive that would clue them in that the less-general generalization is right. All data compatible with the less-general one are compatible with the moregeneral one. Why would a preference for the less-general generalization be a sensible preference to have? What if children preferred this one… x x x x x x x x x x x x x x x x x x x x x x x x x x x x x This is a learning strategy that can result very naturally from a Bayesian learner which uses the Size Principle (Tenenbaum & Griffiths 2001). x x Subset Principle (Wexler & Manzini 1987): In order to learn correctly in this scenario where one generalization covers a subset of the data another generalization covers, children should prefer the less-general generalization. x x x x Solutions to the Subset Problem x …but the language really was this one? This is known as the Subset Problem for language learning. Size Principle Logic Size Principle Logic Has to do with children’s expectation of the data points that they should encounter in the input Has to do with children’s expectation of the data points that they should encounter in the input More-General (AAB) If more-general generalization (AAB) is correct, the child should encounter some data that can only be accounted for by the more-general generalization (like memewe or nanaje). These data would be incompatible with the less-general generalization (AAdi). memewe nanaje Less-General (AAdi) memedi kokodi nanadi More-General (AAB) If the child keeps not encountering data compatible only with the more-general generalization, the less-general generalization becomes more and more likely to be the generalization responsible for the language data encountered. papadi Less-General (AAdi) kokodi memedi kokodi nanadi Size Principle Logic Another way to think about it: probability of generating data point The likelihood that a given data point (like memedi) was generated if the subset is doing the generating is, by definition, higher than the likelihood that data point would be generated if the superset was doing the generating. So, the subset has a higher probability of having produced this data point - it gets favored (+some probability) when this data point is encountered. More-General (AAB) memewe nanaje Less-General (AAdi) memedi kokodi nanadi ...
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This note was uploaded on 12/12/2011 for the course PSYCH 215l taught by Professor Pearl during the Fall '11 term at UC Irvine.

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