Although Bayesian analysis has been in use since Laplace, the Bayesian method of model--comparison has only recently been developed in depth. In this paper, the Bayesian approach to regularisation and model--comparison is demonstrated by studying the inference problem of interpolating noisy data. The concepts and methods described are quite general and can be applied to many other problems. Regularising constants are set by examining their posterior probability distribution. Alternative regularisers (priors) and alternative basis sets are objectively compared by evaluating the evidence for them. `Occam's razor' is automatically embodied by this framework. The way in which Bayes infers the values of regularising constants and noise levels has an elegant interpretation in terms of the effective number of parameters determined by the data set. This framework is due to Gull and Skilling. 1 Data modelling and Occam's razor In science, a central task is to develop and compare models to a...

For manytypes of learners one can compute the statistically "optimal" way to select data. We review how these techniques have been used with feedforward neural networks [MacKay, 1992# Cohn, 1994]. We then showhow the same principles may be used to select data for two alternative, statistically-based learning architectures: mixtures of Gaussians and locally weighted regression. While the techniques for neural networks are expensive and approximate, the techniques for mixtures of Gaussians and locally weighted regression are both efficient and accurate.

Abstract. Active learning differs from "learning from examples " in that the learning algorithm assumes at least some control over what part of the input domain it receives information about. In some situations, active learning is provably more powerful than learning from examples alone, giving better generalization for a fixed number of training examples. In this article, we consider the problem of learning a binary concept in the absence of noise. We describe a formalism for active concept learning called selective sampling and show how it may be approximately implemented by a neural network. In selective sampling, a learner receives distribution information from the environment and queries an oracle on parts of the domain it considers "useful. " We test our implementation, called an SGnetwork, on three domains and observe significant improvement in generalization.

Uncertainty sampling methods iteratively request class labels for training instances whose classes are uncertain despite the previous labeled instances. These methods can greatly reduce the number of instances that an expert need label. One problem with this approach is that the classifier best suited for an application may be too expensive to train or use during the selection of instances. We test the use of one classifier (a highly efficient probabilistic one) to select examples for training another (the C4.5 rule induction program). Despite being chosen by this heterogeneous approach, the uncertainty samples yielded classifiers with lower error rates than random samples ten times larger. 1 Introduction Machine learning algorithms have been used to build classification rules from data sets consisting of hundreds of thousands of instances [4]. In some applications unlabeled training instances are abundant but the cost of labeling an instance with its class is high. In the informatio...

Three Bayesian ideas are presented for supervised adaptive classifiers. First, it is argued that the output of a classifier should be obtained by marginalising over the posterior distribution of the parameters; a simple approximation to this integral is proposed and demonstrated. This involves a `moderation' of the most probable classifier 's outputs, and yields improved performance. Second, it is demonstrated that the Bayesian framework for model comparison described for regression models in (MacKay, 1992a, 1992b) can also be applied to classification problems. This framework successfully chooses the magnitude of weight decay terms, and ranks solutions found using different numbers of hidden units. Third, an information--based data selection criterion is derived and demonstrated within this framework. 1 Introduction A quantitative Bayesian framework has been described for learning of mappings in feedforward networks (MacKay, 1992a, 1992b). It was demonstrated that this `evidence' fram...

We consider the question "How should one act when the only goal is to learn as much as possible?" Building on the theoretical results of Fedorov [1972] and MacKay [1992], we apply techniques from Optimal Experiment Design (OED) to guide the query/action selection of a neural network learner. We demonstrate that these techniques allow the learner to minimize its generalization error by exploring its domain efficiently and completely.We conclude that, while not a panacea, OED-based query/action has muchto offer, especially in domains where its high computational costs can be tolerated.

In many real-world learning tasks, it is expensive to acquire a sufficient number of labeled examples for training. This paper proposes a general method for efficiently training probabilistic classifiers, by selecting for training only the more informative examples in a stream of unlabeled examples. The method, committee-based sampling, evaluates the informativeness of an example by measuring the degree of disagreement between several model variants. These variants (the committee) are drawn randomly from a probability distribution conditioned by the training set selected so far (Monte-Carlo sampling). The method is particularly attractive because it evaluates the expected information gain from a training example implicitly, making the model both easy to implement and generally applicable. We further show how to apply committeebased sampling for training Hidden Markov Model classifiers, which are commonly used for complex classification tasks. The method was implemented and tested for ...

Abstract—Exploratory activities seem to be intrinsically rewarding for children and crucial for their cognitive development. Can a machine be endowed with such an intrinsic motivation system? This is the question we study in this paper, presenting a number of computational systems that try to capture this drive towards novel or curious situations. After discussing related research coming from developmental psychology, neuroscience, developmental robotics, and active learning, this paper presents the mechanism of Intelligent Adaptive Curiosity, an intrinsic motivation system which pushes a robot towards situations in which it maximizes its learning progress. This drive makes the robot focus on situations which are neither too predictable nor too unpredictable, thus permitting autonomous mental development. The complexity of the robot’s activities autonomously increases and complex developmental sequences self-organize without

Passively accepting measurements of the world is not enough, as the data we obtain is always incomplete, and the inferences made from it uncertain to a degree which is often unacceptable. If we are to build machines that operate autonomously they will always be faced with this dilemma, and can only be successful if they play a much more active role. This paper presents such a machine. It deliberately seeks out those parts of the world which maximize the fidelity of its internal representations, and keeps searching until those representations are acceptable. We call this paradigm autonomous exploration, and the machine an autonomous explorer. This paper has two major contributions. The first is a theory that tells us how to explore, and which confirms the intuitive ideas we have put forward previously. The second is an implementation of that theory. In our laboratory we have constructed a working autonomous explorer and here for the first time show it in action. The system is entirely bottom-up and does not depend on any a priori knowledge of the environment. To our knowledge it is the first to have successfully closed the loop between gaze planning and the inference of complex 3D models.

Evolutionary algorithms (EAs) have received increasing interests both in the academy and industry. One main difficulty in applying EAs to real-world applications is that EAs usually need a large number of fitness evaluations before a satisfying result can be obtained. However, fitness evaluations are not always straightforward in many real-world applications. Either an explicit fitness function does not exist, or the evaluation of the fitness is computationally very expensive. In both cases, it is necessary to estimate the fitness function by constructing an approximate model. In this paper, a comprehensive survey of the research on fitness approximation in evolutionary computation is presented. Main issues like approximation levels, approximate model management schemes, model construction techniques are reviewed. To conclude, open questions and interesting issues in the field are discussed.