H. Hirsh, Incremental version-space merging : a general framework for concept learning, Ph.D. dissertation, Stanford University, 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the imperfections in the domain theory may be deliberate. For instance, an incorrect but tractable approximation to an intractable domain theory may be used, as in [Rajamoney and DeJong, 1988] or, EBL may be used inductively (as in [Carbonell et al. 1987; Flann and Dietterich, 1989; Hirsh, 1990] to find some particular specialization of an over general domain theory. Standard explanation based systems cannot handle the multiple explanation problem. Typically, they either assume that there will be only a single explanation for each instance, or that all explanations will be valid. ....

....reduction as a way of collecting informative examples; one would expect such a technique to have a lower time and sample complexity of learning than A EBL. The advantage of A EBL is that experimentation is not always possible. Hirsh has used the incremental version space merging (IVSM) method [Hirsh, 1990] to choose between multiple explanations. Like A EBL, IVSM is a general technique, with strong formal justifications; it is also incremental. However, the IVSM method requires an additional source of information in the form of a concept description language which provides an additional bias to the ....

[Article contains additional citation context not shown here]

Haym Hirsh. Incremental Version Space Merging: A General Framework for Concept Learning. Kluwer Academic Publishers, 1990.

.... the appropriateness of these techniques (with each hand, Sheinwold presents a list of correct bids; possible bids not on the list are thus by inference negative examples) Problem 2, and the lack of a generalization language, rules out use of the technique of incremental version space merging [ Hirsh, 1989 ] Problem 3 rules out use of the MIRO algorithm [ Drastal et al. 1989 ] which could also be considered a theory specialization technique. Finally, the presence of an almost correct initial theory suggests that traditional inductive learning techniques, which cannot use this information ....

....from textbooks, and presentation of techniques that address these subproblems. The techniques developed to solve this problem, however, are of independent interest. ANA EBL is a theory specialization technique, like the techniques described in [ Drastal et al. 1989; Flann and Dietterich, 1989; Hirsh, 1989 ] however, ANA EBL works even in situations in which the original theory is relational and or generates multiple inconsistent explanations, and in which the target theory is disjunctive. Experimental results indicate that the technique is effective on randomly selected examples, as well as on ....

Haym Hirsh. Incremental version space merging: A general framework for concept learning. PhD Thesis, Stanford University Department of Computer Science, 1989.

....are merged regroupments of the special partitions P and P . The step of the algorithm, that determines new regroupments, is left unspeci ed. In practice it is determined s.t. the size of new ABSs is maximally reduced. The merging algorithm is based on the boundary set intersection algorithm [2]. Since the former is intractable, the merging algorithm is intractable as well. Therefore, we consider the algorithm for IPL and UPL concept languages only. In this restricted case the algorithm is based on theorems 4 and 5. The proofs of the theorems use lemmas 4 and 5. Lemma 4 Consider an ....

H. Hirsh. Incremental version-space merging: a general framework for concept learning. PhD thesis, Department of Computer Science, Stanford University, Stanford, CA, 1989.

....with positive and negative training examples. Furthermore, he showed how consistent hypotheses in a CDL are structured as a lattice. Lattices can be described efficiently with an upper and lower bound, which in the case of learning correspond to the most general and most specific hypotheses. Hirsh (1989), extended Mitchell s thesis by showing how many version spaces may be intersected, unioned, and so on, and still be a consistent version space. His work provides the basis of our approach: That hypotheses generated by different agents may be integrated by intersecting each agents version space ....

H. Hirsh (1989). "Incremental Version Space Merging: A General Framework for Concept Learning", Ph.D. Thesis, Stanford University.

....The algorithm will prune the same whether a user chose the threshold based on semantic considerations or pragmatic ones. Given a set of criteria (based on statistical, syntactic, or semantic factors) the set of rules that satisfy these criteria is known as the version space (Mitchell, 1982; Hirsh, 1989), one of the fundamental notions of machine learning. Mitchell describes how the set of most general rules in the version space (the G set) and the set of most speci c rules in the version 10 space (the S set) together are sucient to describe the entire version space. Hirsh relaxes Mitchell s ....

Hirsh, H. (1989). Incremental version-space merging: A general framework for concept learning. Ph.D. thesis, Stanford University.

....with shorter descriptions are preferred. Mitchell (1996) argues that there is no utility in using version spaces for unbiased logical languages. Our work suggest that there may be some utility in producing explicit descriptions of the boundary sets to help the application of a selection bias. Hirsh (1989) extended the original version space model in several ways. Firstly, he defines the mathematical conditions (convexity and definiteness) that are necessary to represent the hypothesis space using boundary sets. Convexity occurs if a subset of a partially ordered set does not contain any holes ....

H. Hirsh (1989). Incremental Version Space Merging: A General Framework for Concept Learning, Ph.D. Thesis, Stanford University.

....pVq (a) Version space based on examples available to agent 1. 0,2 = q 0,3 = p qVp q 0,2,3 = pVq 0 p q AAA AAA 3 = p q 0,3 = p qVp q 1,3 q 0,1,3 = pVq (c) The intersected version spaces. Figure 5: Intersecting Version Spaces 3. 2 The Theory of Version Space Intersection Hirsh (1989) extended the original version space model in several ways. Firstly, he defines the mathematical conditions convexity and definiteness that are necessary to represent the hypothesis space using boundary sets. Convexity occurs if a subset of a partially ordered set does not contain any holes with ....

H. Hirsh (1989). Incremental Version Space Merging: A General Framework for Concept Learning, Ph.D. Thesis, Stanford University.

....with existing knowledge. Before adopting the version space as the basic unit for the communication of inductive inferences, it is necessary to show that two or more version spaces can be combined. It is also necessary to show how deductive inferences can be combined with inductive inferences. Hirsh (1989) proved several relevant results for version spaces manipulation. We describe these and other related work in the next section. We also borrow heavily from Michalski s (1993) Inferential Theory of Learning (ITL) Michalski proposed a set of transformation operators that employ deductive and ....

....agent must maintain the version space. In particular, the agent should never communicate a selected candidate hypothesis as if it had been soundly deduced. In practice, this means it cannot store a selected hypothesis in its knowledge base (unless of course it was the only remaining hypothesis) Hirsh (1989), extends the original version space model in several ways. Firstly he defines the mathematical conditions (convexity and definiteness) that are necessary to represent the hypotheses space using boundary sets. Convexity occurs if a subset of a partially ordered set does not contain any holes ....

[Article contains additional citation context not shown here]

H. Hirsh (1989). Incremental Version Space Merging: A General Framework for Concept Learning, Ph.D. Thesis, Stanford University.

....satisfy certain special properties. We use anti chains to identify and analyze the basic operations and representation optimizations in the version space learning algorithm [10] and the assumption based truth maintenance system (ATMS) 2, 3] Our analysis allows us to (1) extend the known theory [7, 10, 8] of admissibility of concept spaces for incremental version space merging, and (2) develop new, simpler label update algorithms for ATMS s with DNF assumption formulas. Contents 1 Introduction 2 2 Representing Sets as Anti Chains 4 3 Version Spaces 17 4 Assumption Based Truth Maintenance Systems ....

....is given we explore correctness and optimization issues for the algorithms using the basic properties of the anti chain algebra. For the VS and extended ATMS algorithms we conclude with generalizations of known correctness criteria and algorithms. In particular, we extend results of Hirsh [7] and Mellish [8] on the admissibility of the VS algorithm and provide a generalization and simplification of de Kleer s choose construct [3] for the extended ATMS. 4 2 Representing Sets as Anti Chains One way to represent a set is to maintain a list of its elements. Given an ordering for set ....

[Article contains additional citation context not shown here]

Haym Hirsh. Incremental Version Space Merging: A General Framework for Concept Learning. Kluwer Academic Publishers, 1990.

....complexity theory. problems in EBL arises when the domain theory is not adequate to classify every instance [Mitchell et al. 1986] Most approaches to this incomplete theory problem are based on using pre classified training examples to expose and fill in missing parts of the domain theory [Hirsh, 1989, Hall, 1988, Mahadevan, 1989, Danyluk, 1989] For example, one approach involves using determinations to represent gaps in the domain theory, which are filled by extracting implicative rules from the determinations [Russell, 1987, Mahadevan, 1989] A PAC analysis can be used to determine whether ....

H Hirsh. Incremental Version-Space Merging: A General Framework for Concept Learning. PhD thesis, Stanford University., 1989.

....for which induction is even computable. This sets a practical limit on the kinds of knowledge that can be utilized by induction. Among the set representations below this limit, there are a number that generate useful instantiations of KII. Most notably, Incremental Version Space Merging (Hirsh 1990) can be generated by using a boundary set representation for constraints (i.e. version spaces) and an empty representation for preferences; and an algorithm similar to Grendel (Cohen 1992) can be instantiated from KII by representing sets as antecedent description grammars (essentially context ....

....hypothesis from the solution set are sufficient for the vast majority of induction tasks. Most existing induction algorithms involve only the enumeration operator and perhaps an Empty or Unique query. The Candidate Elimination algorithm (Mitchell 1982) and Incremental Version Space Merging (IVSM) (Hirsh 1990) use all four queries, but do not select a hypothesis from the solution set (they return the entire set) The queries and selection of a hypothesis from the solution set can be implemented in terms of a single enumeration operator. The enumeration operator returns n elements of a set, S, where n ....

[Article contains additional citation context not shown here]

Hirsh, H. 1990. Incremental Version Space Merging: A General Framework for Concept Learning. Boston, MA: Kluwer Academic Publishers.

....Therefore, each example agrees with many di#erent structures. Norton uses background knowledge to assign probabilities to structures, combines the evidence from the training example, and picks the most likely concept. Norton s work is an outgrowth of Hirsh s bounded inconsistency learner [ Hirsh, 1990 ] The bounded inconsistency model assumes that every example is made up of some true source example corrupted by a noise model. In addition, given a noisy example, one can e#ciently describe the version space [ Mitchell, 1978 ] that covers all concepts that agree with the possible true sources ....

Haym Hirsh. Incremental version-space merging: a general framework for concept learning. Kluwer Academic, 1990.

....FSA in S k then clearly, the example is positive. When the structurally complete sample set has been acquired, an example that is not accepted by all FSA in G k can be classified as negative. The idea of incremental lattice update was inspired by Hirsh s work on Incremental Version Space Merging [8]. Angluin [1] has proposed an algorithm ID to infer the target grammar from a live complete set of examples using a polynomial number of membership queries. The live complete set can be constructed given a structurally complete sample. A trivial upper bound on the number of membership queries ....

Hirsh, H. Incremental Version-Space Merging: A General Framework for Concept Learning. Kluwer Academic Publishers. 1990.

....FSA in S k then clearly, the example is positive. When the structurally complete sample set has been acquired, an example that is not accepted by all FSA in G k can be classified as negative. The idea of incremental lattice update was inspired by Hirsh s work on Incremental Version Space Merging [8]. The set G in our algorithm, which represents the set of most general FSA of the lattice that do not accept any negative strings identified by the queries during the inference process is analogous to the border set described by Dupont et al. [4] Angluin [1] has proposed an algorithm (ID) to ....

Hirsh, H. Incremental Version-Space Merging: A General Framework for Concept Learning. Kluwer Academic Publishers, '90.

....h . oe f Gamma1 R f R Learner H HR a 1 a 3 a 2 x 3 x 2 x 1 Representation space XR Initial space XI Figure 1: A learning system using representation shift 1989; Hirsh, 1989 ] One advantage of this architecture is that it allows background knowledge to be applied to a learning problem in a highly modular way. Background knowledge is used only to select the space over which learning will occur, via the representationshifting function fR ; standard concept learning ....

Haym Hirsh. Incremental version space merging: A general framework for concept learning. PhD Thesis, Stanford University Department of Computer Science, 1989.

.... 1989; Whitehall, 1990] while others are only capable of specializing an overly general theory [Flann and Dietterich, 1989; Mooney and Ourston, 1989; Cohen, 1990] Many systems do not revise the theory itself but instead revise the operational definition of a concept [Bergadano and Giordana, 1988; Hirsh, 1990; Pazzani et al. 1991] Still other systems rely on active experimentation rather than a provided training set to detect and correct errors [Rajamoney, 1990] Recent experiments with Anapron [Golding and Rosenbloom, 1991] a system that integrates case based and rule based reasoning, also ....

H. Hirsh. Incremental Version-Space Merging: A General Framework for Concept Learning. Kluwer Academic Publishers, Hingham, MA, 1990.

....of Mitchell s [1978] version space approach to concept learning. Mitchell defines a version space to be the set of all concept definitions in a prespecified language that correctly classify training data the positive and negative examples of the unknown concept. The generalized approach [Hirsh, 1990a; Hirsh, 1990b] called incremental version space merging, removes the assumption that there is always some concept definition that correctly classifies all the given data. The paper begins with a description of bounded inconsistency, the form of inconsistency considered by this paper. The paper ....

....version space merging. Experimental results are then presented, followed by an overview of related work and a general discussion. A formal analysis of how the quality of results is influenced by the amount of data used in learning concludes the paper. Further details are presented elsewhere [Hirsh, 1990a; Hirsh, 1990c] 2 Bounded Inconsistency This paper addresses the problem of learning from inconsistent data by solving a subcase of the problem called bounded inconsistency. The underlying assumption for this class of inconsistency is that some small perturbation to the description of any bad ....

[Article contains additional citation context not shown here]

H. Hirsh. Incremental Version-Space Merging: A General Framework for Concept Learning. Kluwer, Boston, MA, 1990. 26

....with bounded inconsistency. Future work will explore such modifications of these and other algorithms, such as neural network learning, to see if they yield comparable experimental results. Acknowledgments The experimental portions of this paper summarize part of the first author s dissertation [Hirsh, 1989b] where more lengthy acknowledgments can be found. Portions of the theoretical results of this paper as well as some of the writing were done while the first author was visiting Bell Labs. David Aha provided the iris data (originally entered by Mike Marshall at NASA Ames and now one of the many ....

H. Hirsh. Incremental Version-Space Merging: A General Framework for Concept Learning. PhD thesis, Stanford University, June 1989.

....criterion from an input port, rather than always using the same built in criterion. A more sophisticated example of a reformulation is IVSM s derivation from the candidate elimination algorithm by converting its examples input port to take a more expressive class of inputs (i.e. version spaces) [3]. A preprocessor transformation adds to the core algorithm a preprocessor that takes a form of input beyond what can be fed directly into the core algorithm s input ports, and translates this broader input into something that one or more of the core input ports can understand. Quinlan s ....

.... this paper, so we will focus here on just four recent knowledgeintensive algorithms, each of which provides the ability to utilize EBL like domain theories, plus possibly some other forms of knowledge: IVSM has the ability to utilize EBL like domain theories plus models of bounded inconsistency [3]. FOCL has the ability to utilize (possibly partial) EBL like domain theories plus constraints on predicate arguments [7] GRENDEL has the ability to specify the hypothesis space via a formal grammar which can include an EBL like domain theory plus some simple ordering information [2] ....

Hirsh, H.. Incremental Version Space Merging: A General Framework for Concept Learning. Kluwer Academic Publishers, Boston, MA, 1990.

No context found.

H. Hirsh, Incremental version-space merging : a general framework for concept learning, Ph.D. dissertation, Stanford University, 1989.

No context found.

H. Hirsh. Incremental Version-Space Merging: A General Framework for Concept Learning. PhD thesis, Stanford University, Palo Alto, CA, June 1989. REFERENCES 36

No context found.

H. Hirsh (1989). Incremental Version Space Merging: A General Framework for Concept Learning, Ph.D. Thesis, Stanford University.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC