Much of human knowledge is organized into sophisticated systems that are often called intuitive theories. We propose that intuitive theories are mentally represented in a logical language, and that the subjective complexity of a theory is determined by the length of its representation in this language. This complexity measure helps to explain how theories are learned from relational data, and how they support inductive inferences about unobserved relations. We describe two experiments that test our approach, and show that it provides a better account of human learning and reasoning than an approach developed by Goodman [1]. What is a theory, and what makes one theory better than another?

We present an agnostic active learning algorithm for any hypothesis class of bounded VC dimension under arbitrary data distributions. Most previous work on active learning either makes strong distributional assumptions, or else is computationally prohibitive. Our algorithm extends the simple scheme of Cohn, Atlas, and Ladner [1] to the agnostic setting, using reductions to supervised learning that harness generalization bounds in a simple but subtle manner. We provide a fallback guarantee that bounds the algorithm's label complexity by the agnostic PAC sample complexity.

We present a simple new criterion for classification, based on principles from lossy data compression. The criterion assigns a test sample to the class that uses the minimum number of additional bits to code the test sample, subject to an allowable distortion. We prove asymptotic optimality of this criterion for Gaussian data and analyze its relationships to classical classifiers. Theoretical results provide new insights into relationships among popular classifiers such as MAP and RDA, as well as unsupervised clustering methods based on lossy compression [13]. Minimizing the lossy coding length induces a regularization effect which stabilizes the (implicit) density estimate in a small-sample setting. Compression also provides a uniform means of handling classes of varying dimension. This simple classification criterion and its kernel and local versions perform competitively against existing classifiers on both synthetic examples and real imagery data such as handwritten digits and human faces, without requiring domain-specific information.

In transfer learning we aim to solve new problems using fewer examples using information gained from solving related problems. Transfer learning has been successful in practice, and extensive PAC analysis of these methods has been developed. However it is not yet clear how to define relatedness between tasks. This is considered as a major problem as it is conceptually troubling and it makes it unclear how much information to transfer and when and how to transfer it. In this paper we propose to measure the amount of information one task contains about another using conditional Kolmogorov complexity between the tasks. We show how existing theory neatly solves the problem of measuring relatedness and transferring the'right' amount of information in sequential transfer learning in a Bayesian setting. The theory also suggests that, in a very formal and precise sense, no other reasonable transfer method can do much better than our Kolmogorov Complexity theoretic transfer method, and that sequential transfer is always justified. We also develop a practical approximation to the method and use it to transfer information between 8 arbitrarily chosen databases from the UCI ML repository.

Much of human knowledge is organized into sophisticated systems that are often called intuitive theories. We propose that intuitive theories are mentally represented in a logical language, and that the subjective complexity of a theory is determined by the length of its representation in this language. This complexity measure helps to explain how theories are learned from relational data, and how they support inductive inferences about unobserved relations. We describe two experiments that test our approach, and show that it provides a better account of human learning and reasoning than an approach developed by Goodman [1]. What is a theory, and what makes one theory better than another?

We present an agnostic active learning algorithm for any hypothesis class of bounded VC dimension under arbitrary data distributions. Most previous work on active learning either makes strong distributional assumptions, or else is computationally prohibitive. Our algorithm extends the simple scheme of Cohn, Atlas, and Ladner [1] to the agnostic setting, using reductions to supervised learning that harness generalization bounds in a simple but subtle manner. We provide a fallback guarantee that bounds the algorithm's label complexity by the agnostic PAC sample complexity.

In transfer learning we aim to solve new problems using fewer examples using information gained from solving related problems. Transfer learning has been successful in practice, and extensive PAC analysis of these methods has been developed. Howeverit is not yet clear how to define relatedness between tasks. This is considered as a major problem as it is conceptually troubling and it makes it unclear how much information to transfer and when and how to transfer it. In this paper we propose to measure the amount of information one task contains about another using conditional Kolmogorov complexity between the tasks. We show how existing theory neatly solves the problem of measuring relatedness and transferring the'right' amount of information in sequential transfer learning in a Bayesian setting. The theory also suggests that, in a very formal and precise sense, no other reasonable transfer method can do much better than our Kolmogorov Complexity theoretic transfer method, and that sequential transfer is always justified. Wealso develop a practical approximation to the method and use it to transfer information between 8 arbitrarily chosen databases from the UCI ML repository.

We present a simple new criterion for classification, based on principles from lossy data compression. The criterion assigns a test sample to the class that uses the minimum numberof additional bits to code the test sample, subject to an allowable distortion. We prove asymptotic optimality of this criterion for Gaussian data and analyze its relationships to classical classifiers. Theoretical results provide new insights into relationships among popular classifiers such as MAP and RDA, as well as unsupervised clustering methods based on lossy compression [13]. Minimizing thelossy coding length induces a regularization effect which stabilizes the (implicit) density estimate in a small-sample setting. Compression also provides a uniform means of handling classes of varying dimension. This simple classification criterionand its kernel and local versions perform competitively against existing classifiers on both synthetic examples and real imagery data such as handwritten digitsand human faces, without requiring domain-specific information.

Much of human knowledge is organized into sophisticated systems that are often called intuitive theories. We propose that intuitive theories are mentally represented ina logical language, and that the subjective complexity of a theory is determined by the length of its representation in this language. This complexity measure helps to explain how theories are learned from relational data, and how they support inductive inferences about unobserved relations. We describe two experiments that test our approach, and show that it provides a better account of human learning and reasoning than an approach developed by Goodman [1]. What is a theory, and what makes one theory better than another?

We present an agnostic active learning algorithm for any hypothesis class of bounded VC dimension under arbitrary data distributions. Most previous workon active learning either makes strong distributional assumptions, or else is computationally prohibitive. Our algorithm extends the simple scheme of Cohn, Atlas, and Ladner [1] to the agnostic setting, using reductions tosupervised learning that harness generalization bounds in a simple but subtle manner. We provide a fallback guarantee that bounds the algorithm's label complexity by the agnostic PAC sample complexity.