Abstract. This paper describes FOIL, a system that learns Horn clauses from data expressed as relations. FOIL is based on ideas that have proved effective in attribute-value learning systems, but extends them to a first-order formalism. This new system has been applied successfully to several tasks taken from the machine learning literature.

. This paper shows that the accuracy of learned text classifiers can be improved by augmenting a small number of labeled training documents with a large pool of unlabeled documents. This is important because in many text classification problems obtaining training labels is expensive, while large quantities of unlabeled documents are readily available. We introduce an algorithm for learning from labeled and unlabeled documents based on the combination of Expectation-Maximization (EM) and a naive Bayes classifier. The algorithm first trains a classifier using the available labeled documents, and probabilistically labels the unlabeled documents. It then trains a new classifier using the labels for all the documents, and iterates to convergence. This basic EM procedure works well when the data conform to the generative assumptions of the model. However these assumptions are often violated in practice, and poor performance can result. We present two extensions to the algorithm that improve ...

Many approaches to Bayesian image segmentation have used maximum a posteriori (MAP) estimation in conjunction with Markov random fields (MRF). While this approach performs well, it has a number of disadvantages. In particular, exact MAP estimates cannot be computed, approximate MAP estimates are computationally expensive to compute, and unsupervised parameter estimation of the MRF is difficult. In this paper, we propose a new approach to Bayesian image segmentation which directly addresses these problems. The new method replaces the MRF model with a novel multiscale random field (MSRF), and replaces the MAP estimator with a sequential MAP (SMAP) estimator derived from a novel estimation criteria. Together, the proposed estimator and model result in a segmentation algorithm which is not iterative and can be computed in time proportional to MN where M is the number of classes and N is the number of pixels. We also develop a computationally effcient method for unsupervised estimation of m...

A new formulation of the image partitioning problem is presented: construct a complete and stable description of an image, in terms of a specified descriptive language, that is simplest in the sense of being shortest. We show that a descriptive language limited to a low-order polynomial description of the intensity variation within each region and a chain-code-like description of the region boundaries yields intuitively satisfying partitions for a wide class of images. The advantage of this formulation is that it can be extended to deal with subsequent steps of the image-understanding problem (or to deal with other image attributes, such as texture) in a natural way by augmenting the descriptive language. Experiments performed on a variety of both real and synthetic images demonstrate the superior performance of this approach over partitioning techniques based on clustering vectors of local image attributes and standard edge-detection techniques. 1 Introduction The partitioning proble...

We describe a method for automatically building statistical shape models from a training set of exam- ple boundaries / surfaces. These models show considerable promise as a basis for segmenting and interpreting images. One of the drawbacks of the approach is, however, the need to establish a set of dense correspondences between all members of a set of training shapes. Often this is achieved by locating a set of qandmarks manually on each training image, which is time-consuming and subjective in 2D, and almost impossible in 3D. We describe how shape models can be built automatically by posing the correspondence problem as one of finding the parameterization for each shape in the training set. We select the set of parameterizations that build the best model. We define best as that which min- imizes the description length of the training set, arguing that this leads to models with good compactness, specificity and generalization ability. We show how a set of shape parameterizations can be represented and manipulated in order to build a minimum description length model. Results are given for several different training sets of 2D boundaries, showing that the proposed method constructs better models than other approaches including manual landmarking - the current gold standard. We also show that the method can be extended straightforwardly to 3D.

This paper describes a technique for learning both the number of states and the topology of Hidden Markov Models from examples. The induction process starts with the most specific model consistent with the training data and generalizes by successively merging states. Both the choice of states to merge and the stopping criterion are guided by the Bayesian posterior probability. We compare our algorithm with the Baum-Welch method of estimating fixed-size models, and find that it can induce minimal HMMs from data in cases where fixed estimation does not converge or requires redundant parameters to converge. 1

This paper reviews the principle of Minimum Description Length (MDL) for problems of model selection. By viewing statistical modeling as a means of generating descriptions of observed data, the MDL framework discriminates between competing models based on the complexity of each description. This approach began with Kolmogorov's theory of algorithmic complexity, matured in the literature on information theory, and has recently received renewed interest within the statistics community. In the pages that follow, we review both the practical as well as the theoretical aspects of MDL as a tool for model selection, emphasizing the rich connections between information theory and statistics. At the boundary between these two disciplines, we find many interesting interpretations of popular frequentist and Bayesian procedures. As we will see, MDL provides an objective umbrella under which rather disparate approaches to statistical modeling can co-exist and be compared. We illustrate th...

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this paper, we confine ourselves to the former issue, and refer the interested reader to Li and Abe (1996), which deals with the latter issue

We consider the following problem. At each point of discrete time the learner must make a prediction; he is given the predictions made by a pool of experts. Each prediction and the outcome, which is disclosed after the learner has made his prediction, determine the incurred loss. It is known that, under weak regularity, the learner can ensure that his cumulative loss never exceeds cL+ a ln n, where c and a are some constants, n is the size of the pool, and L is the cumulative loss incurred by the best expert in the pool. We find the set of those pairs (c; a) for which this is true.