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A Survey of Kernels for Structured Data
"... Kernel methods in general and support vector machines in particular have been successful in various learning tasks on data represented in a single table. Much 'realworld ' data, however, is structured it has no natural representation in a single table. Usually, to apply kernel methods to ..."
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Cited by 121 (3 self)
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Kernel methods in general and support vector machines in particular have been successful in various learning tasks on data represented in a single table. Much 'realworld ' data, however, is structured it has no natural representation in a single table. Usually, to apply kernel methods to 'realworld' data, extensive preprocessing is performed toembed the data into areal vector space and thus in a single table. This survey describes several approaches ofdefining positive definite kernels on structured instances directly.
Probabilistic Modelling, Inference and Learning using Logical Theories
"... This paper provides a study of probabilistic modelling, inference and learning in a logicbased setting. We show how probability densities, being functions, can be represented and reasoned with naturally and directly in higherorder logic, an expressive formalism not unlike the (informal) everyday l ..."
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Cited by 9 (3 self)
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This paper provides a study of probabilistic modelling, inference and learning in a logicbased setting. We show how probability densities, being functions, can be represented and reasoned with naturally and directly in higherorder logic, an expressive formalism not unlike the (informal) everyday language of mathematics. We give efficient inference algorithms and illustrate the general approach with a diverse collection of applications. Some learning issues are also considered.
A Unifying View of Knowledge Representation for Inductive Learning
 In preparation
, 2000
"... This paper provides a foundation for inductive learning based on the use of higherorder logic for knowledge representation. In particular, the paper (i) provides a systematic individualsasterms approach to knowledge representation for inductive learning, and demonstrates the utility of types an ..."
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Cited by 4 (4 self)
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This paper provides a foundation for inductive learning based on the use of higherorder logic for knowledge representation. In particular, the paper (i) provides a systematic individualsasterms approach to knowledge representation for inductive learning, and demonstrates the utility of types and higherorder constructs for this purpose; (ii) gives a systematic way of constructing predicates for use in induced definitions; (iii) widens the applicability of decisiontree algorithms beyond the usual attributevalue setting to the classification of individuals with complex structure; and (iv) shows how to induce definitions which are comprehensible and have predictive power. The paper contains ten illustrative applications involving a variety of types to which a decisiontree learning system is applied. The e#ectiveness of the approach is further demonstrated by applying the learning system to two larger benchmark applications. 1 Introduction Inductive learning focuses on tec...
Higherorder Computational Logic
 Computational Logic: From Logic Programming into the Future
, 2002
"... . This paper presents the case for the use of higherorder logic as a foundation for computational logic. A suitable polymorphicallytyped, higherorder logic is introduced and its syntax and proof theory briefly described. In addition, a metric space of closed terms suitable for knowledge representa ..."
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Cited by 2 (0 self)
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. This paper presents the case for the use of higherorder logic as a foundation for computational logic. A suitable polymorphicallytyped, higherorder logic is introduced and its syntax and proof theory briefly described. In addition, a metric space of closed terms suitable for knowledge representation purposes is presented. The approach to representing individuals is illustrated with some examples, as is the technique of programming with abstractions. The paper concludes by placing the results in the wider context of previous and current research in the use of higherorder logic in computational logic. 1 Introduction In 1974, Robert Kowalski published the seminal idea that predicate logic could be used as a programming language [Kow74]. The setting for Kowalski's idea was firstorder logic, in fact, the Horn clause fragment of that logic. Since 1974, there has been an explosion of research activity that has pushed the fundamental idea in many di#erent directions. Once the idea that ...
Predicate Construction in Higherorder Logic
"... Predicate construction is a guided search process: a space of predicates must be enumerated in some systematic way in order to find, according to some criterion, a suitable predicate for some purpose. Often the search space is large and heuristics are used to guide the search. Typically, predicate c ..."
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Cited by 1 (0 self)
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Predicate construction is a guided search process: a space of predicates must be enumerated in some systematic way in order to find, according to some criterion, a suitable predicate for some purpose. Often the search space is large and heuristics are used to guide the search. Typically, predicate construction is studied and implemented in the context of firstorder logic. In this paper, I outline the foundations of predicate construction in higherorder logic. The main contribution is a method of incremental construction of predicates on higherorder terms that represent individuals. Applications of the approach to machine learning are indicated. 1 1 Introduction Predicate construction is a guided search process: a space of predicates must be enumerated in some systematic way in order to find, according to some criterion, a suitable predicate for some purpose. Often the search space is large and heuristics are used to guide the search. Typically, predicate construction is studied and...
Abstract Probabilistic Reasoning in a Classical Logic
"... We offer a view on how probability is related to logic. Specifically, we argue against the widely held belief that standard classical logics have no direct way of modelling the certainty of assumptions in theories and no direct way of stating the certainty of theorems proved from these (uncertain) a ..."
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We offer a view on how probability is related to logic. Specifically, we argue against the widely held belief that standard classical logics have no direct way of modelling the certainty of assumptions in theories and no direct way of stating the certainty of theorems proved from these (uncertain) assumptions. The argument rests on the observation that probability densities, being functions, can be represented and reasoned with naturally and directly in (classical) higherorder logic. Key words: probabilistic reasoning, classical logic, higherorder logic, integrating logic and probability 1.
A Logical Setting for the Unification of AttributeValue and Relational Learning
, 2000
"... this paper is contained in [Llo00]. Accounts of the application of the logical setting to inductive 1 ..."
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this paper is contained in [Llo00]. Accounts of the application of the logical setting to inductive 1
Predictive Toxicology using a Decisiontree Learner
"... Introduction This extended abstract outlines a submission to The Predictive Toxicology Challenge for 20002001 [PTC]. The Challenge is to obtain models that predict the outcome of biological tests for the toxicity of chemicals using information related to chemical structure only. The models reported ..."
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Introduction This extended abstract outlines a submission to The Predictive Toxicology Challenge for 20002001 [PTC]. The Challenge is to obtain models that predict the outcome of biological tests for the toxicity of chemicals using information related to chemical structure only. The models reported here are based on the approach outlined in [BGCL00]. (Much more detail is given in [BGCL01].) In essence, the learning system is a decisiontree system. However, it is rather more general than conventional decisiontree learners in that it allows the individuals that are to be classified to be represented as certain terms in a higherorder logic rather than as simple feature vectors. The logic allows the use of sets, multisets, lists, graphs and so on, to represent individuals, thereby capturing complex structural information about the individuals [Llo01]. This information is highly relevant to the main aim of the Challenge, which is to predict toxicity from the chemical structure