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11
Infinitary Self Reference in Learning Theory
, 1994
"... Kleene's Second Recursion Theorem provides a means for transforming any program p into a program e(p) which first creates a quiescent self copy and then runs p on that self copy together with any externally given input. e(p), in effect, has complete (low level) self knowledge, and p represents ..."
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Cited by 19 (6 self)
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Kleene's Second Recursion Theorem provides a means for transforming any program p into a program e(p) which first creates a quiescent self copy and then runs p on that self copy together with any externally given input. e(p), in effect, has complete (low level) self knowledge, and p represents how e(p) uses its self knowledge (and its knowledge of the external world). Infinite regress is not required since e(p) creates its self copy outside of itself. One mechanism to achieve this creation is a self replication trick isomorphic to that employed by singlecelled organisms. Another is for e(p) to look in a mirror to see which program it is. In 1974 the author published an infinitary generalization of Kleene's theorem which he called the Operator Recursion Theorem. It provides a means for obtaining an (algorithmically) growing collection of programs which, in effect, share a common (also growing) mirror from which they can obtain complete low level models of themselves and the other prog...
Noisy Inference and Oracles
, 1996
"... A learner noisily infers a function or set, if every correct item is presented infinitely often while in addition some incorrect data ("noise") is presented a finite number of times. It is shown that learning from a noisy informant is equal to finite learning with Koracle from a usual i ..."
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Cited by 7 (2 self)
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A learner noisily infers a function or set, if every correct item is presented infinitely often while in addition some incorrect data ("noise") is presented a finite number of times. It is shown that learning from a noisy informant is equal to finite learning with Koracle from a usual informant. This result has several variants for learning from text and using different oracles. Furthermore, partial identification of all r.e. sets can cope also with noisy input.
Program synthesis in the presence of infinite number of inaccuracies
 in &quot;Proceedings of the 5th Workshop on Algorithmic Learning Theory
, 1994
"... Most studies modeling inaccurate data in Gold style learning consider cases in which the number of inaccuracies is finite. The present paper argues that this approach is not reasonable for modeling inaccuracies in concepts that are infinite in nature (for example, graphs of computable functions). Th ..."
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Cited by 6 (1 self)
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Most studies modeling inaccurate data in Gold style learning consider cases in which the number of inaccuracies is finite. The present paper argues that this approach is not reasonable for modeling inaccuracies in concepts that are infinite in nature (for example, graphs of computable functions). The effect of infinite number of inaccuracies in the input data in Gold’s model of learning is considered in the context of identification in the limit of computer programs from graphs of computable functions. Three kinds of inaccuracies, namely, noisy data, incomplete data, and imperfect data, are considered. The amount of each of these inaccuracies in the input is measured using certain density notions. A number of interesting hierarchy results are shown based on the densities of inaccuracies present in the input data. Several results establishing tradeoffs between the density and type of inaccuracies are also derived. 1 1
Learning from Multiple Sources of Inaccurate Data
 in &quot;Proceedings of the International Workshop on Analogical and Inductive Inference in Dagstuhl
, 1992
"... Abstract. Most theoretical models of inductive inference make the idealized assumption that the data available to a learner is from a single and accurate source. The subject of inaccuracies in data emanating from a single source has been addressed by several authors. The present paper argues in favo ..."
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Cited by 5 (2 self)
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Abstract. Most theoretical models of inductive inference make the idealized assumption that the data available to a learner is from a single and accurate source. The subject of inaccuracies in data emanating from a single source has been addressed by several authors. The present paper argues in favor of a more realistic learning model in which data emanates from multiple sources, some or all of which may be inaccurate. Three kinds of inaccuracies are considered: spurious data (modeled as noisy texts), missing data (modeled as incomplete texts), and a mixture of spurious and missing data (modeled as imperfect texts). Motivated by the above argument, the present paper introduces and theoretically analyzes a number of inference criteria in which a learning machine is fed data from multiple sources, some of which may be infected with inaccuracies. The learning situation modeled is the identification in the limit of programs from graphs of computable functions. The main parameters of the investigation are: kind of inaccuracy, total number of data sources, number of faulty data sources which produce data within an acceptable bound, and the bound on the number of errors allowed in the final hypothesis learned by the machine. Sufficient conditions are determined under which, for the same kind of inaccuracy, for the same
A Survey of Inductive Inference with an Emphasis on Queries
 Complexity, Logic, and Recursion Theory, number 187 in Lecture notes in Pure and Applied Mathematics Series
, 1997
"... this paper M 0 ; M 1 ; : : : is a standard list of all Turing machines, M ..."
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Cited by 4 (0 self)
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this paper M 0 ; M 1 ; : : : is a standard list of all Turing machines, M
Inferring Descriptive Generalisations of Formal Languages
"... In the present paper, we introduce a variant of Goldstyle learners that is not required to infer precise descriptions of the languages in a class, but that must find descriptive patterns, i. e., optimal generalisations within a class of pattern languages. Our first main result characterises those i ..."
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Cited by 2 (1 self)
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In the present paper, we introduce a variant of Goldstyle learners that is not required to infer precise descriptions of the languages in a class, but that must find descriptive patterns, i. e., optimal generalisations within a class of pattern languages. Our first main result characterises those indexed families of recursive languages that can be inferred by such learners, and we demonstrate that this characterisation shows enlightening connections to Angluin’s corresponding result for exact inference. Using a notion of descriptiveness that is restricted to the natural subclass of terminalfree Epattern languages, we introduce a generic inference strategy, and our second main result characterises those classes of languages that can be generalised by this strategy. This characterisation demonstrates that there are major classes of languages that can be generalised in our model, but not be inferred by a normal Goldstyle learner. Our corresponding technical considerations lead to deep insights of intrinsic interest into combinatorial and algorithmic properties of pattern languages. 1
Learning from Streams
"... Learning from streams is a process in which a group of learners separately obtain information about the target to be learned, but they can communicate with each other in order to learn the target. We are interested in machine models for learning from streams and study its learning power (as measure ..."
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Learning from streams is a process in which a group of learners separately obtain information about the target to be learned, but they can communicate with each other in order to learn the target. We are interested in machine models for learning from streams and study its learning power (as measured by the collection of learnable classes). We study how the power of learning from streams depends on the two parameters m and n, where n is the number of learners which track a single stream of input each and m is the number of learners (among the n learners) which have to find, in the limit, the right description of the target. We study for which combinations m, n and m ′ , n ′ the following inclusion holds: Every class learnable from streams with parameters m, n is also learnable from streams with parameters m ′ , n ′. For the learning of uniformly recursive classes, we get a full characterization which depends only on the ratio m; but for general classes the picture is more complin cated. Most of the noninclusions in team learning carry over to noninclusions with the same parameters in the case of learning from streams; but only few inclusions are preserved and some additional noninclusions hold. Besides this, we also relate learning from streams to various other closely related and wellstudied forms of learning: iterative learning from text, learning from incomplete text and learning from noisy text.
Learning and Extending Sublanguages
"... A number of natural models for learning in the limit is introduced to deal with the situation when a learner is required to provide a grammar covering the input even if only a part of the target language is available. Examples of language families are exhibited that are learnable in one model and no ..."
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A number of natural models for learning in the limit is introduced to deal with the situation when a learner is required to provide a grammar covering the input even if only a part of the target language is available. Examples of language families are exhibited that are learnable in one model and not learnable in another one. Some characterizations for learnability of algorithmically enumerable families of languages for the models in question are obtained. Since learnability of any part of the target language does not imply monotonicity of the learning process, we consider also our models under additional monotonicity constraint. 1
This paper
, 2014
"... 1. We introduce a learning paradigm called sensoridentification in the limit from positive data. 2. sensor is a perception module that obfuscates the learner’s input. 3. Exact identification is eschewed for converging to a grammar which generates a language approximating the target language. 4. Suc ..."
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1. We introduce a learning paradigm called sensoridentification in the limit from positive data. 2. sensor is a perception module that obfuscates the learner’s input. 3. Exact identification is eschewed for converging to a grammar which generates a language approximating the target language. 4. Successful approximation is understood as matching up to observationequivalence. 5. Theoretical work exists which addresses other kinds of imperfect presentations, oracles, and the kinds of results obtainable with them [AL88, Ste95, FJ96, CJ01, THJ06]. 2 Motivation (part I) 1. A frontier in robotics is managing uncertainty. 2. Earlier work showed how to use grammatical inference to reduce the uncertainty in environments with potentially adversarial, but rulegoverned behavior [CFK+12, FTH13, FTHC14]. 3. The robot’s capabilities, task, and environment were modeled as finitestate transition systems and product operations brought these elements together to form a game, allowing optimal control strategies to be computed (if they exist). 4. However, that work assumed perfect information about the environment. 3 Motivation (part II) 1. Recent results in game theory [AVW03, CDHR06] shows that optimal strategies can be found even for games with imperfect information (where players only have partial information about the state of the game). 2. The techniques in [CFK+12, FTH13, FTHC14] allow imperfect games to be constructed from imperfect—but consistent—models of the environment. 3. What is missing then is a way to identify such models from imperfect observations. 4. (POMDPs and MDPs address 1player stochastic games, not 2player games.)