We prove bounds on the sample complexity of PAC learning in terms of the doubling dimension of this metric. These bounds imply known bounds on the sample complexity of learning halfspaces with respect to the uniform distribution that are optimal up to a constant factor.

A fundamental problem in artificial intelligence is that nobody really knows what intelligence is. The problem is especially acute when we need to consider artificial systems which are significantly different to humans. In this paper we approach this problem in the following way: We take a number of well known informal definitions of human intelligence that have been given by experts, and extract their essential features. These are then mathematically formalised to produce a general measure of intelligence for arbitrary machines. We believe that this equation formally captures the concept of machine intelligence in the broadest reasonable sense. We then show how this formal definition is related to the theory of universal optimal learning agents. Finally, we survey the many other tests and definitions of intelligence that have been proposed for machines.

We initiate the study of learning from multiple sources of limited data, each of which may be corrupted at a different rate. We develop a complete theory of which data sources should be used for two fundamental problems: estimating the bias of a coin, and learning a classifier in the presence of label noise. In both cases, efficient algorithms are provided for computing the optimal subset of data.

It is well-known that everything that is learnable in the difficult online setting, where an arbitrary sequences of examples must be labeled one at a time, is also learnable in the batch setting, where examples are drawn independently from a distribution. We show a result in the opposite direction. We give an efficient conversion algorithm from batch to online that is transductive: it uses future unlabeled data. This demonstrates the equivalence between what is properly and efficiently learnable in a batch model and a transductive online model.

We initiate the study of learning from multiple sources of limited data, each of which may be corrupted at a different rate. We develop a complete theory of which data sources should be used for two fundamental problems: estimating the bias of a coin, and learning a classifier in the presence of label noise. In both cases, efficient algorithms are provided for computing the optimal subset of data.

It is well-known that everything that is learnable in the difficult online setting, where an arbitrary sequences of examples must be labeled one at a time, is also learnable in the batch setting, where examples are drawn independently from a distribution. We show a result in the opposite direction. We give an efficient conversion algorithm from batch to online that is transductive: it uses future unlabeled data. This demonstrates the equivalence between what is properly and efficiently learnable in a batch model and a transductive online model.

We initiate the study of learning from multiple sources of limited data, each of which may be corrupted at a different rate. We develop a complete theoryof which data sources should be used for two fundamental problems: estimating the bias of a coin, and learning a classifier in the presence of label noise. In both cases, efficient algorithms are provided for computing the optimal subset of data.

We abstract out the core search problem of active learning schemes, to better understand the extent to which adaptive labeling can improve sample complexity. We give various upper and lower bounds on the number of labels which need to be queried, and we prove that a popular greedy active learning rule is approximately as good as any other strategy for minimizing this number of labels.

What makes a neural microcircuit computationally powerful?

We abstract out the core search problem of active learning schemes, to better understand the extent to which adaptive labeling can improve sample complexity. We give various upper and lower bounds on the number of labels which need to be queried, and we prove that a popular greedy active learning rule is approximately as good as any other strategy for minimizing this number of labels.