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74
Property Testing and its connection to Learning and Approximation
"... We study the question of determining whether an unknown function has a particular property or is fflfar from any function with that property. A property testing algorithm is given a sample of the value of the function on instances drawn according to some distribution, and possibly may query the fun ..."
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Cited by 421 (57 self)
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We study the question of determining whether an unknown function has a particular property or is fflfar from any function with that property. A property testing algorithm is given a sample of the value of the function on instances drawn according to some distribution, and possibly may query the function on instances of its choice. First, we establish some connections between property testing and problems in learning theory. Next, we focus on testing graph properties, and devise algorithms to test whether a graph has properties such as being kcolorable or having a aeclique (clique of density ae w.r.t the vertex set). Our graph property testing algorithms are probabilistic and make assertions which are correct with high probability, utilizing only poly(1=ffl) edgequeries into the graph, where ffl is the distance parameter. Moreover, the property testing algorithms can be used to efficiently (i.e., in time linear in the number of vertices) construct partitions of the graph which corre...
The induction of dynamical recognizers
 Machine Learning
, 1991
"... A higher order recurrent neural network architecture learns to recognize and generate languages after being "trained " on categorized exemplars. Studying these networks from the perspective of dynamical systems yields two interesting discoveries: First, a longitudinal examination of the learning pro ..."
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Cited by 214 (16 self)
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A higher order recurrent neural network architecture learns to recognize and generate languages after being "trained " on categorized exemplars. Studying these networks from the perspective of dynamical systems yields two interesting discoveries: First, a longitudinal examination of the learning process illustrates a new form of mechanical inference: Induction by phase transition. A small weight adjustment causes a "bifurcation" in the limit behavior of the network. This phase transition corresponds to the onset of the network’s capacity for generalizing to arbitrarylength strings. Second, a study of the automata resulting from the acquisition of previously published training sets indicates that while the architecture is not guaranteed to find a minimal finite automaton consistent with the given exemplars, which is an NPHard problem, the architecture does appear capable of generating nonregular languages by exploiting fractal and chaotic dynamics. I end the paper with a hypothesis relating linguistic generative capacity to the behavioral regimes of nonlinear dynamical systems.
Map Learning with Uninterpreted Sensors and Effectors
 Artificial Intelligence
, 1997
"... This paper presents a set of methods by which a learning agent can learn a sequence of increasingly abstract and powerful interfaces to control a robot whose sensorimotor apparatus and environment are initially unknown. The result of the learning is a rich hierarchical model of the robot's world (it ..."
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Cited by 129 (20 self)
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This paper presents a set of methods by which a learning agent can learn a sequence of increasingly abstract and powerful interfaces to control a robot whose sensorimotor apparatus and environment are initially unknown. The result of the learning is a rich hierarchical model of the robot's world (its sensorimotor apparatus and environment). The learning methods rely on generic properties of the robot's world such as almosteverywhere smooth e ects of motor control signals on sensory features. At thelowest level of the hierarchy, the learning agent analyzes the e ects of its motor control signals in order to de ne a new set of control signals, one for each of the robot's degrees of freedom. It uses a generateandtest approach to de ne sensory features that capture important aspects of the environment. It uses linear regression to learn models that characterize contextdependent e ects of the control signals on the learned features. It uses these models to de ne highlevel control laws for nding and following paths de ned using constraints on the learned features. The agent abstracts these control laws, which interact with the continuous environment, to a nite set of actions that implement discrete state transitions. At this point, the agent has abstracted the robot's continuous world to a nitestate world and can use existing methods to learn its structure. The learning agent's methods are evaluated on several simulated robots with di erent sensorimotor systems and environments.
XTRACT: A System for Extracting Document Type Descriptors from XML Documents. Bell Labs Tech. Memorandum
, 1999
"... XML is rapidly emerging as the new standard for data representation and exchange on the Web. An XML document can be accompanied by a Document Type Descriptor (DTD) which plays the role of a schema for an XML data collection. DTDs contain valuable information on the structure of documents and thus ha ..."
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Cited by 101 (4 self)
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XML is rapidly emerging as the new standard for data representation and exchange on the Web. An XML document can be accompanied by a Document Type Descriptor (DTD) which plays the role of a schema for an XML data collection. DTDs contain valuable information on the structure of documents and thus have a crucial role in the efficient storage of XML data, as well as the effective formulation and optimization of XML queries. In this paper, we propose XTRACT, a novel system for inferring a DTD schema for a database of XML documents. Since the DTD syntax incorporates the full expressive power of regular expressions, naive approaches typically fail to produce concise and intuitive DTDs. Instead, the XTRACT inference algorithms employ a sequence of sophisticated steps that involve: (1) finding patterns in the input sequences and replacing them with regular expressions to generate “general ” candidate DTDs, (2) factoring candidate DTDs using adaptations of algorithms from the logic optimization literature, and (3) applying the Minimum Description Length (MDL) principle to find the best DTD among the candidates. The results of our experiments with reallife and synthetic DTDs demonstrate the effectiveness of XTRACT’s approach in inferring concise and semantically meaningful DTD schemas for XML databases. 1
Results of the Abbadingo One DFA Learning Competition and a New EvidenceDriven State Merging Algorithm
, 1998
"... . This paper first describes the structure and results of the Abbadingo One DFA Learning Competition. The competition was designed to encourage work on algorithms that scale wellboth to larger DFAs and to sparser training data. We then describe and discuss the winning algorithm of Rodney Price, w ..."
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Cited by 90 (1 self)
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. This paper first describes the structure and results of the Abbadingo One DFA Learning Competition. The competition was designed to encourage work on algorithms that scale wellboth to larger DFAs and to sparser training data. We then describe and discuss the winning algorithm of Rodney Price, which orders state merges according to the amount of evidence in their favor. A second winning algorithm, of Hugues Juille, will be described in a separate paper. Part I: Abbadingo 1 Introduction The Abbadingo One DFA Learning Competition was organized by two of the authors (Lang and Pearlmutter) and consisted of a set of challenge problems posted to the internet and token cash prizes of $1024. The organizers had the following goals:  Promote the development of new and better algorithms.  Encourage learning theorists to implement some of their ideas and gather empirical data concerning their performance on concrete problems which lie beyond proven bounds, particulary in the direction o...
On the Computational Complexity of Approximating Distributions by Probabilistic Automata
 Machine Learning
, 1990
"... We introduce a rigorous performance criterion for training algorithms for probabilistic automata (PAs) and hidden Markov models (HMMs), used extensively for speech recognition, and analyze the complexity of the training problem as a computational problem. The PA training problem is the problem of ap ..."
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Cited by 86 (0 self)
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We introduce a rigorous performance criterion for training algorithms for probabilistic automata (PAs) and hidden Markov models (HMMs), used extensively for speech recognition, and analyze the complexity of the training problem as a computational problem. The PA training problem is the problem of approximating an arbitrary, unknown source distribution by distributions generated by a PA. We investigate the following question about this important, wellstudied problem: Does there exist an efficient training algorithm such that the trained PAs provably converge to a model close to an optimum one with high confidence, after only a feasibly small set of training data? We model this problem in the framework of computational learning theory and analyze the sample as well as computational complexity. We show that the number of examples required for training PAs is moderate  essentially linear in the number of transition probabilities to be trained and a lowdegree polynomial in the example l...
Learning Models of Intelligent Agents
, 1996
"... Agents that operate in a multiagent system need an efficient strategy to handle their encounters with other agents involved. Searching for an optimal interactive strategy is a hard problem because it depends mostly on the behavior of the others. In this work, interaction among agents is represented ..."
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Cited by 84 (2 self)
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Agents that operate in a multiagent system need an efficient strategy to handle their encounters with other agents involved. Searching for an optimal interactive strategy is a hard problem because it depends mostly on the behavior of the others. In this work, interaction among agents is represented as a repeated twoplayer game, where the agents' objective is to look for a strategy that maximizes their expected sum of rewards in the game. We assume that agents' strategies can be modeled as finite automata. A modelbased approach is presented as a possible method for learning an effective interactive strategy. First, we describe how an agent should find an optimal strategy against a given model. Second, we present an unsupervised algorithm that infers a model of the opponent's automaton from its input/output behavior. A set of experiments that show the potential merit of the algorithm is reported as well. Introduction In recent years, a major research effort has been invested in desi...
The minimum consistent DFA problem cannot be approximated within any polynomial
 Journal of the Association for Computing Machinery
, 1993
"... Abstract. The minimum consistent DFA problem is that of finding a DFA with as few states as possible that is consistent with a given sample (a finite collection of words, each labeled as to whether the DFA found should accept or reject). Assuming that P # NP, it is shown that for any constant k, no ..."
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Cited by 82 (4 self)
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Abstract. The minimum consistent DFA problem is that of finding a DFA with as few states as possible that is consistent with a given sample (a finite collection of words, each labeled as to whether the DFA found should accept or reject). Assuming that P # NP, it is shown that for any constant k, no polynomialtime algorithm can be guaranteed to find a consistent DFA with fewer than opt ~ states, where opt is the number of states in the minimum state DFA consistent with the sample. This result holds even if the alphabet is of constant size two, and if the algorithm is allowed to produce an NFA, a regular expression, or a regular grammar that is consistent with the sample. A similar nonapproximability result is presented for the problem of finding small consistent linear grammars. For the case of finding minimum consistent DFAs when the alphabet is not of constant size but instead is allowed to vay with the problem specification, the slightly
Inductive Inference, DFAs and Computational Complexity
 2nd Int. Workshop on Analogical and Inductive Inference (AII
, 1989
"... This paper surveys recent results concerning the inference of deterministic finite automata (DFAs). The results discussed determine the extent to which DFAs can be feasibly inferred, and highlight a number of interesting approaches in computational learning theory. 1 ..."
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Cited by 78 (1 self)
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This paper surveys recent results concerning the inference of deterministic finite automata (DFAs). The results discussed determine the extent to which DFAs can be feasibly inferred, and highlight a number of interesting approaches in computational learning theory. 1