Estimating mutual information from i.i.d. samples drawn from an unknown joint density function is a basic statistical problem of broad interest with multitudinous applications. The most popular estimator is one proposed by Kraskov and St "ogbauer and Grassberger (KSG) in 2004, and is nonparametric and based on the distances of each sample to its @math nearest neighboring sample, where @math is a fixed small integer. Despite its widespread use (part of scientific software packages), theoretical properties of this estimator have been largely unexplored. In this paper we demonstrate that the estimator is consistent and also identify an upper bound on the rate of convergence of the bias as a function of number of samples. We argue that the superior performance benefits of the KSG estimator stems from a curious "correlation boosting" effect and build on this intuition to modify the KSG estimator in novel ways to construct a superior estimator. As a byproduct of our investigations, we obtain nearly tight rates of convergence of the @math error of the well known fixed @math nearest neighbor estimator of differential entropy by Kozachenko and Leonenko.
A conceptually straightforward way to estimate the differential entropy and mutual information is to use a kernel density estimator (KDE) @cite_59 @cite_60 @cite_19 @cite_64 @cite_34 @cite_41 : the densities @math are separately estimated from samples and the estimated densities are then used to calculate the entropy and mutual information via the resubstitution estimator. A typical approach to avoid overfitting is to conduct data splitting (DS): split the samples and use one part for KDE and the other for the resubstitution.
@cite_64 @cite_60 @cite_41 @cite_19 @cite_59 @cite_34
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Purpose – The purpose of this paper is to suggest an alternative to the widely used Times Cited criterion for analysing citation networks. The approach involves taking account of the natures of the papers that cite a given paper, so as to differentiate between papers that attract the same number of citations.Design methodology approach – ArticleRank is an algorithm that has been derived from Google's PageRank algorithm to measure the influence of journal articles. ArticleRank is applied to two datasets – a citation network based on an early paper on webometrics, and a self‐citation network based on the 19 most cited papers in the Journal of Documentation – using citation data taken from the Web of Knowledge database.Findings – ArticleRank values provide a different ranking of a set of papers from that provided by the corresponding Times Cited values, and overcomes the inability of the latter to differentiate between papers with the same numbers of citations. The difference in rankings between Times Cited ... Insufficiency of labeled training data is a major obstacle for automatic video annotation. Semi-supervised learning is an effective approach to this problem by leveraging a large amount of unlabeled data. However, existing semi-supervised learning algorithms have not demonstrated promising results in large-scale video annotation due to several difficulties, such as large variation of video content and intractable computational cost. In this paper, we propose a novel semi-supervised learning algorithm named semi-supervised kernel density estimation (SSKDE) which is developed based on kernel density estimation (KDE) approach. While only labeled data are utilized in classical KDE, in SSKDE both labeled and unlabeled data are leveraged to estimate class conditional probability densities based on an extended form of KDE. It is a non-parametric method, and it thus naturally avoids the model assumption problem that exists in many parametric semi-supervised methods. Meanwhile, it can be implemented with an efficient iterative solution process. So, this method is appropriate for video annotation. Furthermore, motivated by existing adaptive KDE approach, we propose an improved algorithm named semi-supervised adaptive kernel density estimation (SSAKDE). It employs local adaptive kernels rather than a fixed kernel, such that broader kernels can be applied in the regions with low density. In this way, more accurate density estimates can be obtained. Extensive experiments have demonstrated the effectiveness of the proposed methods. Abstract Irregular sampling and “stable sampling” of band-limited functions have been studied by H.J. Landau [H.J. Landau, Necessary density conditions for sampling and interpolation of certain entire functions, Acta Math. 117 (1967) 37–52]. We prove that quasicrystals are sets of stable sampling. To cite this article: B. Matei, Y. Meyer, C. R. Acad. Sci. Paris, Ser. I 346 (2008). We develop a ldquoplug-inrdquo kernel estimator for the differential entropy that is consistent even if the kernel width tends to zero as quickly as 1 N, where N is the number of independent and identically distributed (i.i.d.) samples. Thus, accurate density estimates are not required for accurate kernel entropy estimates; in fact, it is a good idea when estimating entropy to sacrifice some accuracy in the quality of the corresponding density estimate. Multiple-instance learning (MIL) is a variation on supervised learning. Instead of receiving a set of labeled instances, the learner receives a set of bags that are labeled. Each bag contains many instances. The aim of MIL is to classify new bags or instances. In this work, we propose a novel algorithm, MIL-SKDE (multiple-instance learning with supervised kernel density estimation), which addresses MIL problem through an extended framework of ''KDE (kernel density estimation)+mean shift''. Since the KDE+mean shift framework is an unsupervised learning method, we extend KDE to its supervised version, called supervised KDE (SKDE), by considering class labels of samples. To seek the modes (local maxima) of SKDE, we also extend mean shift to a supervised version by taking into account sample labels. SKDE is an alternative of the well-known diverse density estimation (DDE) whose modes are called concepts. Comparing to DDE, SKDE is more convenient to learn multi-modal concepts and robust to labeling noise (mistakenly labeled bags). Finally, each bag is mapped into a concept space where the multi-class SVM classifiers are learned. Experimental results demonstrate that our approach outperforms the state-of-the-art MIL approaches. Abstract Documents in computer-readable form can be used to provide information about other documents, i.e. those they cite. To do this efficiently requires procedures for computer recognition of citing statements. This is not easy, especially for multi-sentence citing statements. Computer recognition procedures have been developed which are accurate to the following extent: 73 of the words in statements selected by computer procedures as being citing statements are words which are correctly attributable to the corresponding documents. The retrieval effectiveness of computer-recognized citing statements was tested in the following way. First, for eight retrieval requests in inorganiic chemistry, average recall by search of Chemical Abstracts Service indexing and Chemical Abstracts abstract text words was found to be 50 . Words from citing statements referring to the papers to be retrieved were then added to the index terms and abstract words as additional access points, and searching was repeated. Average recall increased to 70 . Only words from citing statements published within a year of the cited papers were used. The retrieval effect of citing statement words alone (published within a year) without index or abstract terms was the following: average recall was 40 . When just the words of the titles of the cited papers were added to those citing statement words, average recall increased to 50 . We present simple and computationally efficient nonparametric estimators of R 'enyi entropy and mutual information based on an i.i.d. sample drawn from an unknown, absolutely continuous distribution over @math . The estimators are calculated as the sum of @math -th powers of the Euclidean lengths of the edges of the generalized nearest-neighbor' graph of the sample and the empirical copula of the sample respectively. For the first time, we prove the almost sure consistency of these estimators and upper bounds on their rates of convergence, the latter of which under the assumption that the density underlying the sample is Lipschitz continuous. Experiments demonstrate their usefulness in independent subspace analysis. We present two classes of improved estimators for mutual information @math , from samples of random points distributed according to some joint probability density @math . In contrast to conventional estimators based on binnings, they are based on entropy estimates from @math -nearest neighbor distances. This means that they are data efficient (with @math we resolve structures down to the smallest possible scales), adaptive (the resolution is higher where data are more numerous), and have minimal bias. Indeed, the bias of the underlying entropy estimates is mainly due to nonuniformity of the density at the smallest resolved scale, giving typically systematic errors which scale as functions of @math for @math points. Numerically, we find that both families become exact for independent distributions, i.e. the estimator @math vanishes (up to statistical fluctuations) if @math . This holds for all tested marginal distributions and for all dimensions of @math and @math . In addition, we give estimators for redundancies between more than two random variables. We compare our algorithms in detail with existing algorithms. Finally, we demonstrate the usefulness of our estimators for assessing the actual independence of components obtained from independent component analysis (ICA), for improving ICA, and for estimating the reliability of blind source separation. A citing sentence is one that appears in a scientific article and cites previous work. Citing sentences have been studied and used in many applications. For example, they have been used in scientific paper summarization, automatic survey generation, paraphrase identification, and citation function classification. Citing sentences that cite multiple papers are common in scientific writing. This observation should be taken into consideration when using citing sentences in applications. For instance, when a citing sentence is used in a summary of a scientific paper, only the fragments of the sentence that are relevant to the summarized paper should be included in the summary. In this paper, we present and compare three different approaches for identifying the fragments of a citing sentence that are related to a given target reference. Our methods are: word classification, sequence labeling, and segment classification. Our experiments show that segment classification achieves the best results. In the random sampling setting we estimate the entropy of a probability density distribution by the entropy of a kernel density estimator using the double exponential kernel. Under mild smoothness and moment conditions we show that the entropy of the kernel density estimator equals a sum of independent and identically distributed (i.i.d.) random variables plus a perturbation which is asymptotically negligible compared to the parametric rate n sup -1 2 . An essential part in the proof is obtained by exhibiting almost sure bounds for the Kullback-Leibler divergence between the kernel density estimator and its expected value. The basic technical tools are Doob's submartingale inequality and convexity (Jensen's inequality). In a document network such as a citation network of scientific documents, web-logs, etc., the content produced by authors exhibits their interest in certain topics. In addition some authors influence other authors' interests. In this work, we propose to model the influence of cited authors along with the interests of citing authors. Moreover, we hypothesize that apart from the citations present in documents, the context surrounding the citation mention provides extra topical information about the cited authors. However, associating terms in the context to the cited authors remains an open problem. We propose novel document generation schemes that incorporate the context while simultaneously modeling the interests of citing authors and influence of the cited authors. Our experiments show significant improvements over baseline models for various evaluation criteria such as link prediction between document and cited author, and quantitatively explaining unseen text. We analyze the estimation of information theoretic measures of continuous random variables such as: differential entropy, mutual information or Kullback-Leibler divergence. The objective of this paper is two-fold. First, we prove that the information theoretic measure estimates using the k-nearest-neighbor density estimation with fixed k converge almost surely, even though the k-nearest-neighbor density estimation with fixed k does not converge to its true measure. Second, we show that the information theoretic measure estimates do not converge for k growing linearly with the number of samples. Nevertheless, these nonconvergent estimates can be used for solving the two-sample problem and assessing if two random variables are independent. We show that the two-sample and independence tests based on these nonconvergent estimates compare favorably with the maximum mean discrepancy test and the Hilbert Schmidt independence criterion. A new form of document coupling called co-citation is defined as the frequency with which two documents are cited together. The co-citation frequency of two scientific papers can be determined by comparing lists of citing documents in the Science Citation Index and counting identical entries. Networks of co-cited papers can be generated for specific scientific specialties, and an example is drawn from the literature of particle physics. Co-citation patterns are found to differ significantly from bibliographic coupling patterns, but to agree generally with patterns of direct citation. Clusters of co-cited papers provide a new way to study the specialty structure of science. They may provide a new approach to indexing and to the creation of SDI profiles. Scholars are increasingly citing electronic “web references” which are not preserved in libraries or full text archives. WebCite is a new standard for citing web references. To “webcite” a document involves archiving the cited Web page through www.webcitation.org and citing the WebCite permalink instead of (or in addition to) the unstable live Web page. This journal has amended its “instructions for authors” accordingly, asking authors to archive cited Web pages before submitting a manuscript. Almost 200 other journals are already using the system. We discuss the rationale for WebCite, its technology, and how scholars, editors, and publishers can benefit from the service. Citing scholars initiate an archiving process of all cited Web references, ideally before they submit a manuscript. Authors of online documents and websites which are expected to be cited by others can ensure that their work is permanently available by creating an archived copy using WebCite and providing the citation information including the WebCite link on their Web document(s). Editors should ask their authors to cache all cited Web addresses (Uniform Resource Locators, or URLs) “prospectively” before submitting their manuscripts to their journal. Editors and publishers should also instruct their copyeditors to cache cited Web material if the author has not done so already. Finally, WebCite can process publisher submitted “citing articles” (submitted for example as eXtensible Markup Language [XML] documents) to automatically archive all cited Web pages shortly before or on publication. Finally, WebCite can act as a focussed crawler, caching retrospectively references of already published articles. Copyright issues are addressed by honouring respective Internet standards (robot exclusion files, no-cache and no-archive tags). Long-term preservation is ensured by agreements with libraries and digital preservation organizations. The resulting WebCite Index may also have applications for research assessment exercises, being able to measure the impact of Web services and published Web documents through access and Web citation metrics. @PARASPLIT [J Med Internet Res 2005;7(5):e60] Citation relationship between scientific publications has been successfully used for scholarly bibliometrics, information retrieval and data mining tasks, and citation-based recommendation algorithms are well documented. While previous studies investigated citation relations from various viewpoints, most of them share the same assumption that, if paper1 cites paper2 (or author1 cites author2), they are connected, regardless of citation importance, sentiment, reason, topic, or motivation. However, this assumption is oversimplified. In this study, we employ an innovative "context-rich heterogeneous network" approach, which paves a new way for citation recommendation task. In the network, we characterize 1) the importance of citation relationships between citing and cited papers, and 2) the topical citation motivation. Unlike earlier studies, the citation information, in this paper, is characterized by citation textual contexts extracted from the full-text citing paper. We also propose algorithm to cope with the situation when large portion of full-text missing information exists in the bibliographic repository. Evaluation results show that, context-rich heterogeneous network can significantly enhance the citation recommendation performance. Historically, papers have been physically bound to the journal in which they were published; but in the digital age papers are available individually, no longer tied to their respective journals. Hence, papers now can be read and cited based on their own merits, independently of the journal's physical availability, reputation, or impact factor (IF). We compare the strength of the relationship between journals' IFs and the actual citations received by their respective papers from 1902 to 2009. Throughout most of the 20th century, papers' citation rates were increasingly linked to their respective journals' IFs. However, since 1990, the advent of the digital age, the relation between IFs and paper citations has been weakening. This began first in physics, a field that was quick to make the transition into the electronic domain. Furthermore, since 1990 the overall proportion of highly cited papers coming from highly cited journals has been decreasing and, of these highly cited papers, the proportion not coming from highly cited journals has been increasing. Should this pattern continue, it might bring an end to the use of the IF as a way to evaluate the quality of journals, papers, and researchers. © 2012 Wiley Periodicals, Inc. Insufficiency of labeled training data is a major obstacle for automatically annotating large-scale video databases with semantic concepts. Existing semi-supervised learning algorithms based on parametric models try to tackle this issue by incorporating the information in a large amount of unlabeled data. However, they are based on a "model assumption" that the assumed generative model is correct, which usually cannot be satisfied in automatic video annotation due to the large variations of video semantic concepts. In this paper, we propose a novel semi-supervised learning algorithm, named Semi Supervised Learning by Kernel Density Estimation (SSLKDE), which is based on a non-parametric method, and therefore the "model assumption" is avoided. While only labeled data are utilized in the classical Kernel Density Estimation (KDE) approach, in SSLKDE both labeled and unlabeled data are leveraged to estimate class conditional probability densities based on an extended form of KDE. We also investigate the connection between SSLKDE and existing graph-based semi-supervised learning algorithms. Experiments prove that SSLKDE significantly outperforms existing supervised methods for video annotation. The insufficiency of labeled training data is a major obstacle in automatic image annotation. To tackle this problem, we propose a semi-supervised manifold kernel density estimation (SSMKDE) approach based on a recently proposed manifold KDE method. Our contributions are twofold. First, SSMKDE leverages both labeled and unlabeled samples and formulates all data in a manifold structure, which enables a more accurate label prediction. Second, the relationship between KDE-based methods and graph-based semi-supervised learning (SSL) methods is analyzed, which helps to better understand graph-based SSL methods. Extensive experiments demonstrate the superiority of SSMKDE over existing KDE-based and graph-based SSL methods. In recent years scholars have built maps of science by connecting the academic fields that cite each other, are cited together, or that cite a similar literature. But since scholars cannot always publish in the fields they cite, or that cite them, these science maps are only rough proxies for the potential of a scholar, organization, or country, to enter a new academic field. Here we use a large dataset of scholarly publications disambiguated at the individual level to create a map of science-or research space-where links connect pairs of fields based on the probability that an individual has published in both of them. We find that the research space is a significantly more accurate predictor of the fields that individuals and organizations will enter in the future than citation based science maps. At the country level, however, the research space and citations based science maps are equally accurate. These findings show that data on career trajectories-the set of fields that individuals have previously published in-provide more accurate predictors of future research output for more focalized units-such as individuals or organizations-than citation based science maps. Abstract It is now well-known that one can reconstruct sparse or compressible signals accurately from a very limited number of measurements, possibly contaminated with noise. This technique known as “compressed sensing” or “compressive sampling” relies on properties of the sensing matrix such as the restricted isometry property . In this Note, we establish new results about the accuracy of the reconstruction from undersampled measurements which improve on earlier estimates, and have the advantage of being more elegant. To cite this article: E.J. Candes, C. R. Acad. Sci. Paris, Ser. I 346 (2008).