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This paper focuses on the relation between computational learning theory and resource-bounded dimension. We intend to establish close connections between the learnability/nonlearnability of a concept class and its corresponding size in terms of effective dimension, which will allow the use of powerful dimension techniques in computational learning and viceversa, the import of learning results into complexity via dimension. Firstly, we obtain a tight result on the dimension of online mistake-bound learnable classes. Secondly, in relation with PAC learning, we show that the polynomial-space dimension of PAC learnable classes of concepts is zero. This provides a hypothesis on effective dimension that implies the inherent unpredictability of concept classes (the classes that verify this property are classes not efficiently PAC learnable using any hypothesis). Thirdly, in relation to space dimension of classes that are learnable by membership query algorithms, the main result proves that polynomial-space dimension of concept classes learnable by a membership-query algorithm is zero.

This paper focuses on the relation between computational learning theory and resource-bounded dimension. We intend to establish close connections between the learnability/nonlearnability of a concept class and its corresponding size in terms of effective dimension, which will allow the use of powerful dimension techniques in computational learning and viceversa, the import of learning results into complexity via dimension. Firstly, we obtain a tight result on the dimension of online mistake-bound learnable classes. Secondly, in relation with PAC learning, we show that the polynomial-space dimension of PAC learnable classes of concepts is zero. This provides a hypothesis on effective dimension that implies the inherent unpredictability of concept classes (the classes that verify this property are classes not efficiently PAC learnable using any hypothesis). Thirdly, in relation to space dimension of classes that are learnable by membership query algorithms, the main result proves that polynomial-space dimension of concept classes learnable by a membership-query algorithm is zero.

These original contributions converge on an exciting and fruitful intersection of three historically distinct areas of learning research: computational learning theory, neural networks, and symbolic machine learning. Bridging theory and practice, computer science and psychology, they consider general issues in learning systems that could provide constraints for theory and at the same time interpret theoretical results in the context of experiments with actual learning systems.In all, nineteen chapters address questions such as, What is a natural system? How should learning systems gain from prior knowledge? If prior knowledge is important, how can we quantify how important? What makes a learning problem hard? How are neural networks and symbolic machine learning approaches similar? Is there a fundamental difference in the kind of task a neural network can easily solve as opposed to those a symbolic algorithm can easily solve?

This thesis addresses problems from two areas of theoretical computer science. The first area is that of computational learning theory, which is the study of the phenomenon of concept learning using formal mathematical models. The goal of computational learning theory is to investigate learning in a rigorous manner through the use of techniques from theoretical computer science. Much of the work in this field is in the context of "probably approximately correct" (PAC) model of learning, which is carried out in a probabilistic environment. Of particular interest are the questions of determining for which classes of concepts the PAC-learning problem is tractable and discovering efficient learning algorithms for such classes. The second area from which topics are drawn is that of online algorithms for graph-theoretic problems. Many problems in such fields as communications, transportation, scheduling, and networking can be reduced to that of finding a good graph algorithm. After an introduction in Chapter 1, some background information is provided in Chapter 2 on the field of computational learning theory. In Chapter 3 it is shown that for any concept class having a particular closure property, the existence of a graph algorithm implies that the class is PAC-learnable. Chapter 4 defines a variation on the standard PAC model of learning called semi-supervised learning, a model which permits the rigorous study of learning situations where the teacher plays only a limited role. Chapter 5 deals with the problem of prediction as performed by deterministic finite automata, counter machines, and deterministic pushdown automata. Chapter 6 investigates the power and the performance of online algorithms for a certain class of graph problems, referred to as vertex labeling problems. (77 references) (JJK)

This thesis addresses problems from two areas of theoretical computer science. The first area is that of computational learning theory, which is the study of the phenomenon of concept learning using formal mathematical models. The goal of computational learning theory is to investigate learning in a rigorous manner through the use of techniques from theoretical computer science. Much of the work in this field is in the context of "probably approximately correct" (PAC) model of learning, which is carried out in a probabilistic environment. Of particular interest are the questions of determining for which classes of concepts the PAC-learning problem is tractable and discovering efficient learning algorithms for such classes. The second area from which topics are drawn is that of online algorithms for graph-theoretic problems. Many problems in such fields as communications, transportation, scheduling, and networking can be reduced to that of finding a good graph algorithm. After an introduction in Chapter 1, some background information is provided in Chapter 2 on the field of computational learning theory. In Chapter 3 it is shown that for any concept class having a particular closure property, the existence of a graph algorithm implies that the class is PAC-learnable. Chapter 4 defines a variation on the standard PAC model of learning called semi-supervised learning, a model which permits the rigorous study of learning situations where the teacher plays only a limited role. Chapter 5 deals with the problem of prediction as performed by deterministic finite automata, counter machines, and deterministic pushdown automata. Chapter 6 investigates the power and the performance of online algorithms for a certain class of graph problems, referred to as vertex labeling problems. (77 references) (JJK)

This thesis addresses problems from two areas of theoretical computer science. The first area is that of computational learning theory, which is the study of the phenomenon of concept learning using formal mathematical models. The goal of computational learning theory is to investigate learning in a rigorous manner through the use of techniques from theoretical computer science. Much of the work in this field is in the context of "probably approximately correct" (PAC) model of learning, which is carried out in a probabilistic environment. Of particular interest are the questions of determining for which classes of concepts the PAC-learning problem is tractable and discovering efficient learning algorithms for such classes. The second area from which topics are drawn is that of online algorithms for graph-theoretic problems. Many problems in such fields as communications, transportation, scheduling, and networking can be reduced to that of finding a good graph algorithm. After an introduction in Chapter 1, some background information is provided in Chapter 2 on the field of computational learning theory. In Chapter 3 it is shown that for any concept class having a particular closure property, the existence of a graph algorithm implies that the class is PAC-learnable. Chapter 4 defines a variation on the standard PAC model of learning called semi-supervised learning, a model which permits the rigorous study of learning situations where the teacher plays only a limited role. Chapter 5 deals with the problem of prediction as performed by deterministic finite automata, counter machines, and deterministic pushdown automata. Chapter 6 investigates the power and the performance of online algorithms for a certain class of graph problems, referred to as vertex labeling problems. (77 references) (JJK)

This thesis addresses problems from two areas of theoretical computer science. The first area is that of computational learning theory, which is the study of the phenomenon of concept learning using formal mathematical models. The goal of computational learning theory is to investigate learning in a rigorous manner through the use of techniques from theoretical computer science. Much of the work in this field is in the context of "probably approximately correct" (PAC) model of learning, which is carried out in a probabilistic environment. Of particular interest are the questions of determining for which classes of concepts the PAC-learning problem is tractable and discovering efficient learning algorithms for such classes. The second area from which topics are drawn is that of online algorithms for graph-theoretic problems. Many problems in such fields as communications, transportation, scheduling, and networking can be reduced to that of finding a good graph algorithm. After an introduction in Chapter 1, some background information is provided in Chapter 2 on the field of computational learning theory. In Chapter 3 it is shown that for any concept class having a particular closure property, the existence of a graph algorithm implies that the class is PAC-learnable. Chapter 4 defines a variation on the standard PAC model of learning called semi-supervised learning, a model which permits the rigorous study of learning situations where the teacher plays only a limited role. Chapter 5 deals with the problem of prediction as performed by deterministic finite automata, counter machines, and deterministic pushdown automata. Chapter 6 investigates the power and the performance of online algorithms for a certain class of graph problems, referred to as vertex labeling problems. (77 references) (JJK)

1 online resource

Computer task automation is part of the natural progression of encoding information. This thesis considers the automation process to be a question of whether it is possible to automatically learn the encoding based on the behavior of the system to be described. A variety of representation languages are considered, as are means for the learner to acquire a variety of types of data about the system in question. The learning process is abstracted as a learning problem in which the goal is to efficiently collect sufficient information to identify some hidden concept using a particular language. The source of information about the concept is its relationship to some class of examples that is assumed to be reasonably available even if the concept is not. The goal of inquiry is to produce a learning algorithm that automates encoding of any representation (or to show that none is possible). It is argued that learning algorithms exist for two natural representation languages: propositional Horn sentences and the CLASSIC description logic, a natural first-order class used in the knowledge representation community. A new method is introduced for modeling uncertainty in the information being collected. Tools that have been developed in computational learning theory can be used for automation in real world tasks outside learning theory. Twenty-two figures are included. (Contains 101 references.) (Author/SLD)

Theoretical tools from cognitive science were used to put together a framework for a fine-grained theory of how students learn elementary algebra in the classroom. Developing the framework included assessing the shortcomings of current models, evaluating whether unified theories of cognition can be adapted for learning mathematics in the classroom, and discussing the extension of these theories. Protocols were collected from an eighth-grade class using the University of Chicago School Mathematics Project algebra text in an urban middle school. Audiotapes were made of student classroom conversations in working groups. Audiotapes from three students are quoted. Analyzing the data provides a framework for a fine-grained theory. Data suggest that in the initial stages of learning algebra, visual clues play a more important role than does syntactic or semantic understanding. Directly related is the importance of examples. Data also suggest that the more novel the problem, the more students are likely to rely on visual clues. Students in the early stages of learning tend to do mathematics problems based on how the symbols are arranged on the page, rather than syntactically deconstructing the expression or the underlying semantics. It is suggested that although a production system architecture is applicable to doing and learning mathematics in the classroom, students do not compose productions as quickly and easily as suggested by some theories. (Contains 25 references.) (SLD)

Includes bibliographical references

Includes bibliographical references