In this paper, we present a novel unsupervised algorithm for word sense disambiguation (WSD) at the document level. Our algorithm is inspired by a widely-used approach in the field of genetics for whole genome sequencing, known as the Shotgun sequencing technique. The proposed WSD algorithm is based on three main steps. First, a brute-force WSD algorithm is applied to short context windows (up to 10 words) selected from the document in order to generate a short list of likely sense configurations for each window. In the second step, these local sense configurations are assembled into longer composite configurations based on suffix and prefix matching. The resulted configurations are ranked by their length, and the sense of each word is chosen based on a voting scheme that considers only the top k configurations in which the word appears. We compare our algorithm with other state-of-the-art unsupervised WSD algorithms and demonstrate better performance, sometimes by a very large margin. We also show that our algorithm can yield better performance than the Most Common Sense (MCS) baseline on one data set. Moreover, our algorithm has a very small number of parameters, is robust to parameter tuning, and, unlike other bio-inspired methods, it gives a deterministic solution (it does not involve random choices).
There is a broad range of methods designed to perform WSD @cite_0 @cite_7 @cite_18 . The most accurate techniques are supervised @cite_15 , but they require annotated training data which is not always available. In order to overcome this limitation, some researchers have proposed various unsupervised or knowledgde-based WSD methods @cite_19 @cite_24 @cite_5 @cite_22 @cite_26 @cite_37 @cite_17 @cite_2 @cite_25 . Since our approach is unsupervised and based on WordNet @cite_36 @cite_13 , our focus is to present related work in the same direction. extend the gloss overlap algorithm of by using WordNet relations. proposed a brute-force algorithm for global WSD by employing the extended Lesk measure @cite_19 @cite_24 to compute the semantic relatedness among senses in a given text. However, their BF approach is not suitable for whole text documents, because of the high computational time. More recently, have proposed and compared three stochastic algorithms for global WSD as alternatives to BF search, namely a Genetic Algorithm, Simulated Annealing, and Ant Colony Optimization. Among these, the authors @cite_5 @cite_26 have found that the Ant Colony Algorithm yields better results than the other two.
@cite_18 @cite_26 @cite_37 @cite_22 @cite_7 @cite_36 @cite_0 @cite_19 @cite_24 @cite_2 @cite_5 @cite_15 @cite_13 @cite_25 @cite_17
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Abstract Objective The aim of this study was to investigate relations among different aspects in supervised word sense disambiguation (WSD; supervised machine learning for disambiguating the sense of a term in a context) and compare supervised WSD in the biomedical domain with that in the general English domain. Methods The study involves three data sets (a biomedical abbreviation data set, a general biomedical term data set, and a general English data set). The authors implemented three machine-learning algorithms, including (1) naive Bayes (NBL) and decision lists (TDLL), (2) their adaptation of decision lists (ODLL), and (3) their mixed supervised learning (MSL). There were six feature representations (various combinations of collocations, bag of words, oriented bag of words, etc.) and five window sizes (2, 4, 6, 8, and 10). Results Supervised WSD is suitable only when there are enough sense-tagged instances with at least a few dozens of instances for each sense. Collocations combined with neighboring words are appropriate selections for the context. For terms with unrelated biomedical senses, a large window size such as the whole paragraph should be used, while for general English words a moderate window size between 4 and 10 should be used. The performance of the authors' implementation of decision list classifiers for abbreviations was better than that of traditional decision list classifiers. However, the opposite held for the other two sets. Also, the authors' mixed supervised learning was stable and generally better than others for all sets. Conclusion From this study, it was found that different aspects of supervised WSD depend on each other. The experiment method presented in the study can be used to select the best supervised WSD classifier for each ambiguous term. A critical porblem faced by current supervised WSD systems is the lack or manually annotated training data. Tackling this data acquisition bottleneck is crucial, in order to build high-accuracy and wide-coverage WSD systems. In this paper, we show that the approach of automatically gathering training examples from parallel texts is scalable to a large set of nouns. We conducted evaluation on the nouns of SENSEVAL-2 English all-words task, using fine-grained sense scoring. Our evaluation shows that training on examples gathered from 680MB of parallel texts achieves accuracy comparable to the best system of SENSEVAL-2 English all-words task, and significantly outperforms the baseline of always choosing sense 1 of WordNet. Despite being impactful on a variety of problems and applications, the generative adversarial nets (GANs) are remarkably difficult to train. This issue is formally analyzed by arjovsky2017towards , who also propose an alternative direction to avoid the caveats in the minmax two-player training of GANs. The corresponding algorithm, called Wasserstein GAN (WGAN), hinges on the 1-Lipschitz continuity of the discriminator. In this paper, we propose a novel approach to enforcing the Lipschitz continuity in the training procedure of WGANs. Our approach seamlessly connects WGAN with one of the recent semi-supervised learning methods. As a result, it gives rise to not only better photo-realistic samples than the previous methods but also state-of-the-art semi-supervised learning results. In particular, our approach gives rise to the inception score of more than 5.0 with only 1,000 CIFAR-10 images and is the first that exceeds the accuracy of 90 on the CIFAR-10 dataset using only 4,000 labeled images, to the best of our knowledge. Despite superior training outcomes, adaptive optimization methods such as Adam, Adagrad or RMSprop have been found to generalize poorly compared to Stochastic gradient descent (SGD). These methods tend to perform well in the initial portion of training but are outperformed by SGD at later stages of training. We investigate a hybrid strategy that begins training with an adaptive method and switches to SGD when appropriate. Concretely, we propose SWATS, a simple strategy which switches from Adam to SGD when a triggering condition is satisfied. The condition we propose relates to the projection of Adam steps on the gradient subspace. By design, the monitoring process for this condition adds very little overhead and does not increase the number of hyperparameters in the optimizer. We report experiments on several standard benchmarks such as: ResNet, SENet, DenseNet and PyramidNet for the CIFAR-10 and CIFAR-100 data sets, ResNet on the tiny-ImageNet data set and language modeling with recurrent networks on the PTB and WT2 data sets. The results show that our strategy is capable of closing the generalization gap between SGD and Adam on a majority of the tasks. The evaluation of several tasks in lexical semantics is often limited by the lack of large amounts of manual annotations, not only for training purposes, but also for testing purposes. Word Sense Disambiguation (WSD) is a case in point, as hand-labeled datasets are particularly hard and time-consuming to create. Consequently, evaluations tend to be performed on a small scale, which does not allow for in-depth analysis of the factors that determine a systems' performance. In this paper we address this issue by means of a realistic simulation of large-scale evaluation for the WSD task. We do this by providing two main contributions: First, we put forward two novel approaches to the wide-coverage generation of semantically aware pseudowords (i.e., artificial words capable of modeling real polysemous words); second, we leverage the most suitable type of pseudoword to create large pseudosense-annotated corpora, which enable a large-scale experimental framework for the comparison of state-of-the-art supervised and knowledge-based algorithms. Using this framework, we study the impact of supervision and knowledge on the two major disambiguation paradigms and perform an in-depth analysis of the factors which affect their performance. Sufficient training examples are the fundamental requirement for most of the learning tasks. However, collecting well-labelled training examples is costly. Inspired by Zero-shot Learning (ZSL) that can make use of visual attributes or natural language semantics as an intermediate level clue to associate low-level features with high-level classes, in a novel extension of this idea, we aim to synthesise training data for novel classes using only semantic attributes. Despite the simplicity of this idea, there are several challenges. First, how to prevent the synthesised data from over-fitting to training classes? Second, how to guarantee the synthesised data is discriminative for ZSL tasks? Third, we observe that only a few dimensions of the learnt features gain high variances whereas most of the remaining dimensions are not informative. Thus, the question is how to make the concentrated information diffuse to most of the dimensions of synthesised data. To address the above issues, we propose a novel embedding algorithm named Unseen Visual Data Synthesis (UVDS) that projects semantic features to the high-dimensional visual feature space. Two main techniques are introduced in our proposed algorithm. (1) We introduce a latent embedding space which aims to reconcile the structural difference between the visual and semantic spaces, meanwhile preserve the local structure. (2) We propose a novel Diffusion Regularisation (DR) that explicitly forces the variances to diffuse over most dimensions of the synthesised data. By an orthogonal rotation (more precisely, an orthogonal transformation), DR can remove the redundant correlated attributes and further alleviate the over-fitting problem. On four benchmark datasets, we demonstrate the benefit of using synthesised unseen data for zero-shot learning. Extensive experimental results suggest that our proposed approach significantly outperforms the state-of-the-art methods. A novel algorithm based on random forests with surrogate splits is proposed to address the classification problem of incomplete data without imputation.The algorithm allows each tree to cast a vote even the voting process is interrupted by missing attributes.Experimental results on various acknowledged datasets show that the proposed method is robust and efficient. Random forests (RF) is known as an efficient algorithm in classification, however it depends on the integrity of datasets. Conventional methods in dealing with missing values usually employ estimation and imputation approaches whose efficiency is tied to the assumptions of data features. Recently, algorithm of surrogate decisions in RF was developed and this paper proposes a random forests algorithm with modified surrogate splits (Adjusted Weight Voting Random Forest, AWVRF) which is able to address the incomplete data without imputation.Differing from the present surrogate method, in AWVRF algorithm, when the primary splitting attribute and the surrogate attributes of an internal node are all missing, the undergoing instance is allowed to exit at the current node with a vote. Then the weight of the vote is adjusted by the strength of the involved attributes and the final decision is made by weighted voting. AWVRF does not comprise imputation step, thus it is independent of data features.AWVRF is compared with the methods of mean imputation, LeoFill, knnimpute, BPCAfill and conventional RF with surrogate decisions (surrRF) using 50 times repeated 5-fold cross validation on 10 acknowledged datasets. In a total of 22 experiment settings, the method of AWVRF harvests the highest accuracy in 14 settings and the largest AUC in 7 settings, exhibiting its superiority over other methods. Compared with surrRF, AWVRF is significantly more efficient and remain good discrimination of prediction. Experimental results show that the present AWVRF algorithm can successfully handle the classification task for incomplete data. An acid test for any new Word Sense Disambiguation (WSD) algorithm is its performance against the Most Frequent Sense (MFS). The field of WSD has found the MFS baseline very hard to beat. Clearly, if WSD researchers had access to MFS values, their striving to better this heuristic will push the WSD frontier. However, getting MFS values requires sense annotated corpus in enormous amounts, which is out of bounds for most languages, even if their WordNets are available. In this paper, we propose an unsupervised method for MFS detection from the untagged corpora, which exploits word embeddings. We compare the word embedding of a word with all its sense embeddings and obtain the predominant sense with the highest similarity. We observe significant performance gain for Hindi WSD over the WordNet First Sense (WFS) baseline. As for English, the SemCor baseline is bettered for those words whose frequency is greater than 2. Our approach is language and domain independent. We propose in this paper a new approach to train the Generative Adversarial Nets (GANs) with a mixture of generators to overcome the mode collapsing problem. The main intuition is to employ multiple generators, instead of using a single one as in the original GAN. The idea is simple, yet proven to be extremely effective at covering diverse data modes, easily overcoming the mode collapsing problem and delivering state-of-the-art results. A minimax formulation was able to establish among a classifier, a discriminator, and a set of generators in a similar spirit with GAN. Generators create samples that are intended to come from the same distribution as the training data, whilst the discriminator determines whether samples are true data or generated by generators, and the classifier specifies which generator a sample comes from. The distinguishing feature is that internal samples are created from multiple generators, and then one of them will be randomly selected as final output similar to the mechanism of a probabilistic mixture model. We term our method Mixture Generative Adversarial Nets (MGAN). We develop theoretical analysis to prove that, at the equilibrium, the Jensen-Shannon divergence (JSD) between the mixture of generators’ distributions and the empirical data distribution is minimal, whilst the JSD among generators’ distributions is maximal, hence effectively avoiding the mode collapsing problem. By utilizing parameter sharing, our proposed model adds minimal computational cost to the standard GAN, and thus can also efficiently scale to large-scale datasets. We conduct extensive experiments on synthetic 2D data and natural image databases (CIFAR-10, STL-10 and ImageNet) to demonstrate the superior performance of our MGAN in achieving state-of-the-art Inception scores over latest baselines, generating diverse and appealing recognizable objects at different resolutions, and specializing in capturing different types of objects by the generators. We show that the standard beam-search algorithm can be used as an efficient decoder for the global linear model of Zhang and Clark (2008) for joint word segmentation and POS-tagging, achieving a significant speed improvement. Such decoding is enabled by: (1) separating full word features from partial word features so that feature templates can be instantiated incrementally, according to whether the current character is separated or appended; (2) deciding the POS-tag of a potential word when its first character is processed. Early-update is used with perceptron training so that the linear model gives a high score to a correct partial candidate as well as a full output. Effective scoring of partial structures allows the decoder to give high accuracy with a small beam-size of 16. In our 10-fold cross-validation experiments with the Chinese Tree-bank, our system performed over 10 times as fast as Zhang and Clark (2008) with little accuracy loss. The accuracy of our system on the standard CTB 5 test was competitive with the best in the literature. Word sense disambiguation (WSD) is a difficult problem in Computational Linguistics, mostly because of the use of a fixed sense inventory and the deep level of granularity. This paper formulates WSD as a variant of the traveling salesman problem (TSP) to maximize the overall semantic relatedness of the context to be disambiguated. Ant colony optimization, a robust nature-inspired algorithm, was used in a reinforcement learning manner to solve the formulated TSP. We propose a novel measure based on the Lesk algorithm and Vector Space Model to calculate semantic relatedness. Our approach to WSD is comparable to state-of-the-art knowledge-based and unsupervised methods for benchmark datasets. In addition, we show that the combination of knowledge-based methods is superior to the most frequent sense heuristic and significantly reduces the difference between knowledge-based and supervised methods. The proposed approach could be customized for other lexical disambiguation tasks, such as Lexical Substitution or Word Domain Disambiguation. Computer Vision has recently witnessed great research advance towards automatic facial points detection. Numerous methodologies have been proposed during the last few years that achieve accurate and efficient performance. However, fair comparison between these methodologies is infeasible mainly due to two issues. (a) Most existing databases, captured under both constrained and unconstrained (in-the-wild) conditions have been annotated using different mark-ups and, in most cases, the accuracy of the annotations is low. (b) Most published works report experimental results using different training testing sets, different error metrics and, of course, landmark points with semantically different locations. In this paper, we aim to overcome the aforementioned problems by (a) proposing a semi-automatic annotation technique that was employed to re-annotate most existing facial databases under a unified protocol, and (b) presenting the 300 Faces In-The-Wild Challenge (300-W), the first facial landmark localization challenge that was organized twice, in 2013 and 2015. To the best of our knowledge, this is the first effort towards a unified annotation scheme of massive databases and a fair experimental comparison of existing facial landmark localization systems. The images and annotations of the new testing database that was used in the 300-W challenge are available from http: ibug.doc.ic.ac.uk resources 300-W_IMAVIS . Many methods, including supervised and unsupervised algorithms, have been developed for extractive document summarization. Most supervised methods consider the summarization task as a two-class classification problem and classify each sentence individually without leveraging the relationship among sentences. The unsupervised methods use heuristic rules to select the most informative sentences into a summary directly, which are hard to generalize. In this paper, we present a Conditional Random Fields (CRF) based framework to keep the merits of the above two kinds of approaches while avoiding their disadvantages. What is more, the proposed framework can take the outcomes of previous methods as features and seamlessly integrate them. The key idea of our approach is to treat the summarization task as a sequence labeling problem. In this view, each document is a sequence of sentences and the summarization procedure labels the sentences by 1 and 0. The label of a sentence depends on the assignment of labels of others. We compared our proposed approach with eight existing methods on an open benchmark data set. The results show that our approach can improve the performance by more than 7.1 and 12.1 over the best supervised baseline and unsupervised baseline respectively in terms of two popular metrics F1 and ROUGE-2. Detailed analysis of the improvement is presented as well. Algorithms for data-driven learning of domain-specific overcomplete dictionaries are developed to obtain maximum likelihood and maximum a posteriori dictionary estimates based on the use of Bayesian models with concave Schur-concave (CSC) negative log priors. Such priors are appropriate for obtaining sparse representations of environmental signals within an appropriately chosen (environmentally matched) dictionary. The elements of the dictionary can be interpreted as concepts, features, or words capable of succinct expression of events encountered in the environment (the source of the measured signals). This is a generalization of vector quantization in that one is interested in a description involving a few dictionary entries (the proverbial "25 words or less"), but not necessarily as succinct as one entry. To learn an environmentally adapted dictionary capable of concise expression of signals generated by the environment, we develop algorithms that iterate between a representative set of sparse representations found by variants of FOCUSS and an update of the dictionary using these sparse representations.Experiments were performed using synthetic data and natural images. For complete dictionaries, we demonstrate that our algorithms have improved performance over other independent component analysis (ICA) methods, measured in terms of signal-to-noise ratios of separated sources. In the overcomplete case, we show that the true underlying dictionary and sparse sources can be accurately recovered. In tests with natural images, learned overcomplete dictionaries are shown to have higher coding efficiency than complete dictionaries; that is, images encoded with an overcomplete dictionary have both higher compression (fewer bits per pixel) and higher accuracy (lower mean square error). We present a new efficient algorithm for the search version of the approximate Closest Vector Problem with Preprocessing (CVPP). Our algorithm achieves an approximation factor of O(n sqrt log n ), improving on the previous best of O(n^ 1.5 ) due to Lag arias, Lenstra, and Schnorr hkzbabai . We also show, somewhat surprisingly, that only O(n) vectors of preprocessing advice are sufficient to solve the problem (with the slightly worse approximation factor of O(n)). We remark that this still leaves a large gap with respect to the decisional version of CVPP, where the best known approximation factor is O(sqrt n log n ) due to Aharonov and Regev AharonovR04 . To achieve these results, we show a reduction to the same problem restricted to target points that are close to the lattice and a more efficient reduction to a harder problem, Bounded Distance Decoding with preprocessing (BDDP). Combining either reduction with the previous best-known algorithm for BDDP by Liu, Lyubashevsky, and Micciancio LiuLM06 gives our main result. In the setting of CVP without preprocessing, we also give a reduction from (1+eps)gamma approximate CVP to gamma approximate CVP where the target is at distance at most 1+1 eps times the minimum distance (the length of the shortest non-zero vector) which relies on the lattice sparsification techniques of Dadush and Kun DadushK13 . As our final and most technical contribution, we present a substantially more efficient variant of the LLM algorithm (both in terms of run-time and amount of preprocessing advice), and via an improved analysis, show that it can decode up to a distance proportional to the reciprocal of the smoothing parameter of the dual lattice MR04 . We show that this is never smaller than the LLM decoding radius, and that it can be up to an wide tilde Omega (sqrt n ) factor larger. Abstract Motivated by the success of powerful while expensive techniques to recognize words in a holistic way (, 2013; , 2014; , 2016) object proposals techniques emerge as an alternative to the traditional text detectors. In this paper we introduce a novel object proposals method that is specifically designed for text. We rely on a similarity based region grouping algorithm that generates a hierarchy of word hypotheses. Over the nodes of this hierarchy it is possible to apply a holistic word recognition method in an efficient way. Our experiments demonstrate that the presented method is superior in its ability of producing good quality word proposals when compared with class-independent algorithms. We show impressive recall rates with a few thousand proposals in different standard benchmarks, including focused or incidental text datasets, and multi-language scenarios. Moreover, the combination of our object proposals with existing whole-word recognizers (, 2014; , 2016) shows competitive performance in end-to-end word spotting, and, in some benchmarks, outperforms previously published results. Concretely, in the challenging ICDAR2015 Incidental Text dataset, we overcome in more than 10 F -score the best-performing method in the last ICDAR Robust Reading Competition (Karatzas, 2015). Source code of the complete end-to-end system is available at https: github.com lluisgomez TextProposals . The nearestor near-neighbor query problems arise in a large variety of database applications, usually in the context of similarity searching. Of late, there has been increasing interest in building search index structures for performing similarity search over high-dimensional data, e.g., image databases, document collections, time-series databases, and genome databases. Unfortunately, all known techniques for solving this problem fall prey to the of dimensionality." That is, the data structures scale poorly with data dimensionality; in fact, if the number of dimensions exceeds 10 to 20, searching in k-d trees and related structures involves the inspection of a large fraction of the database, thereby doing no better than brute-force linear search. It has been suggested that since the selection of features and the choice of a distance metric in typical applications is rather heuristic, determining an approximate nearest neighbor should su ce for most practical purposes. In this paper, we examine a novel scheme for approximate similarity search based on hashing. The basic idea is to hash the points Supported by NAVY N00014-96-1-1221 grant and NSF Grant IIS-9811904. Supported by Stanford Graduate Fellowship and NSF NYI Award CCR-9357849. Supported by ARO MURI Grant DAAH04-96-1-0007, NSF Grant IIS-9811904, and NSF Young Investigator Award CCR9357849, with matching funds from IBM, Mitsubishi, Schlumberger Foundation, Shell Foundation, and Xerox Corporation. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the VLDB copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Very Large Data Base Endowment. To copy otherwise, or to republish, requires a fee and or special permission from the Endowment. Proceedings of the 25th VLDB Conference, Edinburgh, Scotland, 1999. from the database so as to ensure that the probability of collision is much higher for objects that are close to each other than for those that are far apart. We provide experimental evidence that our method gives signi cant improvement in running time over other methods for searching in highdimensional spaces based on hierarchical tree decomposition. Experimental results also indicate that our scheme scales well even for a relatively large number of dimensions (more than 50). We revisit a problem introduced by Bharat and Broder almost a decade ago: how to sample random pages from the corpus of documents indexed by a search engine, using only the search engine’s public interface? Such a primitive is particularly useful in creating objective benchmarks for search engines. The technique of Bharat and Broder suffers from a well-recorded bias: it favors long documents. In this paper we introduce two novel sampling algorithms: a lexicon-based algorithm and a random walk algorithm. Our algorithms produce biased samples, but each sample is accompanied by a weight, which represents its bias. The samples, in conjunction with the weights, are then used to simulate near-uniform samples. To this end, we resort to four well-known Monte Carlo simulation methods: rejection sampling, importance sampling, the Metropolis-Hastings algorithm, and the Maximum Degree method. The limited access to search engines force our algorithms to use bias weights that are only “approximate”. We characterize analytically the effect of approximate bias weights on Monte Carlo methods and conclude that our algorithms are guaranteed to produce near-uniform samples from the search engine’s corpus. Our study of approximate Monte Carlo methods could be of independent interest. Experiments on a corpus of 2.4 million documents substantiate our analytical findings and show that our algorithms do not have significant bias towards long documents. We use our algorithms to collect fresh comparative statistics about the corpora of the Google, MSN Search, and Yahoo! search engines. We use distributed computing tools to provide a new perspective on the behavior of cooperative biological ensembles. We introduce the Ants Nearby Treasure Search (ANTS) problem, a generalization of the classical cow-path problem [10, 20, 41, 42], which is relevant for collective foraging in animal groups. In the ANTS problem, k identical (probabilistic) agents, initially placed at some central location, collectively search for a treasure in the two-dimensional plane. The treasure is placed at a target location by an adversary and the goal is to find it as fast as possible as a function of both k and D, where D is the distance between the central location and the target. This is biologically motivated by cooperative, central place foraging, such as performed by ants around their nest. In this type of search there is a strong preference to locate nearby food sources before those that are further away. We focus on trying to find what can be achieved if communication is limited or altogether absent. Indeed, to avoid overlaps agents must be highly dispersed making communication difficult. Furthermore, if the agents do not commence the search in synchrony, then even initial communication is problematic. This holds, in particular, with respect to the question of whether the agents can communicate and conclude their total number, k. It turns out that the knowledge of k by the individual agents is crucial for performance. Indeed, it is a straightforward observation that the time required for finding the treasure is Ω(D + D2 k), and we show in this paper that this bound can be matched if the agents have knowledge of k up to some constant approximation. We present a tight bound for the competitive penalty that must be paid, in the running time, if the agents have no information about k. Specifically, this bound is slightly more than logarithmic in the number of agents. In addition, we give a lower bound for the setting in which the agents are given some estimation of k. Informally, our results imply that the agents can potentially perform well without any knowledge of their total number k, however, to further improve, they must use some information regarding k. Finally, we propose a uniform algorithm that is both efficient and extremely simple, suggesting its relevance for actual biological scenarios. We consider the problem of using a large unlabeled sample to boost performance of a learning algorit,hrn when only a small set of labeled examples is available. In particular, we consider a problem setting motivated by the task of learning to classify web pages, in which the description of each example can be partitioned into two distinct views. For example, the description of a web page can be partitioned into the words occurring on that page, and the words occurring in hyperlinks t,hat point to that page. We assume that either view of the example would be sufficient for learning if we had enough labeled data, but our goal is to use both views together to allow inexpensive unlabeled data to augment, a much smaller set of labeled examples. Specifically, the presence of two distinct views of each example suggests strategies in which two learning algorithms are trained separately on each view, and then each algorithm’s predictions on new unlabeled examples are used to enlarge the training set of the other. Our goal in this paper is to provide a PAC-style analysis for this setting, and, more broadly, a PAC-style framework for the general problem of learning from both labeled and unlabeled data. We also provide empirical results on real web-page data indicating that this use of unlabeled examples can lead to significant improvement of hypotheses in practice. *This research was supported in part by the DARPA HPKB program under contract F30602-97-1-0215 and by NSF National Young investigator grant CCR-9357793. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. TO copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and or a fee. COLT 98 Madison WI USA Copyright ACM 1998 l-58113-057--0 98 7... 5.00 92 Tom Mitchell School of Computer Science Carnegie Mellon University Pittsburgh, PA 15213-3891 mitchell+@cs.cmu.edu